Author: Bob Dancer

Posted on by — 4 Comments

Do You Change the Strategy?

Bob Dancer

The promotion I’m going to talk about today happened several years ago and I may be off on some of the details. For the sake of this column, assume the details are as I present them. The purpose of this column is to explain how to evaluate and play a promotion that might come up in the future, rather than describe exactly one that has come and gone a while back.

The promotion was at a casino in California, and the best game for dollars at this casino was 9/6 Bonus Poker Deluxe (although many players played Double Double Bonus or some other game.) The BPD game is like Jacks or Better, except all quads pay 400 and two pair just gives you your money back. This game returns 99.64%, the slot club paid 0.25%, and there were mailers of $200 four times a month (almost weekly, but not quite) if you played at least $300,000 coin-in over the previous three months. Players who played this much also received free rooms and meals. On occasion there were other promotions as well — in addition to multiple other casinos relatively nearby.

  If the player played exactly $100,000 in a month, the mailers were worth 0.8%. If you played twice that much, the mailers were worth 0.4%.

The promotion required you to get all 13 quads, and when you did, you received an extra $500. And then you could immediately start on your next 13 quads. To find out how much this is worth percentage-wise requires a bit of calculation. As a first approximation, I’m going to assume all quads are equally likely to occur — at a rate of one quad per 428 hands. Using this approximation, let’s see how many hands it takes to get each of the 13 quads.

I used Excel. I figured it would take 428 hands to get the first quad. The second one would be 428*13/12 = 464 because only 12 of the ranks would count towards getting all 13. The third one would be 428*13/11 = 506 because now there are only 11 “new” quads. When we get down to the 13th quad, the formula becomes 428*13/1 = 5,464 — which is how many hands on average it’s going to take to get the last one. We add these all up and we get 17,694 hands. If this takes you 20 hours, this is a $25 per hour addition to an already positive game ($500/20 hours = $25 per hour).

  At $5 per hand, 17,694 hands will cost you $88,470 coin-in during which time you should have hit 41 quads (most of which duplicated a quad you have already claimed). Since 41 quads are worth an extra $500, this means that each quad, on average is worth 400 + 500/41 = $412 (approximately). Putting this into WinPoker or some other video poker program will tell you the game is worth 100.2% — plus the slot club, plus the mailers, plus whatever other promos they decided to run at the same time. You can figure it out more precisely, if you like, but this was close enough for me to understand what was going on.

This was a nice promotion. It takes 5+ hours each way to drive there from Las Vegas. I was told about it at the time and decided I didn’t want to drive that far at least twice a month. It might be worth more than $30 per hour when I’m there, but it kills more than ten hours round trip each time I go and there are car expenses to consider.

One lady, “Joyce,” who regularly made the trip posed the following question to me: Let’s say I had all of the quads completed except kings. I was dealt KK443. How do I play the hand?

In normal 9/6 BPD, the correct play is to hold both pairs. In the way Joyce set up the problem, when you collect four kings, you get $900 instead of the normal $400. If you always collected $900 instead of $400 for a quad, the correct play would be just to hold the kings. So, this time, what do I do? A group of friends were there, including “Dave,” who is probably more knowledgeable about video poker than I am. He traveled from Las Vegas to Southern California because he was no longer welcome as a player in most-or-all Las Vegas casinos.

Before I reveal my answer, what would you do? Would you just hold the kings, or would you hold both pairs?

I told her that I would hold both pairs. And from KKK44, I’d hold all five cards.

“Yes!” exclaimed Dave. “That’s what I told you! Now that he tells you the same thing, Joyce, how will you play that hand?” 

“I’ll just hold the kings, whether from two pair or full house. Whatever you two so-called experts say, holding the kings makes more sense to me.”

It’s a $0.72 error to try for the kings from two pair (where you have about a 1/360 chance to connect) and more than $11 when you hold KKK rather than a full house (where you have 2/47 chances to connect). The 100.20% figure assumes you are going to use the same strategy all the way through. 

Joyce seems to be confusing getting the 13 quads more quickly rather than making the most money.

It was a lucrative enough promotion that Joyce was still a favorite even with these “misplays” (depending on how well she played the rest of the hands). But it was a more lucrative play for Dave, who didn’t make these unforced errors.

Posted on by — 7 Comments

Categorizing Hands

Bob Dancer

A friend and I were discussing 4-card straights with one deuce in NSU. The ones that are ever held are in the range of W567 – WTJQ. Each of the six possible ranges (i.e., W567, W678, W789, W89T, W9TJ, WTJQ) have different rules on which fifth cards require you to hold the deuce by itself, and which ones require you to hold the straight. Usually just the rank of the fifth card matters, but there are two separate cases where it matters whether that fifth card is suited with one of the other cards in the hand.

As an example, with W567, if the fifth card is an A, K, or Q, you hold the bare deuce. If it’s a J or a T, you hold W567. If it’s a 9, 8, 4, 3, you hold the 5-card straight. If it’s a 5, 6, or 7, you hold the 3-of-a-kind. And if it’s another deuce, you simply hold both deuces and discard the other three cards.

The exact rules for these hands are found in the Dancer/Daily NSU strategy card and Winner’s Guide. I’m not planning on going over all of the rules today — but the chart at the bottom, courtesy of Jimmy Jazz, covers the subject well.

My friend asked me how I practiced these hands using WinPoker. 

