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Wasting an Ace

I was playing $10 Bonus Poker at the M Resort in Las Vegas at 5 a.m. one morning. I know it’s too early for most players to be at a casino but there was a method to my madness. The machines I want to play are at a bar in a room that is frequently rented out for luncheons or other functions. If an organization rents out the room, they expect the room to be devoid of players for the duration. If I get there early enough, there’s a really good chance I can finish my play uninterrupted.

I was dealt 2♠ 2♥ 2♣ 8♦ 9♦. I tossed the diamonds, of course, and was fortunate to draw 2♦ A♦, making the final hand four deuces with an ace “kicker.”

This was a $2,000 jackpot and I quietly waited for an attendant. They have a system at the M where jackpots trigger some sort of electronic message which gets relayed fairly quickly to a floor person. I typically bring a book along in case this takes awhile. At this time of day, they have a skeletal crew because there are relatively few patrons compared to other times of the day and things can back up if two or more jackpots happen at the same time.

When the attendant came up, he smiled and said, “Very good! With a kicker!” Were I playing Double Double Bonus, the hand would be worth $8,000. Had I been playing Triple Double Bonus or Deuces Bonus on the same machine for the same denomination, the jackpot would have been worth $20,000 rather than a “measly” $2,000. When he first saw the number pop up on the screen, he assumed there was another zero because after all, it was a $10 game and good jackpots on such a big game must be “YUGE!” (or however you spell this year’s new word).

When he finally realized that the game I was playing didn’t pay extra for good kickers, he told me I had wasted the ace. I could have used it so much more lucratively in other games.

I smiled. I took this as friendly “advice” from someone who meant well.

“True,” I said. “But unfortunately they don’t let you pick the game after you hit the jackpot! I guess I’ll just have to live with this.”

To my mind, I didn’t waste the ace. “Wasting the ace” presumably is based on the theory that we only get so many 2222A jackpots in our playing career and we must maximize the value of each one.

I don’t subscribe to that theory. There is no video poker scorekeeper in the sky keeping track of how many times I’ve received that particular hand.

The 99.45% version of Deuces Bonus, with appropriate play, yields such a hand every 36,200 hands. It’s possible to get two or three of those jackpots in the same day. It’s possible to go several hundred thousand hands without hitting it. Whether I stay on the same machine or switch lots of time; whether I leave for the day after losing or winning some predetermined amount or keep playing straight through; whether I average four hours of play every three months or 40 hours a week–none of those things matter.

What does matter? The return on the game is one important factor. If Triple Double Bonus is the highest paying game in a casino within the range of denominations I prefer — and I can afford the swings — and if I play there at all, that’s the game I’m playing. If Bonus Poker pays the most, I’ll play that.

The first game has a sky-high variance. That means it’s very exciting and you’ll either win or lose a ton. The second game has one of the lowest variances in video poker. For some players that means it’s the most boring. How exciting or boring a game is isn’t in my list of major concerns.

The slot attendant had to come back to pay me. He didn’t actually give me $2,000 in cash (although he would have if I wanted it that way), but rather left the 200 credits on the machine so I could continue playing.

He was still a bit sorry for me that I had wasted that ace, but I assured him that I wouldn’t lose any sleep over it — and getting the fourth deuce was good news and I was happy with the hand. He shrugged like I was really confused but he didn’t want to embarrass somebody who couldn’t understand his point. And then he left.

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A Mistake That Didn’t Cost Me

I happen to believe that mistakes cost you — even when they don’t. Say you were playing 9/6 Double Double Bonus for single line dollars, five coins bet, and were dealt 3♦ K♠ K♥ 3♣ 8♦.  Assume you’re knowledgeable enough and disciplined enough to know that holding KK33 is correct — but you were playing fast and only held KK because you saw the high pair but didn’t see two pair.

Further, assume the three cards you draw are 5♠ A♥ 9♣. Holding the kings only you end up with five credits. Had you held the two pair and ended up with the same draw (specifically only the 5♠), you would still end up with five credits. Many people believe this to be a no harm-no foul “non-event.”

I believe it cost you $1.16 in EV which is the difference in EV between holding KK33 and KK.

While it is true that you can’t take EV to the bank, my decisions in video poker (including which games to play, where, and when) all come down to EV. Over time, my actual results and my EV results will be fairly close.

They will never (okay, extremely rarely) be EXACTLY the same, but close enough. If they happened to be exactly the same and I played one more hand, they would usually be different. (If you want actual results and EV results to be identical all of the time, consider playing a change machine. You insert a hundred-dollar bill and get out five twenties. Put one of them back in and receive four fives. Put one of them back in and receive five ones. Then you take all that to the cashier and receive a $100 bill. Repeat. What fun!)

