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Bobby Vegas — So I Like Numbers

Bobby Vegas: Friends Don’t Let Friends Play Triple-Zero Roulette

Trigger warning: about to toot my own horn.

And a caveat. I screw up. I make mistakes. I’ve gone bankrupt once, been broke twice. I’m not now. What’s important is not the mistakes, it’s the lessons learned.

Paying for groceries, I’m adding the numbers upside down using my own approximation technique faster than checkout employee can scan. I say, “That’s … $39.60 … or thereabouts.” When the total comes to $39.69, the checkout girl looks at me like I’m from Mars. “How’d you do that?!”

I shrug. “I like numbers.”

My ex and I loved going on bookstore dates. She read autobiographies. Me? Math history, Feynman, Edward Thorp, maybe brush up on some probability theory. She just shook her head.

In business tech specs, efficiency ratios, wholesale volume discounts, I easily stated, “That’ll save you 20% or $2,300 a month and the ROI is 19 months.” Again: “How’d you do that?” For me, the numbers are just … there. Multiplication, division, percentages, they’re all just OBVIOUS, in some cases instantaneous.

When I became obsessed with roulette, spending 18 months in the NC State fifth-floor math library absorbing everything on nonlinear dynamics, recurrence and chaos theory, I just loved it. The daily lean into the right headspace often took 30 minutes, but it felt so good! Was it weird, composing a 45-page heuristic paper on Nonlinear Dynamic Short-Term Recurrence Theory applied to roulette, when I barely made it out of high school alive?

Every time I searched out someone to talk with, like folks working on weather prediction, they got real uncomfortable. “I have a Master’s and you left me behind 20 minutes ago.”

When I found my people, like Laurence Scott (roulette prediction) and Chuck Webber (recurrence theory), I was finally no longer the fishnerd looking for water. But it’s okay. Ask me about applying the birthday paradox to double wheel roulette and see me light up.

I like math. It’s clean, clear, concise. I like video poker for those reasons. I find the decision tree very relaxing. It massages my brain.

But when faced with craps, I freeze up. Too many chaotic variables, like the yahoo rolling, for starters. Craps is a good game; I’m just not made for that particular decision tree. Card counters are memory geeks, too. But again, I’m just not wired up for live action. I’m way too transparent to have to bluff and lie.

I believe my most valuable skill is recognizing opportunity before others, way before. Like energy-efficient lighting in the ’80s, LEDs in the ’90s, or specific Vegas-value plays. And applying them in creative ways.

When Mrs. Luttenton, my seventh-grade advanced math teacher, crammed trigonometry down our throats, we hated her. She was mean, demanding, and ugly. Apologies Mrs Luttenton, wherever you are. But thank you for being such a math drill sergeant.

And kids? Put away the phone and think.

Yes, I find math relaxing.

So sue me.

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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.

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Hope for Atlantic City, Crisis at Caesars

Rumors of Atlantic City‘s imminent demise—mostly spread by Big Gaming itself—proved exaggerated last month. Casino revenues ticked up 2.5% to $236.5 million. Table play, up 14%, carried the Boardwalk, as slots won 1% less. And one less weekend day didn’t even hurt. Golden Nugget had a bad month, however, falling 13% into last place with $10 million. Volatile Caesars Atlantic City, by contrast, had a bully March, shooting up 17.5% to $19.5 million. Scarcely outdone was Borgata, vaulting 15% to $67 million. Some of that evidently came at the cost of Hard Rock Atlantic City, down 4% to $42.5 million. Ocean Casino Resort rounded out the top three with $35.5 million, up 2%.

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Hypocrisy on the Boardwalk

Top casino executives convened in Atlantic City to predict fire, flood, famine and pestilence should New York City go ahead with casino megaresorts. Well, casinos are definitely coming to Gotham … less likely coming to New Jersey horse tracks. What does Big Gaming propose to do? Hold its breath until it turns blue? It sounds like a prelude to corporate welfare. Cue also the predictable refusal to ban smoking in A.C.’s casinos, the subject of protests outside Hard Rock Atlantic City, where the East Coast Gaming Conference was being held.

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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

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A Mild Vegas Recovery Ahead?

First, the good news. That “inclusive pricing” strategy that the Las Vegas Strip filched from Downtown is working. The bad news is that it will probably be quickly abandoned, turning a promising recovery in Las Vegas into an anemic one, at best. Given all the misguided economic “policy” coming out of Washington, D.C., a nascent Vegas bounce-back could yet be smothered in the crib. It’s not like those fellows ever bankrupted a casino, is it? Oh, wait …

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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.