I use the fixed card feature in the advanced hand section. I put the program in “Show” mode, so I’m just hitting the enter button and it’s either dealing me five new cards or telling me how to play the cards that were previously dealt. I key in, perhaps, 2♠ 5♠ 6♦ 7♣ and let the computer randomly select the fifth card for me. While I’m going to be dealt lots of 3-of-a-kinds and 5-card straights, I’m going to get several where the fifth card is a T, J, Q, K, or A — and in this last set of cards, it won’t take me long to notice that when the fifth card is a T or J, the computer holds the W567, and when the fifth card is an A, K, or Q, the computer just holds the deuce.

Once I have these mastered, I change the 5♠ to perhaps an 8♥ and continue. This time I’m practicing W678 hands.

My friend nodded and said his brain didn’t work that way. In his mind, he saw 2♠ 5♠ 6♦ 7♣ K♠ as unique in terms of the suits of all the cards and the position all the cards were in. 

I was flabbergasted! Letting the deuce and the king be any suit, and the 5, 6, and 7 be different suits from one another (but possibly the same suit as the deuce and/or the king), we have 384 different combinations of these five cards. And since there are 120 different ways for these five cards to be displayed in the five positions, this means 46,080 permutations for ways to display this “one” hand. If my friend had to learn each of these 46,080 hands separately (instead of just once), then video poker is a much more difficult game for him than it is for me!

And further, I group W567 where the last card is an A, K, or Q as one thing to remember. Perhaps my friend has to remember all 138,240 permutations separately! I can’t believe this is the case for him — because, after all, W567 hands are only one of many hands to master. Of the 2.6 million possible hands (2,598,960, actually), that number doesn’t include the 120 different ways each of these hands can be displayed. Surely, he doesn’t attempt the task of memorizing what to do on each of the 311,875,200 cases for every 52-card game.

My advice to him was to learn to categorize. That combination is a 3-card royal, for example, and that one is a 4-card straight flush. In NSU, 3-card royals are all treated the same as each other — but that isn’t the case for many other games. Similarly, a consecutive 4-card straight flush is played the same as a 4-card straight flush with one gap, but that’s not always the case in other games. 

If all 4-card flushes are treated the same as each other in a particular game, that’s the way I learn them. If a 4-card flush with one high card is played differently than a 4-card flush with two high cards in another game (such as 9-7 Double Bonus), that’s the way I categorize them when I’m playing that game.

I only concentrate on penalty cards when they matter. In 9-6 Double Double Bonus, for example, KQJK9 is played differently than KQJKT, so when I’m playing that game, I pay attention to straight penalties to KQJ, but not to KQT, where they don’t matter strategically.

For each game, I’m trying to learn the fewest number of things I can that will let me play the game perfectly. If you want to know which categories I recommend, they are simply the ones used on the Dancer/Daily strategy cards and Winner’s Guides. 

Will this work for you? I’m not sure. It depends on the way your brain works. I’ve trained my brain to work efficiently at playing video poker well. Or perhaps I was born with a brain that allows me to play video poker well. Probably some sort of combination between the two. But whatever the type of brain you have going in, I’m confident that it can be trained to work better at individual tasks. And if playing video poker well is a task at which you wish to do well, then I’m pretty sure you can get better than you are now.

I know I can get better. Which is why, after being a player for more than 30 years, I still study before I make a major play.

I was discussing this article with Jimmy Jazz, and he showed me a chart he made when he was first studying 4-card straights with one deuce in this game. While the information in the chart is exactly the same as is found in the Dancer/Daily strategy card and Winners Guide for this game, the chart is prepared well. Possibly some of my readers will find Jimmy’s presentation easier to understand. So, I asked for permission to show this chart to you, and Jimmy graciously consented.

ST4 with one deuce in NSU

Each of the six rows represent individual hands.

Key:
Gray: unsuited cards dealt with one deuce

Light Blue: If this is fifth card, hold all five cards

Brownish/Orange: If this is fifth card, hold ST4

Yellow: If this is fifth card, hold deuce by itself

Violet: If this card is suited with one of the cards in gray boxes, hold deuce by itself. If this card is unsuited with the cards in gray box, hold deuce by itself

Gray – 3 cards dealt in addition to deuce

Orange –  ST4 is this is 5th card

Yellow – Deuce only if this is 5th card

Blue – Hold straight if this is 5th card

Purple – if 5th card is unsuited w/other 3 ST4, else deuce

Posted on by — 16 Comments

Quit While You’re Ahead?

Bob Dancer

In my February 24 blog, I wrote that earlier this year I hit four royal flushes on an 11-day trip to Harrah’s Cherokee — and the four royals spanned all four suits — clubs, diamonds, hearts, and spades — although not in that order. Within a few hours of the posting of the blog, a reader named Mike (actually, his name is listed as “mike,” but I’m going to exercise my author’s prerogative and refer to him with a capitalized first letter) posted three separate times that since I was over-royaled, I should quit gambling or I will surely give it all back. 

I responded to his posts by saying that I would discuss his theory at length soon — and today’s post is that response. 

Mike’s “Quit While You’re Ahead” philosophy is one of the two most popular money management theories out there. The other theory is that when you get ahead you should keep going so as to ride the winning wave as long as it lasts.

These two theories contradict each other. One says when you get ahead you should quit. The other says when you get ahead you should keep going. They can’t both be right.

But they can both be wrong — and my belief is that this is the case. Both theories are wrong because neither one addresses the key factor for gambling success. That key factor is: Are you the favorite to win or not?

If the house is favored to win, then Mike’s theory makes some sense — sort of. Under this environment, you will lose in the long run, whether you are currently over-royaled or not. A better strategy, in my opinion, is to not play at all in this situation.

If, on the other hand, you have the advantage in this gambling proposition, and you have the bankroll to survive the swings, then continuing to bet will lead to financial gains in the long run — again, whether you are currently over-royaled or not.