Each misplay I make costs me EV, and over time, those mistakes add up.

In the last week of August, there was a promotion at the Palms where video poker players received either a 2x or 3x multiplier every day. The base slot club returns 0.25%, so this means you would get either 0.50% or 0.75%. They limited the number of bonus points you could get to 80,000, so this meant if you received a 2x multiplier you could play $80,000 coin-in and if you received a 3x multiplier you could play $40,000 coin-in to max out your bonus points.

If this doesn’t make sense, don’t worry about it. Supposedly on October 1, Red Rock Resorts (formerly called Station Casinos) will be taking over and what is now Palms may be called something like Palms Station and be incorporated into the Boarding Pass system.

Since Station Casino has cut me off from receiving benefits long ago, along with several hundred other players, I do not anticipate playing at this casino once it changes ownership. And before October 1, I will convert my remaining Palms Club points to free play so I don’t have to worry about converting them once the casino changes names. If for some reason the conversion to Palms Station doesn’t go through, I can always start earning Palms Club points all over again.

Anyway, the only “decent” Ultimate X games at Palms that offer slot club points are 15-9-4-4-3 Deuces Wild. In the Ten Play version, this game returns 99.44%. With single or double points, a player is “under water” on the game, although that can possibly be made up with drawings, other promotions, and mailers. With triple points, the player has a slight advantage — with the drawings, other promotions, and mailers still on the table.

So I play this game during triple point days and avoid it otherwise. The machines come in 50¢ and $1 denominations, meaning $50 or $100 per 100-coin max bet. You can play it for Triple Play or Five Play with smaller maximum bets, but when you do the EV on the game is only 99.13% or 99.27% respectively. Not for me.

The strategy I use, which I will teach in my September 28 class at South Point, is broken down by the sum of the multipliers active at any one time. The multipliers may be anywhere between 10x and 120x. In the one-deuce section, for example, I recommend one strategy for multiplier sums between 10x and 31x, another strategy between 32x and 53x, a third strategy between 54x and 75x, and a fourth strategy between 76x and 120x.

So there are four different (but similar) strategies in the zero-deuce section and four more for the two-deuce section. In the three-deuce section, there are only two strategies for multipliers below 96x, and six more for those rare cases where it’s above 96x. For four deuces, there is only one strategy no matter what the multiplier sum is. I’m not going to tell you what it is.

In 2016, I’ve only played this game four times because it’s been rare when the conditions are good enough. So I haven’t committed this strategy to memory. It’s tougher than average to memorize and it’s a long time between opportunities, so I practice maybe a half hour before potential play and bring the strategy sheets with me.

The Palms is fewer than 10 miles from my home, so it’s not terribly inconvenient to go in and check whether my multiplier would be 2x (which means I wouldn’t play) or 3x (which means I would.) Every day I had the strategy with me — in case. I would show up slightly after midnight because there would be less competition for the machines at that hour. I’m not the only one who plays this game on 3x point days.

On Monday, August 29, I received a 2x multiplier. Tuesday, August 30, I received a 3x multiplier, and I sat down and played 40,000 points. I ended up a small winner, which was fortunate. Ultimate X has a VERY high variance and on any particular day, your score can be quite a bit ahead or quite a bit behind.

The last three days of the week, I received 2x multipliers each time and didn’t play. But I didn’t know it before I got there. So I practiced a bit, took my strategy with me, and was well rested when I showed up.

My strategy, which is on three sheets of 8½” x 11” paper is carried in a library book. If it takes awhile to be paid (like, for example, on an “in my dreams” hand of a dealt straight flush followed by a dealt royal which would pay $240,000 or $480,000 depending on which denomination I was dreaming about), I’ll read my book. Also, the sheets of copy paper last longer if they are protected by being in a book rather than carried loosely.

The last time I went to check my multiplier, however, I made a mistake. I had two library books checked out and the book I put my strategy in was not the one I ended up taking to the casino. So had the multiplier been 3x (it wasn’t), I wouldn’t have had the strategy with me.

Had I received the correct multiplier, I would have asked the attendant to lock up the machine, gone home to pick up the strategy, and been back within a half hour or so. It would have been a tad inconvenient, but not an EV loss, unless you want to argue that time is money and gas isn’t free and I wouldn’t have a good rejoinder to that. Still, I need to be more careful and wish I hadn’t made this mistake.

If this machine and opportunity is still available after October 1, you’ll have to find out from somebody else. I don’t expect to be welcome there.