So the question becomes — am I the favorite to win at Harrah’s Cherokee playing $5 NSU Deuces Wild? I’ve been through this math in previous columns and suffice it to say I’m positive that I have a not-insignificant advantage while playing there. For practical purposes, the advantage is only available for those players who play one of a few varieties of five-coin $5 video poker which adds up to $25 a hand. One of those games is NSU Deuces Wild. There are others. There are also $5 video poker games there where the player does not have the advantage.

One of the key aspects to success at gambling is having the bankroll to survive the swings of the game you are playing. The swings for $5 NSU are not trivial. I’ve had losing trips where I’ve lost more than $20,000. For many players, losses of that size would be disastrous. I’m fortunate enough to have the bankroll to be able to fade those swings.

When Mike talks about me being over-royaled, he seems to believe there’s a video poker scorekeeper in the sky whose job it is to even things out. I don’t believe such a scorekeeper exists. Every hand of NSU I play gives me a 1-in-43,456 chance of connecting on a royal — whether I’ve already had many royals this (week, month, year, lifetime, whatever) or if I’ve never hit a royal at all. How many royals I’ve hit, and how recently, do not affect my 1-in-43,456 chance of collecting a royal on the very next hand I play. 

It’s possible that Mike doesn’t believe the last sentence of the previous paragraph. I’ve based my career on the assumption that IGT machines have random number generators that deal the cards fairly — meaning each unseen card has an equal chance of appearing next. While there have been times my results have been luckier than average (the four royals in 11 days is the most recent example of this) and other times when my results are pretty bad for a period of time, over time the math has worked out. 

I never know how long a winning streak will last. I never know how long a losing streak will last. What I can usually figure out, however, is whether I have the advantage or not and whether I have the bankroll to survive the swings. And when I have both of those things, I’m going to continue to play.

It’s possible Mike doesn’t have access to games where he has the advantage — or the skill and bankroll to play those games if he did have access to them. That could lead to his “Quit While You’re Ahead” belief. And that belief may be relevant in the world he plays in. But that doesn’t mean that people who can find good games should be subject to his belief system.

Posted on by — 3 Comments

Reducing the Variance

Bob Dancer

Last week I wrote that I played ten-coin $5 9/7 Double Bonus Good Times Pay for a promotion at Caesars Atlantic City. This is a relatively rare game with multipliers, and if you’re not familiar with how the multipliers work you might want to read (or re-read) last week’s article before you tackle this one.

Over the first four days of play, including the play-up bonuses I received for every $150,000 worth of coin-in and the weekly free play for the week that ended Saturday and also for the week that began Sunday, I was ahead about $25,000 for the trip. This figure includes the 0.08% I earned in Next Day Bounceback. It’s not a large percentage, but I had played almost $1 million in coin-in so far and it adds up. The figure doesn’t include the Reward Credits I had earned (which I will redeem at Caesars Sportsbook) or the value of the Tier Credits (including one day with a 5x multiplier).

I had hit four aces three times (with 1x, 2x, 3x multipliers for $4,000, $8,000, and $12,000 respectively), lots of quad 2s-4s, many with multipliers of 4x and higher, and six quad 5s-Ks with multipliers of 5x ($6,250), 6x ($7,500), or 7x ($8,750) — along with a slew of these lesser quads with lesser multipliers. I failed to hit a royal flush, with or without a multiplier. While not unexpected with the 20,000 hands I had played, a royal flush would have been welcome! Suffice it to say, I was enjoying this trip to Atlantic City — other than the fact that there was a blizzard going on outside and I had to stay an extra day and a half more than I originally planned. 

For my last day, I had $140,000 remaining to play to pick up Bonnie’s and my last two play-up bonuses — requiring perhaps four hours of play on the $50-per-hand game. On earlier trips I had sometimes lost a considerable amount on these same machines. I could play five coins per game, for $25 per hand, on the same machine, forgoing the multipliers and requiring eight hours of play. This had no effect on the 99.1% expected return on the game, but it greatly lowered the variance.

I decided to play the extra hours at the lower variance as a sort of money-management gambit. I had a very nice score going this trip and I wanted to “take it home.” I could have skipped playing the last day at all, guaranteeing I would take the money home, but I believed the extra play was an intelligent risk to take. Playing for the last bonuses on my card and Bonnie’s had an EV of more than $1,000 and I didn’t want to pass that up. So long as I was going to be at the casino anyway, it made sense to play.

At $25 per hand, you get “jackpots” of quads, straight flushes, or (I wish) royal flushes every 400 hands or so — meaning every $10,000 in coin-in. I put the word jackpot in quotation marks because quad 5s-Ks return “only” $1,250, which is lower than the W2-G threshold that has been in effect since January 1. In the $50-per-hand game, half the time these quads would be accompanied by a multiplier of 2x or larger, triggering a W2-G, but in the $25-per-hand game there are no multipliers. 

As a first approximation, the average of 14 “jackpots” would consist of no royal flush, one straight flush, and one quad in each of the 13 ranks. To be sure, it wouldn’t be impossible to connect on a royal flush, and straight flushes are about half as likely as any individual quad. Aces come about more frequently than other quads because from AA332, you just hold the aces, but from hands like KK447, it’s correct to hold KK44. Additionally, to it is proper to hold a single ace more often than any other specific high card. Quad jacks, queens, and kings come about more frequently than the remaining ranks because you’ll hold a single high card but not a single low card. Also, a pair of these high cards is more valuable than most 4-card flushes and all 4-card open-ended straights, but 22-TT are less valuable than any of these 4-card combinations. Finally, quad 22s-44s are each slightly more likely than quad 5s-Ts because when the same hand contains a suited QJ9 or JT9, you hold a pair of 2s-4s but not 5s-Ts.

That’s a lot of caveats, but as a first approximation, hitting no royal flush, one straight flush, and one each of the quads is about what figures to happen. 

Unfortunately, I ran very badly. While I did receive one straight flush and no royal flush just like my first approximation predicted, the quads were woefully short. I didn’t hit aces at all. I hit one quad (instead of three) in the 2-4 range, and four quads (instead of nine) in the 55-KK range. Even after collecting my bonuses and the NDB from the day before, I ended up losing about $17,500 on the day instead of winning the $1,000 my prediction said I “should” have won. No fun at all.

It’s tempting to conclude that my strategy of playing $25 per hand and forgoing the multipliers instead of $50 per hand was a failure. After all, sustaining a loss of the size I did can hardly be called a success.

I disagree with this conclusion — and the entire reason for this article is to explain why I believe my strategy worked well.

Had I played $50 per hand, there would only have been half as many hands played. Earning quads at the same rate as I actually did, I would have received three “jackpots” instead of six. While we will never know what the multipliers would have been on these three “jackpots,” an average of 2x would have resulted in a loss of at least $10,000 more than I actually had. 

That means my strategy was actually a success — even though a very expensive one. You have to make your decisions before you know the results — and live with those decisions. Just because the decision turned out badly this particular time doesn’t mean the decision itself was a mistake.

This is a concept many people just don’t get. Some people “learn” how to think by watching football and listening to the commentators. Football commentators, for example, often proclaim running the ball out of the end zone on a kickoff is a mistake if a kickoff is only returned to the 18-yard line rather than starting out at the 20- or 25-yard line that would have resulted from catching the ball in the end zone and staying there. That’s an easy comment to make — and wrong. The kick returner doesn’t know the result of his run before he runs. He needs to make his decision based on his read of what he sees is happening and what strategy his team is planning to use this particular time.

Running out of the end zone in a particular situation may or may not have been a mistake based on the information available to the decision maker before the run took place. Coaches can help kick returners make better decisions based on the hang time of the ball and other factors. But using where the receiver ended up being tackled as the sole criteria of whether it was a mistake or not is a foolish way to judge things. And it gives the kick returner no ability to make better decisions in the future.

However many of you criticize me for my decision to play $25 a hand rather than $50, I’m convinced it was the correct decision. To my detractors, I suggest you’re watching too much football on television and believing what the commentators say!

Posted on by — 4 Comments

A Change in Strategy?

Bob Dancer

Last November, I played during a promotion at Caesars Atlantic City. It was a juicy promotion — and I took a bath. I mentioned in an article that the best video poker I could find for high stakes was 9/6 Double Double Bonus (98.98%). A reader responded that they have 9/7 Double Bonus (99.11%) for $10 on a few machines. Although the DB game pays more than the DDB game, it’s much more difficult to play well. As it turns out, I played 10/7 DB for many hundreds of hours back when I was first starting — eventually co-wrote a Winners Guide on that game — and have taught classes (Beginners, Intermediate, and, occasionally, Advanced) several dozen times. In the past few years, I played the dollar version of that game at Arizona Charlie’s Decatur and Four Queens until they took the games out at both places. Suffice it to say, I know the game well and the extra difficulty of DB over DDB is a non-factor for me.

I looked and couldn’t find these machines. How hard could it be? There aren’t that many video poker machines in the High Limit Slot area at Caesars. The reader sounded knowledgeable, so I looked harder. I found the game, but it was not what I was expecting.

The game is single-line Good Times Pay for $5. If you bet five coins, you get regular 9/7 DB. If you bet between six and ten coins, you get multipliers on every hand. These do not affect the 99.11% return on the well-played game, but the multipliers do greatly affect the variance.

On the 10-coin version, for example, there are 30 boxes from which the multiplier may be randomly drawn. Fifteen of those boxes are 1x. Ten of those boxes are 2x. And the remaining five boxes are one each: 3x, 4x, 5x, 6x, and 7x. The mean value of the multipliers is 2x, and since you play 10 coins to earn these multipliers instead of the normal five, the overall return isn’t affected. 

You learn the value of the multiplier as soon as you bet and before you select the cards to hold. For knowledgeable players, the size of the multiplier doesn’t affect how the hands are played. But it can easily affect the emotions. Consider a 6x multiplier when dealt AAA82. You’re going to hold the aces, of course, but if they connect, you’ll have a $24,000 jackpot rather than the typical $4,000 the hand regularly pays. That can get the heart pumping a little.

It’s easy to dream of getting the royal flush with a 7x multiplier, which pays a very attractive $140,000 on these machines, but you only get that multiplier 1-in-30 royals. Because you hold flush kickers in this game, royals only come about every 48,000 hands or so — making the cycle for the royal with a 7x multiplier 1,440,000 hands. I am almost certainly never going to play that many hands on these machines — but it could happen. And if I’m forced to put up with a 6x multiplier instead, winning a measly $120,000, I’ll find a way to deal with it. Not even Bob Dancer runs well all of the time!

The 9/7 version of the game is played the same as the 10/7 version with two major differences. On a hand like AA442, you hold two pair when playing 10/7 and just the aces when playing 9/7. This is a major mistake when played incorrectly — around $1.80 times whatever multiplier you have for the $50 bet.

The second difference consists of a 4-card flush with two high cards along with a pair of kings, queens, or jacks (like K KQ73). You hold the kings in 10/7 and the 4-flush in 9/7. This mistake is not worth much —less than two cents times the multiplier for the same $50 bet. Still, I’ve made a history of seeking the correct play even when smaller than this, and see no reason to stop now.