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Six-and-a-Half Little Words

I was having my morning bagel at the coffee shop when I saw two boys sitting at a table waiting on their parents, who were in line. The older boy was 7 or 8 years old, and he was teaching some card game to his little brother, who looked 4 years old, 5 max. Continue reading Six-and-a-Half Little Words

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Not Very Well Thought Out

In a recent online blog, Jean Scott wrote how she’d  run a slot club.

Among other things, she said: “I’d never run an unfair promotion, like a slot-point marathon where quarter players are competing with $5 players. People like a promotion where everyone has at least a chance to win.”

If she owned a casino she could run any promotions she wanted. If she ran a casino without owning it, it’s hard to imagine her keeping her job. With suggestions like she put forth here, it’s hard to believe any casinos would seriously consider her suggestions. Let’s look at what her ideas would cover:

  1. Assume a casino executive wants to get more play out of his $5 machines. He believes giving $25,000 away to players for a slot marathon might be a good way to draw in the players he wants. Jean would tell that casino manager not to do it because a 25¢ player wouldn’t have a chance. If I were advising the casino, I might tell him to go ahead — depending on a variety of factors. I’d also advise any 25¢ player who asked for my advice not to bother competing. It’s not smart to bring a knife to a gun fight.

 

  1. Jean advocated doing away with all promotions geared for seniors because players under 50 have no chance to win. Personally I think senior drawings make sense for players and casinos.

 

  1. At the Palms, on certain days of the week, if you play $500 in coin-in you get either a movie ticket or car wash coupon. Jean would do away with these promotions because some people can’t afford to play that much.

 

  1. Caesars Entertainment awards Seven Stars players a free cruise every year. Jean apparently advocated that Caesars stop doing this because it discriminates against players who aren’t Seven Stars.

 

  1. The South Point invites almost 1,000 of their top players to a player appreciation party every year — where you get a nice dinner including an open bar, some chance at door prizes, $500 in free play, and some new electronic something. One year it was a top-of-the-line iPad. One year a Kindle Fire. One year it was a computer tablet. One year it wasn’t electronics but dinner for two at Michael’s, the South Point gourmet restaurant — where ordering $300 in entrees and a $200 bottle of wine — or more — was quite acceptable. I would tell Michael Gaughan that this is a fine gesture and is appreciated by these players. According to her words, Jean would tell him to stop it because it’s unfair. If you can’t invite everybody, you shouldn’t invite anybody.

 

  1. I presume she would do away with VIP check-in and rules that allow VIPs to stand in much shorter lines at the buffet, the cashier, and other places. And VIPs should pay the same resort fees that everybody else does. And while we’re at it, let’s forget about their amenity baskets (not that there’s much in them anymore.)

 

Do I seriously think Jean advocates these things? No. Of course not. It’s what she wrote many years ago in an article she recently found when cleaning her computer files.  She may have meant it long ago, but if actions speak louder than words, she doesn’t mean it now.

Jean used to be a quarter player (weren’t we all!) and probably wrote the first draft of this back in those days. She saw the world through the eyes of a quarter player and believed the casino should go out of its way to take care of quarter players. It was a ridiculously self-centered idea then — and much more so today.

Now she’s accumulated some wealth and knowledge and plays for bigger stakes. Today she takes advantage of senior promotions, free cruises, VIP check-in, and sometimes participates in promotions where she has to play a certain amount to receive certain benefits — which her earlier words said were unfair promotions. If she’s invited to a VIP party she thinks looks interesting, do you really think she’s going to pass it up because other players weren’t invited? If you do, you have a much different opinion of her than I have.

Possibly she was desperate for a column and borrowed an old one without thinking it though. I truly understand sometimes having nothing to write about — and on occasion I have recycled some of my own. But I always try to proof them first and bring them up to date.

In this blog, Jean seemed to lose sight of the fact that casinos are in business to make money. Casino promotions are geared for the benefit of the casinos, not players. Jean seemed to think that casinos should make all promotions for the benefit of players — especially low limit players. Why on earth would casinos want to do that?

Although this was originally written maybe 20 years ago, quarter video poker players today are not particularly valuable to casinos. Casinos make more off of bigger players — and slot players — and so reward them accordingly. Many casinos today reward players based on Average Daily Theoretical — which means the amount a player can be expected to lose playing particular machines.

The ADT on quarter video poker machines is very small. I’m not putting down quarter players, and casinos put out machines for them. But quarter players shouldn’t expect the casino world to revolve around them. And this entire article was geared towards giving the quarter players the best chance to win. Of all the things casinos worry about, that’s pretty far down the list.

Players who want to advise casinos how to operate have to get out of their own narrow perceptions and try to see what motivates casinos. If a player can’t do that, he/she should know the proffered advice is going to be laughed at ignored.