There are a few less common differences that aren’t worth much. On this trip, I ignored them. If another promotion comes about that’s at least as good as the one I’m playing, I just might study the relevant section of the Winners Guide and play with the more-accurate strategy.

My trip was scheduled from Friday February 20 to Monday evening, February 23. There was free play to pick up and a play-up promotion in February. Unfortunately, that part of the country got slammed with a severe snow-and-wind situation and I wasn’t able to fly home until Wednesday morning, February 25. The play up allowed enough optional iterations so playing for an extra day and a half was a feasible option. It was no problem getting my room-comp extended.

I didn’t count the number of times I was dealt a high pair (other than aces) and a four-flush with two high cards, but it must have been a couple of dozen times or so. With average luck on 24 trials, I should have drawn a flush 4.5 times. This time, however, I drew the flush zero times — throwing away a high pair every time. With an average-sized multiplier, I threw away at least $1,200 — and surely some of the time the high pair would have turned into trips, full houses, or (it’s a long shot) quads.

It crossed my mind that since going for the flush was only worth pennies more than holding the high pair, and the play certainly wasn’t successful on this trip, that maybe I should start holding the high pair. I know many players would have made this adjustment (if they weren’t already holding the high pair to start with!)

While the subject did cross my mind, I didn’t act on it. I continued to hold the four-flush every time — and will do so in the future. I believe the right play is the right play — even when I run badly. My career is based on my strongly held belief that over time it will even out, and making the best play every time will lead to better results than making lesser plays.

Some of you will follow my lead on this and some won’t. Without calling any of you names, the saying that starts, “You can lead a horse to water . . .) seems appropriate here.

Posted on by — 34 Comments

What Should We Do with Jerry Ice 33?

Bob Dancer

Author’s note: When I originally wrote this more than a month ago, Jerry Ice could be counted on to post several times a month. Since I wrote this, he has largely disappeared. It’s possible he’s decided that commenting here is not a game he wants to play anymore — which would be a fine result so far as I’m concerned. I’m running this blog anyway in case that was not Jerry’s decision.

I’ve been writing and teaching for more than 30 years. My national “fame” started in the late 1990s when I began writing for the monthly magazines Strictly Slots and Casino Player which were both distributed for free in a number of casino hotel rooms around the country — in addition to people buying regular subscriptions.  I’ve had a weekly blog, for various publications, almost continuously since then. I’ve participated in online video poker blogs periodically for longer than that.

For whatever reason, I have always attracted detractors. In each online forum where I’ve participated, there have usually been one or more people who take regular shots at me. At first, I started to respond to defend myself, but this often led to several people joining in — each one changing the argument slightly — and I learned quickly that I couldn’t win against this type of attack coming from several directions at once. So, I largely ignored it.

Surprisingly, to me at least, when I started the Gambling with an Edge radio show — which morphed into a podcast — people began criticizing me less. Which was fine with me.

I’ve been blogging on the Las Vegas Advisor website for more than a decade — and it provides a forum where readers can respond to my columns. And I have the tool, should I wish to use it, of removing any posts I choose to — for whatever reason.

So far there is only one person who is permanently banned from posting comments to my blogs. It took awhile for this situation to arise — and Anthony Curtis became involved in enforcing the ban — but so far, it’s holding.

Which brings me to the man, I assume, who posts under the name Jerry Ice 33. I’m going to refer to him as Jerry. I don’t know who he is — although it’s possible I know him under a different name.

Jerry regularly comments on my blogs — and a high percentage of his comments are derogatory towards me. He likes to say I’m cheap. He likes to tell us I treat Bonnie poorly. He’s made other negative comments as well. And he posts the same complaints over and over again.

Some of you have responded to Jerry, suggesting he lay off the criticism. While I appreciate the support, this forum is supposed to be about becoming more successful at gambling, and not a discussion of whether or not I’m a flawed human being.  ( I plead guilty to being flawed — although I do think my frugality has been a major factor in my success, and I’m positive Bonnie thinks her life is working well and she is loved by me.)

While I can continue to ignore Jerry, I feel he’s becoming disruptive. My personal belief is that if he isn’t getting value from reading this blog, he should spend his time doing something else. Repeatedly and repetitively suggesting he’s not a Bob Dancer fan doesn’t improve the experience for anybody else who reads the blogs.

So, what shall I do? I’m asking you as a group and hoping many of you respond. Should I let him be or should I start removing negative posts from him? If I start removing negative posts and he continues anyway, I’ll talk to Anthony about permanently barring him from the site.

I’m not sure what kind of majority I’ll need in order to start removing his posts (if, indeed, there’s a majority at all). It’s possible Jerry could apologize and all will be forgiven — but I’m not holding my breath on that one.

So, what do you think?
Second author’s note: I recent came across Dan Ariely’s book, Misbelief: Why do Rational People Believe Irrational Things, which addresses the type of “Internet bullying” I went through — and to a lesser degree than before am still going through with Jerry. The book was eye-opening to me, but more complicated than I wished to summarize in an additional blog.

Posted on by — 6 Comments

Why Would They Do That?

Bob Dancer

I’ve written recently about looking for certain slot machines to be reset — because some of them, not many, reset to conditions favorable to the player. A reader who calls himself jstewa22 wrote a number of posts saying this didn’t make any sense to him. Why would a machine reset in such a way? A very good question, to be sure. Today’s blog attempts to address this question.