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What Are You Trying to Get?

My niece Jessica, in her late 20s, recently married Blake. They live in Southern California. I asked them beforehand to choose their wedding present from me — either a check or a Vegas weekend. They chose the latter and then asked if it could include some video poker lessons. Sure, no problem.

In mid-August they came to town. I got them a nice hotel room, Penn and Teller tickets, and Bonnie and I took them out to a nice dinner. And, of course, a video poker lesson.

Jessica is NOT a gambler at all, but her new husband has been to Vegas a lot. Jessica wanted a game where she could have fun gambling and not lose more than $5 or $10 an hour. I got them a room at the Palms, where they have three machines that include penny Fifty Play 9/6 Jacks or Better. So long as she played five hands or fewer at a time, it would basically be impossible for her to out-lose her budget.

I used my normal class notes. I was unsure whether they’d be appropriate. Jessica has an engineering degree from an Ivy League school and my beginner Jacks or Better class is geared for people with average IQs. I don’t’ know Blake’s academic background, but I’ve known him for a couple of years and he’s pretty bright.

My classes are typically interactive with me asking questions to all of the students. So I went to their hotel suite, sat between them, and used the PowerPoint presentation on my laptop. I quickly concluded that asking Jessica most of the questions made more sense than switching back and forth, simply because the concepts were foreign to her and Blake was way ahead of her as a player.

One of the problem hands was A♠ K♠ 3♦ 4♦ 5♦ and I asked Jessica whether she should hold the black cards or the red cards? The way the class is set up, the diamonds are included in Rule 8 (3-card straight flush that is either consecutive or contains two high cards) and the spades are included in Rule 9 (two suited high cards). The ground rules of the class say you pick the rule that comes first, so in this case you hold the diamonds. (Note: this was a beginner’s class. Intermediate and Advanced classes have different rules.)

Jessica understood that I wanted her to pick the earlier rule, but then she asked, “What are you trying to get when you hold the diamonds?”

I thought I’d heard every beginner’s question fifty times, but this was a new one — and I’m not sure I gave her an answer that made her happy.

I clicked over to the Video Poker for Winners software and called up this hand by going to ANALYZE àSELECT SPECIFIC CARDS. I entered these five cards and then clicked on ANALYZE THIS HAND. I then clicked on SHOW DETAILS.

On the spreadsheet that showed up, the software said there were 1,081 different combinations of cards you could draw to 3♦ 4♦ 5♦. Of those 1,081 combinations, 941 of them give you no winning score at all, 18 of them give you Jacks or Better (paying 5 coins), 27 of them give you two pair (paying 10), 9 times you get 3-of-a-kind (paying 15), 41 times you get a straight (paying 20), 42 times you get a flush (paying 30), and 3 times you get a straight flush (paying 250). From that starting position, it’s impossible to get a full house, 4-of-a-kind, or royal flush.

To get the Expected Value of holding that combination, you take a weighted average of all those. That is, (5*18 + 10*27 + 15*9 + 20*41 + 42*30 + 3*250)/1081. If it’s been awhile since you studied math, you do all of the multiplication first — and then do the addition — and then the division. If the parentheses weren’t there, it would be a different order. The answer comes out to be 3.0759 (listed in the leftmost column on the spreadsheet), which means on average this hand is worth that many coins. Most players don’t want to do this math at all, which is okay so long as you have the appropriate software available. But you should probably at least know how the numbers are calculated.

I’d LIKE to get a straight flush when I hold 3♦ 4♦ 5♦, simply because that’s the highest-paying end result of what’s possible, but I can’t really say I’m TRYING for it. I’m looking for the combination of cards to hold with the highest EV — which is NOT necessarily the one with the biggest possible prize.

When holding A♠ K♠, there are now 16,215 combinations and the software gives the number of combinations hitting each category — the highest of which is a royal flush for 4,000 coins. But the average is “only” 2.9402 coins. Whether that’s high or low is only relevant in comparison to the EV of other possibilities in the hand. Since 3.0759 is higher than 2.9402, we hold the diamonds. Had the diamonds been 3♦ 4♦ 6♦ instead, with an EV of 2.6688, we would have held the spades.

My answer of “I’m not really trying for anything” didn’t particularly satisfy her the first time she heard it, but if she reads the Winner’s Guide and practices on the software (wedding presents, of course), I’m sure she’ll catch on if she wants to. (I suspect she won’t want to — I couldn’t even talk them into getting and using a player’s card!)

Still, I’m glad she asked the question. I don’t think I’ve heard it before — and now I have a good answer if I hear it again.