First of all, keep in mind that gaming manufacturers (IGT, Aristocrat, Konami, etc.) are not owned or run by casinos. They are separate entities. Manufacturers need to walk a fine line between casinos and players. To be successful, the game must be profitable for the casinos and interesting to the players.

Also keep in mind that game designers aren’t, for the most part, also advantage players. The game designers might pick a reset number out of the blue — resetting to 12 sounds good, perhaps — and go with it. 

The game manufacturers possibly don’t know the return for the machine when reset at 12 (or any other number). They know the overall Return to Player (RTP) (typically between 85% and 95%) over time, but may not have the return broken out at every possible reset number. 

Advantage players, however, make it a point to know when a game is positive. We collect data and analyze what we find. When we do find a game that resets positively, we play until the game is no longer positive.

A famous example of this happened a few years ago when New Jersey allowed online gambling. I wasn’t involved in this bonanza, and might have some details wrong, but it went something like this.

On the game Ocean Magic, the game reset positively FOR EVERY PLAYER FOR EVERY DENOMINATION. So, a player signed up, deposited money, probably collected a signup bonus, and then played off all denominations and number of coins — of which there were lots. When that player had run through all of the possibilities, he was done gambling and ready to cash out — often thousands of dollars ahead.

That player would then do the same thing using the identities of as many people as he could talk into it. How much these people were paid to let the APs use their name and accounts was open to negotiation. But if a player could get dozens (or even dozens of dozens!) of additional names so Ocean Magic would reset for every one of them, think of the windfall!

It didn’t take long for the New Jersey Gaming Commission (or whatever the organization is called) to notice this pattern: players sign up, play all the Ocean Magic combinations, and then cash out. When the NJGC figured it out, they stopped it. They either got the Ocean Magic manufacturer to change the reset numbers or stopped offering the game.

I heard there were lawsuits against the players for “taking advantage” of the situation. As I understand it, players eventually got paid — but many were barred from playing online in New Jersey thereafter at one or more casinos. The players who spotted this did quite well for themselves until it was shut down. Today there are ways to play Ocean Magic with an advantage, but not when the game is originally reset.

How could this happen? I’m not really sure, but I am sure it did happen. Somebody somewhere didn’t dot all the i’s and cross all of the t’s. This was another case of “the early bird gets the worm.” The early discoverers made out like bandits. The rest of us just heard about it after it was no longer profitable.

While I know of four different games that are positive at reset, at least some of the time, you’ll never see me identify which games those are. The reason is simple. I assume some number of my readers are casino employees. If I told them which games are beatable in this way, you can bet that the opportunity would dry up essentially immediately. Casinos would demand that manufacturers fix this problem — or the casino would no longer offer the game. And since a game that casinos won’t buy (or lease) is no good at all to a manufacturer, the manufacturers will comply with the casinos’ wishes.

Even if the knowledgeable player can figure out how to make thousands of dollars when these particular games are reset, resets don’t happen very often, and the games are still wildly profitable to the casinos.

Consider the opposite side of this: One game that definitely is NOT beatable at reset is Buffalo Power Pay. When this game is reset, all of the betting options have the Major at 30 and the Mega at 50. When the numbers are at this level, the game returns 80% or so. It takes a while for the Major and Mega to be built up so it’s profitable for to the players.

But at some major casinos in Las Vegas, these games are reset by the casinos several times a week! This is equivalent to letting the players build up progressives, and then the casino confiscates the money that the players built up. I’ve asked Bob Nersessian about this, and his belief is that it is patently illegal to do this. And casinos are doing it time and time again.

A player who complained about this to the casino would thereby identify himself as a player who paid attention to such numbers — and, for the most part, casinos don’t appreciate such players. The player who complained would be, in effect, outing himself as a player the casino wishes to kick out. Because of this, players do not complain about this to the casinos.

There’s another way for games to reset positively — and that is for the new starting number to be selected at random! Sometimes it’s positive for the player. Usually not. But it does happen from time to time. On these games, just playing regularly, players have noticed the reset number — and sometimes it is positive after the bonus round is played. Sharp players are alert to this!

I’m not sure my explanation will satisfy jstewa22. After all, the explanation is basically “shit happens on occasion, but alert players can take advantage of this.” 

I think jstewa22 was thinking that casinos and/or manufacturers were INTENTIONALLY doing this, and that simply didn’t make sense to him. As well it shouldn’t. These organizations are in the business of making money off of players — not supporting APs. I’m certain casinos and manufacturers are definitely NOT doing this on purpose. But there are a lot of moving parts and a lot of decision makers, and sometimes somebody somehow someway drops the ball.

Posted on by — 13 Comments

How Lucky Was It?

Bob Dancer

Last week I wrote about completing a royal flush cycle (one or more royals in each suit) within one trip. I was very lucky, to be sure, but just how lucky?

I have a hard time calculating how lucky something was after the fact. You can massage the numbers and come up with all sorts of probabilities. There is not one absolutely correct answer that everybody can agree on.

Let’s start with the 11-day trip. I used all of it, hitting the club royal on my last day there. Most players never have an 11-day out-of-town casino trip in their entire career! I’ve had 14-day trips to Cherokee. I would have been just as delighted to complete the cycle on one of those trips. But I never did.

It’s not the length of the trip, of course, that determines your chances, but rather the number of hands played. Near as I can tell, I played about 62,000 video poker hands. I know how many points I earned during the trip, but some of my play was on slots. I record my points earned each day, but not how that number of points is broken down between slots and video poker.

I know I’m going to be using the word “cycle” in a different way now, but a “royal cycle” is the number of hands, on average, to hit a royal flush in a particular game. In Jacks or Better the number is right around 40,000, and that’s the commonly used number for video poker royal cycles. But NSU has a longer cycle, 43,456 hands, because you play hands differently in this game.