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I Was a BMX Voyeur

This likely will be a one-off column. It’s not about video poker. For me it’s not even about gambling, although I did make a few bucks betting on it. For me it’s about some kid I’ve known about for 20 years, who lives only a few miles from me, competing in the Rio Olympics in an obscure sport I knew nothing about until recently. It was a damn exciting experience for me and I want to tell you about it. If you want to read about video poker, come back next week.

Mike Fields is vice president at videopoker.com, also known as Action Gaming. Before that he was head of video poker for IGT. I met Mike more than 20 years ago. I was just coming up as a video poker expert. Mike was already established working for a gaming manufacturer. We met at a gaming show — enjoyed talking to each other — and have stayed friends. Mostly business friends, but with a good dose of personal relationship as well. There were fewer than 40 people invited to Bonnie’s and my wedding. Mike Fields was one of them.

I heard about his son, Connor, many times through the years. I met Connor once — with his dad — at a mall shortly before Christmas. A charity my wife was helping asked for donations to give gifts for underprivileged kids and Connor decided that since biking was his passion, he’d like to donate a bicycle. And he did.

connorfields

For the past several years, Connor Fields has been competing in BMX racing — with BMX standing for bicycle moto-cross. It’s an event for really crazy people. Up to eight cyclists start at the top of a steep eight-meter (26.25-feet) ramp. When the gate drops, they go speeding downhill and are up to about 40 miles per hour in two and a half seconds. Just to make it a little more exciting and dangerous, it’s legal to throw elbows and punches to the head as you jockey for position. Although the cyclists are pedaling throughout the race, the vast majority of their speed is gained in this initial eight-meter descent.

Once they reach the bottom of the ramp, they still have a long way to go even though it is definitely a sprint race. The BMX course has bunches of hills to navigate. The early ones come back-to-back and the cyclists become airborne as they go up one small hill — fly over the next one — and land going downhill. Although they could be going slower and actually go up and down each hill — that’s not a strategy for winning.

The corners of the track are called berms and they are banked so the bikers can take them at speed. Whether you take them high or low depends on how fast you are going and where you are compared to the other riders. Giving a “friendly elbow” to help a competitor go “over the top” of the berm to an off-course grassy landing is part of the game. Before the finish line, there are several low hills, called the rhythm section, which are far enough apart that you need to go up and down each one and jumping from one to the other isn’t a strategy any of the cyclists used at the Olympics.

Tracks are all similar — and all a bit different. Many are dirt. The one at the Olympics had a synthetic surface much like you see on a running track. I’m sure Connor can tell you how the texture of the BMX track is different from the texture of a running track and why, but I can’t.

The entire race takes 35 seconds or so for the winners. A bit longer if you crashed along the way. When one cyclist goes down, often one or more others get tangled up in the mess. The track isn’t all that wide and all the racers are trying to get to the front. Interestingly, if you go down in a BMX race and you can still walk, you pick up your bike and carry it to the finish line.

In most preliminary races, the top four go on to ride in the next round and the slowest four are eliminated. Whether you’re first or fourth in one round affects your position on the track in the next round, but your score doesn’t carry over. For example, even if the fourth place cyclist was a quarter of a second slower than the winner in the quarter-finals, they start off even in the semi-finals time-wise.

There were LOTS of stories about Connor Fields before the Olympics (Google him if you don’t believe this). He was injured earlier in 2016 and couldn’t compete in the Olympic time trials, but because of his skill, he was given a coaches’ exemption and was selected as a member of the five-person U.S. Olympic team (three men, two women). Since he’s a local boy here in Las Vegas, local TV and newspapers mentioned him all the time.

I didn’t get to see any of the races in real time, but I’d read the results every night. On Wednesday, August 17, I checked the results and saw Connor came in fourth place. I was very disappointed. He was really hoping for a medal, which only go three deep, and to go all that way and come up just short was awful.

As I read further, I realized that yes he was in fourth place, but these were individual time trials used for seeding purposes. The top 32 racers moved on to the quarter-finals the next day — and Connor was doing just fine.

On Thursday, August 18, there was blood on the track. Several of the riders went down hard, including one of the pre-race favorites — Joris Daudet from France. http://www.nbcolympics.com/video/bmxers-took-some-hard-hits-quarterfinals

Fields and the other two Americans, Nic Long and Corben Sharrah, survived and would race again Friday. Sixteen riders were left.

On Friday, August 19, the semi-finals got it down to eight riders, and shortly thereafter the finals ended it all. In the finals, which included two Americans — Connor Fields and Nic Long. Both Americans got off to fast starts and about 20 seconds in were in first and second position with Long holding a slight advantage. Connor passed Long, as did one Dutch rider and one Colombian, who passed him in a photo finish, so the Americans ended up with the Gold and near miss for the bronze. http://www.nbcolympics.com/news/team-usas-connor-fields-led-bmx-finals-start-finish-takes-home-gold

On the woman’s side, American Alise Post took home a silver, so it was an excellent showing for Team USA. I’m sure Alise has her own story and it’s every bit as exciting as Connor’s, but I’ve never met her and didn’t follow the women’s races at all.

We’re going to try to get Connor Fields as a guest on the radio show. It isn’t really about gambling, but his dad is a sponsor of the show, and hey, how many Olympic champions have you met? I want to ask him about the final race.

When he and Nic Young were neck and neck with 10 seconds to go, it’s possible Connor knew he was going to win. You know your teammates pretty well and Fields is a better finisher than Young is. But what if it was neck and neck with 3 seconds to go? You and your teammate are both going for the gold — and you felt that a well-timed elbow would push you by your teammate.

If it was for the Olympic gold, would you elbow your teammate?

(I mentioned earlier that I made some money gambling on this. With a friend, I took Connor Fields against the field at 5-1. I risked $10 (which I would have paid if Connor lost) and collected $50 when he won. It probably wasn’t a good bet, odds-wise, but sports are more exciting when you have a little wager on it, and this was pocket-change money between friends. The $50 win is nice, but I’m REALLY happy for Connor and Mike Fields!)

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Does it Matter?

You’re at your favorite casino. You’ve played a lot all month and are now there for the big drawing. Here’s the way it works:

Ten winners get called — they have a minute and a half to show up and identify themselves. If one or more spots are unclaimed after 90 seconds, more names are called. Eventually there are 10 contestants to “play the game.” Good news! You’re one of the chosen few — but I’m not going to tell you now whether you were first or last.

The way the game works is that 10 unmarked envelopes, in numbered spaces, are on a big board. Prizes total $25,000. The distribution of the prizes in the envelopes is:

First                        $10,000

Second                    $4,000

Third – Fifth                $2,000 each

Sixth – Tenth                 $1,000 each

 

Any of the players may end up with any of the envelopes. The first player drawn has the biggest choice. The last player drawn has no choice at all, but clearly it’s better to have this “no choice” rather than not to have been called at all.

Here are the questions: What’s your EV (expected value) if you get the first choice? What’s your EV if you barely make it in and you end up taking the last envelope? (We’re assuming the envelopes are indistinguishable from one another. I’ve been at drawings where actual cash was in the envelopes and the envelope with 100 C-notes inside was quite a bit fatter than the ones with “only” 10 Benjamins. In that drawing, you definitely wanted to be first to pick because visual inspection of the envelopes contained valuable information.)

The answer, of course, is “it depends.” (I like questions where this is the answer. That gives me something to write about!)

For the first player to select, the EV is clearly $2,500. A total of $25,000 is being given away to 10 players, and $25,000 divided by 10 is $2,500. This is as simple as an EV calculation gets.

For the second player, his actual EV depends on what the first player chose. If the first player selected a $1,000 envelope, then the second player’s EV is $24,000 divided by nine, which is $2,667. If the first player selected the $10,000 envelope, then the second players EV drops to $15,000 divided by nine, which is $1,667.

By the time we get down to the last player, there will be one envelope left and the EV is whatever prize hasn’t been claimed — meaning $10,000; $4,000; $2,000; or $1,000.

How do you take a weighted average of that?

Before I answer that question, let’s change this discussion a little. Assume each of the players selected an envelope but didn’t open them until the very end when they opened them together. In that case, each of the players has an EV of $2,500. There is still $25,000 in the prize pool, so far as they know, and they each have one in 10 chances to get any of the prizes.

Now, change it again. Assume you are the last person in line but you put earphones and blinders on until it’s your turn. Based on the information you have, you now have the same $2,500 EV as you would if everybody opened the envelopes at the same time!

If you are watching what happens and you’re still last, and you do this many times, on average your EV will be $2,500 — with variance!

Mathematically, on average it doesn’t matter whether you pick first or last. It can matter psychologically however. You see the $10,000 and $4,000 envelopes opened by somebody else and it’s a real downer if you’re somebody who sweats your daily scores! But sometimes getting called last will mean you see all of the smaller envelopes being opened and you’re left with the big one! On average it doesn’t matter, but if you want to feel bad about it, knock yourself out.

Since there are five $1,000 envelopes out of 10 total, half the time the last guy will end up with $1,000. (Of course, half the time the first guy — with complete freedom to choose any of the envelopes — also gets $1,000.)

When the first guy picks $10,000 (which will happen 10% of the time), it LOOKS like having the first choice was a big advantage. But it really wasn’t. He just made a lucky pick.