Calling 62,000 hands 1.4 royal cycles is as close as I can get. The 43,456 number is fairly precise (I could tell you that number is 43,456.27, which would be more precise, but hardly more useful), while the 62,000 number is an educated guesstimate. Using the Binomial Theorem, connecting on exactly four royals in 1.4 cycles happens about 4% of the time, and connecting on four or more royals in 1.4 cycles happens about 5.6% of the time.

If I connect on exactly four royals, all four suits will be present only about 9% of the time. Were I fortunate enough to have connected on five-or-more royals (I wish!), it would have been easier to have all four suits represented. Not a lock, of course, but easier.

Now what do we do with the club royal being dealt? The “dealt-ness” of that royal was overkill. I would have also completed the cycle even if I had needed to draw one or more cards to get the club royal. 

But the royal being dealt allows me to jack up my numbers when I tell people how rare this was. (It’s not something I normally do, but I’m discussing it here because there are always “How rare was it anyway?” questions.)

The dealt royal arrives approximately every 650,000 hands. But since at the time it hit, I needed the royal in clubs to complete the cycle, those only come around one-quarter as often — or about every 2,600,000 hands. 

All these things had to happen on the same trip — namely playing 62,000 hands, collecting at least four royals, having every suit being accounted for in those four or more royals, and (this one is optional), one of these had to be dealt. To determine how likely all of this is, you need to multiply all of these probabilities together. I’ll let others do it, because I’m not at all convinced that figuring out how likely something was to happen — after you know it did happen — is a meaningful exercise at all.

There’s more on this trip. The deuces cycle in this game is about 5,356 hands. In 62,000 hands you have 11.6 of these cycles. I collected 12 sets of deuces — which is essentially spot on given the imprecision of the 62,000 number. The thing is, one of those sets of deuces was dealt. 

Being dealt a specific quad happens every 54,167 hands, on average — so in 62,000 hands “it figures” I would have collected one or more. Mathematically, even though 62,000 is larger than 54,167, I was still a slight underdog to hit exactly one set of dealt deuces on the trip, although I was a sizeable favorite to collect one or more.

What this has to do with anything is that on the same trip I was dealt a royal and dealt deuces! (I was also dealt four aces with a deuce, which is another rare event that is called a 5-of-a-kind for $400 in $5 NSU Deuces Wild and it’s the kind of hand that makes you wish you were playing a different game!) Being dealt a royal is rare enough. But also being dealt deuces is even more rare!

It was, to be sure, a trip to remember!

Sometimes casinos restrict players who have too much success. I’m hoping that’s not the case here.

Posted on by — 15 Comments

Pedaling Hard for the Cycle

Bob Dancer

In baseball, a player “goes for a cycle” if he hits a single, double, triple, and home run in one game. These don’t happen too often — just twice in the 2025 Major League Baseball season, for example. The more at bats a player has, the more likely he can get these four specific hits in a single game.

There is no direct analog in video poker, but several of us have called hitting royal flushes in each of the four suits in a single “trip,” to be a cycle. The word “trip” is somewhat open to interpretation. I accomplished my first one in a day, playing 10¢ Hundred Play 8-5 Bonus Poker some 25 years ago at the Silverton when they had a promotion where the player could earn a Rolex watch if he played some large number of points in a month. I don’t remember why I felt it necessary to do this in one day, but I played many hours and earned the Rolex and the cycle. I didn’t write about my cycle at the time because I felt doing it on Hundred Play was “unfair.” You do, after all, collect a royal every hour or two in that game, so collecting a lot of royals is not a major accomplishment.

In 2026, I had a chance to do it on a single-line game. Last week I wrote about braving the weather to reach Harrah’s Cherokee for an 11-day trip. Although I played some slots, my video poker game of choice was $5 NSU Deuces Wild. 

On day 2, I connected on a royal flush in diamonds. I usually do not take pictures of my royals, and I didn’t this time either. On day 3, however, I connected on a royal flush in spades — this time memorializing it with my iPhone camera. On day 5, I hit a royal flush in hearts and, for the first time, began thinking of completing the cycle. On my trips of this length, I usually connect on one or two royal flushes, so with six days left, I had a decent shot at collecting at least one additional one. 

Hitting a royal, though, is not the same as hitting a club royal. All royals on this game pay the same $20,000, no matter the suit, but I wouldn’t qualify for the cycle unless it was specifically in clubs. And even if I did, I didn’t have a picture of my diamond royal flush, so I would have no “proof.” I decided this wasn’t a problem. Even if I had a picture of the diamond royal flush, there would be no proof that I was the one who hit it and did so on this particular trip. If someone wanted to doubt what I claimed, there would be plenty of room, with or without a picture.

I thought about how far I would go to hit this royal. On a hand such as K♣ Q♣ A♠ 3♣ 6♠, for example, it’s about a 4¢ mistake for the $5 five-coin player to hold the suited KQ rather than throw everything away. Most NSU players ignore the penalty cards on this type of hand, I believe, and hold the KQ. Making this mistake would give me a 1-in-16,215 chance of getting the club royal and completing the cycle on this particular play. While it would only be a slim chance, it would still be bigger than the zero chance I would have if I tossed all five cards. Plus, if and when I do indeed hit the club royal, nobody is going to ask me what five cards were dealt to me on the hands that ended up being royals. 

I decided I didn’t want to change my strategy. If the royal comes while I’m playing correctly, great. If it doesn’t, so be it. But I wasn’t going to be making intentional misplays (even those worth very little) in order to accomplish this feat. What I would do, I decided, was play longer hours. Instead of my normal $150,000 coin-in per day, I would play $180,000. This wouldn’t be cheating at all, at least not to my mind.

It’s one thing, of course, to claim the high ground with an “I’d never do that” promise when it’s hypothetical. There are a number of different hands similar to the one I listed above — but they don’t happen very often. I did get a couple of these hands after I was down to only needing one more suited royal to complete the cycle, one in hearts and one in spades, but nothing in clubs. I wasn’t really tested as to whether I would fudge correct strategy to complete my goal.

Before a hand arose causing me to think about “being flexible” in my strategy, the machine took the decision out of my hands by dealing me a club royal. A dealt royal is a 1-in-650,000 hand event. A dealt royal in clubs is only ¼ as likely as that. But that’s what happened.

As it turned out, I accidentally left my iPhone in my hotel room that day, so I couldn’t take a picture of the hand. I asked the slot attendant if she could take a picture of it and text it to me. Well, no, personal cell phones weren’t allowed for employees when they were working. They used iPads at this casino to process jackpots, and to be sure the iPads have cameras, but it’s a limited Wi-Fi that they use which only allows internal communication within the company.

However, she could AirDrop the picture. I had heard of AirDrop before, but had never used it and wasn’t sure how it worked. But I was told that if I brought my phone within the five remaining hours of this lady’s shift, I could get the picture via AirDrop. I agreed. It didn’t occur to me at the time to leave the royal on the screen for a half-hour while I walked 15 minutes each way to my hotel room. They probably would have agreed to that, but I don’t know for sure.

But the AirDrop worked so I have the picture which I’m sharing here. The way you know the royal was dealt is that above each card it says “HELD.” If I had to draw one or more cards, there would be fewer than five “HELD” indications.

So, I ended up getting the cycle. That’s my story and I’m sticking to it! Plus I am now tech savvy enough to use AirDrop!

In my career, I’ve had a number of “braggable” jackpots in casinos. Not that I needed another one, but this one was very welcome and very likely the last time I will ever complete a cycle in one trip! This was my first extended trip of 2026, and it starts off my year with a nice plus score.  

Often when someone experiences a rare hand, or combination of hands, the question of “Just how rare was this?” arises. That strikes me as a worthy topic for next week’s blog. After all, if I can’t get at least two blogs out of this, it couldn’t have been all that rare!

Posted on by — 11 Comments

Money in the Bank

Bob Dancer

Not long ago Bonnie and I invited a friend to join us for dinner at a casino restaurant. The friend, a woman in the same improv group in which I participate, was not a gambler. “Sandy” was a senior citizen and was retired. 

At one point, Bonnie and I told Sandy of a time I was playing in downtown Las Vegas and had gone through all of my cash on hand. I was playing a slot machine, in significant positive territory, and I didn’t want to walk away and leave the machine for others to capitalize on. So, I called Bonnie and asked her to get some cash and take Lyft to downtown (Bonnie no longer drives.) She agreed.

Sandy asked how much we were talking about. 

I didn’t remember for sure, but I told her it was probably $10,000. It was very likely more than enough, but if she was going to make the trip, we wanted to make sure we didn’t run out again.

Sandy remarked that this was way too large of an amount not to be earning interest.

I conceded her point — but suggested that it was a different calculation for a professional gambler.

“How come?” she asked. “Interest given up is interest given up, no matter what your profession is.”

I changed the subject, but have been thinking about this. While Sandy wasn’t wrong, here is my thinking on the subject:

  1. Gamblers have bigger cash swings than most people. Sometimes the swings go against you, and you need a “cushion” available for when that happens. If you have lines of credit at every casino you frequent, this can serve as a sort of short-term cushion. While I have lines of credit at a number of casinos, I regularly frequent casinos where this is not the case for me. So, I need a buffer.
  1. Gamblers for “large” stakes need bigger cushions than gamblers for smaller stakes. I’ve had some monthly negative scores in excess of $30,000 over the past few years. I need a way to cope with these swings. Overall, I’m a winning player, but not every week or month (or even, occasionally, year).
  1. Banks do not like large regular cash deposits and withdrawals from gamblers. Numerous gamblers have had banks terminate their accounts for such activity. I’m not sure why banks act this way, but they do. Perhaps they’re nervous about money laundering situations and don’t want to risk it.
  1. Even if banks did allow large cash deposits and withdrawals from gamblers, banks are not always near the casinos and not always open when the money is needed. Casinos are open 24 hours. Banks aren’t. 
  1. Sometimes casinos will lock up a machine for a few hours for a player. Sometimes they won’t. If a player has cash in a safety deposit box at a bank or casino near several other casinos, this can be used to fulfill cash needs for those casinos fairly quickly.
  1. If I did run out of cash, I have gambling friends I can count on to lend me short-term money. I very much try to avoid this because if I borrow, I have to be willing and able to lend money to others. While most gamblers to whom I have lent money have paid me back reasonably promptly, there have been exceptions. I would rather not open this door.
  1. I don’t know Sandy’s exact financial circumstances, but I suspect she is living closer to the edge than I am. She needs to make every penny count, so to speak, and to earn them while she can. So, she has developed rules of thumb that serve her well for this purpose. A good rule for most people is to keep your money working for you and don’t leave money uninvested.

While I don’t consider myself wealthy, I have enough money to comfortably gamble for considerable stakes without threatening my lifestyle or retirement status. So, I can afford to keep more cash around than many other people can. Very little of that is at home (for safety reasons). Most is spread out in safety deposit boxes in casinos I frequent.