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When Experts Say Opposite Things

When I was in graduate school 45 years ago, plus or minus, I heard about an incident many years prior to that at the University of Chicago. It appears that there was an elevator for a campus building with a “Students Only” sign on it. One professor entered and was challenged, presumably in a friendly way, because he wasn’t a student. The professor answered, “We are all students. I study much more today than when I was your age.”

I’m that way too. I study gambling as much or more today as I ever did. One “advantage” of hosting a radio show about gambling is that I am “forced” to read gambling books that I wouldn’t otherwise pick up. I read the book in order to try to ask interesting questions of our guests. This gives me a much broader grasp of gambling than most players have.

I have many gurus — in the sense that I listen to what they have to say and try to apply it to my own situation. Two (of many) are Ed Miller and Richard Munchkin. Recently I realized that they said virtually the opposite thing about a subject — although ironically they both respect each other and would probably agree with the point of view of the other guy.

Sounds strange, right? Let me continue.

Ed Miller writes a lot about No Limit Hold’Em cash games with an emphasis on low stakes games. His recent book, The Course: Serious Hold’Em Strategy for Smart Players, is an excellent treatise on how to make money in $1-$2 and $2-$5 games. We’ve spoken about the book on the air, but we barely scratched the surface of what the book holds.

Near the end of the book is a section entitled “The Pitfalls of Running Good.” Miller says, “Running good out of the gate is one of the worst things that can happen to players. If they rack up big wins early on, a couple of bad things can happen. First, they develop unrealistic expectations. . . . Second, these early wins reinforce bad habits.”

I’m not going to quote his entire argument, but I found it persuasive. You need to guard against the dangers of running good. And Miller discusses several ways to do that.

Richard Munchkin, of course, is my co-host on the Gambling with an Edge radio show. However much I’ve prepared to listen to what our guest has to say on the air, I’m always eager to hear what Richard has to say as well. Although I often prepare a script beforehand and Richard knows where I’m going to go in the discussion, I never know beforehand what he’s going to say and I find that interesting and educational.

On more than one occasion, Munchkin has opined that a disproportionate number of successful gamblers ran good at the beginning. Why? Because a disproportionate number of the players who ran bad quit gambling! Somebody who always seems to lose has a tendency to give up and conclude that gambling is not for him.

So Ed Miller says running good at the beginning is one of the worst things to happen to you and Richard Munchkin says it happened to most successful gamblers. Not exactly contradicting each other — but close.

After mulling this over for a while, I decided they’re both right!

Running good does create some unreasonable expectations and bad habits, but gamblers who end up successful eventually learn to deal with these things. (If they don’t, they’re not successful gamblers. Nobody runs good forever.)

However bad running good is in terms of learning to play the game the right way, I’ll take it every day! While I understand Miller’s argument, I’d rather be $10,000 ahead than $10,000 behind. And so would you.

As to whether Munchkin was right about today’s successful players running good at the start, I started to examine whether it was true for me in particular. A case could be made that it was — but it also doesn’t matter. Anecdotal evidence about any one player (including me) doesn’t come close to proving or disproving any statement starting with “Most players . . .”

But I found Richard’s argument persuasive as well. The early loser tends to quit. The early winners tend to keep going. He’s looking at tendencies — not something that is correct 100% of the time.

I like it better when my gurus disagree with each other. It forces me to think about the arguments and come to my own conclusions. That’s how I improve my craft. And the fact that these two gurus are addressing games other than video poker means I always have to see if what they said applies to my game as well. Again, that’s how I improve my craft.

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How Much Do You Steal from Casinos?

I sometimes post on the forum at wizardofvegas.com. It’s hosted by Michael Shackleford, the “Wizard of Odds,” who’s a long time friend and former radio show co-host.

Recently someone there started a thread, “Have you ever stolen from your employer?” They included a poll and, early on as I write this, half (3 out of 6) of the responders say they have never stolen from their employers. With a sample size of six, no conclusions can be made. But as the sample size increases, surely the number of people admitting to theft from their employers will increase.

In Dan Ariely’s “The Honest Truth About Dishonesty: How We Lie to Everyone — Especially Ourselves,” he makes the case that most people sometimes steal at least minor amounts of stuff. While not all of us are employed, we all frequent casinos (or you’re wasting your time reading my columns). So I thought I’d change the topic to how often we steal from these places.

Defining what is actually stealing isn’t easy — even if we use Supreme Court Justice Potter Stewart’s (used in a significantly different context), “I know it when I see it.” Let’s look at things that may or may not qualify:

  1. Getting a comped room/show/meal and selling it to somebody else. The fact that it is comped means the casino knows it is giving it away and is fine with that. Casinos have policies against selling comps, but that doesn’t make it illegal or immoral. If you give the room/show/meal away to a friend or relative and don’t charge him for it, does that change the “theft or not?” discussion in your mind? What if you were upfront with your host and said your niece was coming and you needed a room for her? To me, this latter situation (which I’ve done recently) is perfectly okay. I’m not sure where the dividing line is, though.
  2. Loading up on toiletries, toilet paper, etc., from your hotel room and taking it home with you. If you’re fine with this, how about extending it to towels? Or bedsheets? Where do you draw the line?
  3. You’re playing blackjack betting two reds (total $10) next to another player betting two greens (total $50) on a stupid 6-5 game. Officially it’s a $25 minimum table but you were grandfathered in because previously it was a $10 table and you can play the lower stakes until you leave. You both get blackjacks and the dealer pays you both $60. Do you immediately speak up and say, “No. You should have only paid me $12?” I wouldn’t speak up (not that I play blackjack anymore — and certainly not on a 6-5 game), but some players would.
  4. You cash in chips at the cage for $175, but somehow the cashier miscounts your chips and gives you $200 instead. Do you return the excess $25? I would, but some players wouldn’t.
  5. Morally, it’s tough to distinguish between the two previous cases. The rule I use (as do many other players) is that if a casino worker will personally be responsible for making up the shortfall, I give the money back. Taking money from somebody who is working for wages is just plain wrong in my opinion. If it will just go into the pot as a casino loss, as in the overpayment on the blackjack table, I’ll keep quiet. I am in the casino to make money after all. But just because I have a rule of thumb to guide my actions doesn’t mean that it’s any the less theft.
  6. I’m married to Bonnie, but used to be married to a woman named Shirley. Let’s say I still have some of Shirley’s old slot club cards and I still use the same mailing address as when I was with her. If Shirley got a “come on back and we’ll give you $200 in free play” offer in the mail and I came in and played off that money, how wrong would that be? For me personally, it isn’t going to happen. I am too well known. Even casinos that allow me to play have some reservations about it, so I’m not going to do anything that could backfire on me. What’s right or wrong shouldn’t depend on the consequences if you’re caught. But it’s probably a factor to most people. Decades ago if this happened, I probably would have gone in and picked up the free play without any qualms whatsoever.
  7. Playing on a spouse’s slot club card is allowed at some places and not at others. Where it’s allowed, I take advantage of it and play on Bonnie’s card. There are players with players’ cards in 50-100 different names. To me this is clearly wrong, but I can see the argument that it’s just a matter of degree.
  8. Is that morally different from entering free football contests (where you need to pick who is going to win) in LOTS of different names and coordinating the picks to eliminate duplicate entries?
  9. I know a guy who found a wallet in the casino. He turned it in to security almost immediately. But since he REALLY had to go to the bathroom at just that moment, he took the wallet with him inside a stall. What he did with the wallet inside that stall, we’ll never know for sure. Makes you wonder, though.
  10. Dealers are sometimes sloppy and expose their hole cards. There are players who specialize in seeking out such dealers and using that information to beat the house. Legally, thanks to the Einbinder case, these players are on solid ground (in Nevada anyway — maybe not so much at Indian casinos). Does the fact that it’s legal have any bearing on whether it’s moral? If players discovered that performing a particular action (perhaps tipping) made the dealers even more readable, is that unspoken collusion a type of stealing?
  11. You’re playing blackjack at casinos that will award you airfare if you lose enough money. You have perfected rat holing, meaning hiding chips on your person surreptitiously so the chips in front of you are a lot less than what you actually have. The pit boss writes down that you lost $6,000 when you actually came out ahead. You do this at six casinos during the trip and turn in printed receipts for the same flight all six times. You even went further. You ordered the tickets at full price — printed off multiple copies of the tickets — and then cancelled those tickets and booked the same flight at half the amount. You got the larger amount reimbursed six times for imaginary losses. Was the line between being clever and immoral ever crossed here? At what point? There will be some who say that’s just business as usual — and others will say the line was not only crossed, it was obliterated.

I could go on, but that’s enough for today. Most of us, myself included, consider ourselves to be moral, law-abiding people. And we all do things from time to time that are difficult or impossible to explain to somebody who takes an opposing point of view. And if somebody disagrees with you, they often take a “holier-than-thou” attitude about it.

I do the best I can and suggest you do the same.

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D T B

Bonnie’s family accepts that I’m a successful gambler. They also believe that the methods and discipline I use to succeed involve far more study than they want to invest — especially since it will never be more than an occasional hobby for any of them. Continue reading D T B