Tag: video poker

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You’re Not Ready Yet

Immediately after one of my classes at the South Point, a man, “Joe,” came up to me and asked if I would mentor him in becoming a professional video poker player. He told me he had plenty of bankroll and wanted to turbocharge his learning process. He had heard that I would do private consulting for $250 an hour with a two-hour minimum and that did not present a problem for him.

I had another engagement after class, so we scheduled a lunch date for the near future. Although I have food comps at casinos, I preferred having the conversation at a local Applebee’s where the chances of being overheard by other players was far less. I don’t pay retail for food in Vegas very often, but this was one of those times.

In the time before I met with Joe, I tried to figure out what kind of person I would be willing to mentor. Assuming he had the bankroll, I figured the main criteria were:

a. His personality was acceptable to me. This isn’t a particularly high bar to cross, but there are a few people I just don’t enjoy hanging out with. I didn’t want a long-term relationship with somebody like that.

b. He was smart enough. Video poker is applied math. Not everybody is capable of learning it at a high level.

c. He had some history of success at the game and could study on his own. When I’m consulting with somebody two hours at a time, I don’t really care how good they are when they come to me. I’ll spend the two hours doing my best to improve their skill and knowledge level. But a mentoring relationship is a longer-term affair and spending dozens of hours while moving somebody from beginner to intermediate isn’t how I want to spend my time.

Okay. After Joe and I ordered lunch, I asked him where he lived and how he got his bankroll. I had spoken to Joe a few times previously and he passed the personality test, such as it is. He had sent me a number of emails over the past few years with questions and/or suggestions for the Gambling with an Edge radio show. These emails led me to believe he was smart enough to succeed at this.

Joe told me he was 49 years old, lived on the East Coast, and had recently inherited more than $2 million. He planned to retire from the Air Force Reserve in a few months and was looking at how he wanted to spend the rest of his life.

Joe had listened to a number of the radio shows and it really sounded like I enjoyed my life more than he enjoyed his. Plus, he had read my Million Dollar Video Poker autobiography and was fascinated with the life of a gambler. He decided he wanted to invest a portion of his inheritance, maybe $200,000, to see if he had the aptitude to maybe be the next Bob Dancer.

I asked him how many of the Winner’s Guides he had closely studied. He told me he had purchased a set but had yet to open them up. I asked him how much time he had spent with a computer program such as Video Poker for Winners. He told me he hadn’t purchased a copy of that yet but it was next on his list.

I told him he wasn’t ready for mentoring yet. In the next six months, I suggested he learn two games at the professional level — perhaps Jacks or Better and NSU Deuces Wild. Using the Winner’s Guides and the software, this wasn’t such a formidable task. But neither was it a trivial one.

Then, I wanted him to spend at least two weeks straight in Las Vegas or another casino city gambling 30 hours a week. At the end of that, if he still wanted me to mentor him, he knew how to get in touch with me. I would give him a test on the two games, and if he knew the games at a high level, we could revisit the mentoring idea.

Joe was in love with the idea of being a gambler, but he hadn’t had any actual experience. It’s hard work to get to the professional level at one game — let alone two. Playing 60 hours will turn out to be a boring experience for many people.

Video poker is a grind-it-out affair. It’s one thing to be fascinated by what appears to be a glamorous life. It’s another thing entirely to go through the process of getting good at some games and then successfully playing those games for 60 hours without going totally bonkers.

Can Joe do this?

I don’t know. If he can’t, he was never going to be a success at gambling anyway. If he can master two games and still be interested in being mentored after some real-life experience, then at least he will be going into this with his eyes wide open rather than looking through the rose-colored glasses he seems to be wearing today.

On one of our radio shows, Richard Munchkin told us that he periodically gets these kinds of requests from people wishing to learn blackjack. Richard tells them to learn basic strategy completely for four different games — i.e. with or without standing on soft 17 and with or without the ability to double after splitting. Once they know all four of these basic strategies, come back and see him again.

Richard tells me he’s never had somebody come back to him with these four strategies memorized.

I guess Richard’s experience influenced how I dealt with Joe. The task I gave Joe is more difficult than learning four basic strategies — each of which is more than 90% identical with the others. Jacks or Better and Deuces Wild are games very different from each other.

Still, if Joe passes this test, he’ll be a worthy student and I won’t mind at all working with him.

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Why Did You Print the Wrong Information?

I received an email from a player who told me that he found an error in Dream Card. I was definitely interested. If I verified that it was an error, I would send the information along to the folks at IGT (who manufacture the game), videopoker.com (who invented the game), and the player community. Whether IGT and videopoker.com chose to “fix” the problem in their next release would be up to them, but even if they did, older versions might still be out there and players should be warned about it.

Please note that this falls into the realm of “hearsay.” I didn’t see the error, and the man who told me about it said it happened to his son. There’s plenty of room in there for some misunderstanding to have taken place. Still, the situation is interesting on a couple of different levels which makes it worth talking about.

Curiously, I came away concluding that yes, there may have been an error with Dream Card in this situation, but it wasn’t the error I got the email about!

Here’s the situation. The player was playing 9/6 Jacks or Better Dream Card. Dream Card moves a 99.54% game to 99.56% — with a much bigger variance.

The dealt hand was A♠ K♠ Q♠ Q♦ DC, where DC indicates a Dream Card which is supposed to be the best possible card given the first four. The machine chose the T♠, giving the player a 4-card royal flush. The player wanted the Dream Card to be another queen, giving him 3-of-a-kind.

I told him that a 4-card royal was much superior to a 3-of-a-kind. I suggested he enter the hand A♠ K♠ Q♠ Q♦ T♠ on Video Poker for Winners and see that the 4-card royal is worth 92.34 coins. Then if he entered the hand A♠ K♠ Q♠ Q♦ Q♣, he would see the value of the trip queens is 21.51. If the reader hasn’t gone through the exercise of checking the value of combinations using VPW or other quality software, it’s an educational process to go through. It’s not difficult and it is eye-opening.

“So,” I asked, “why on earth would you prefer 3-of-a-kind to a 4-card royal flush? It’s not close!”

“Well, my son uses the Dancer-Daily strategy card and that card says 3-of-a-kind is better. If it isn’t better, why did you print the wrong information?”

Hmm, this could be embarrassing. I do have a good explanation for that but I can see where the confusion arose. The first two lines in both the Basic Strategy and the Advanced Strategy for that game are as follows:

 

RF5; SF5; 4-OF-A-KIND; FULL HOUSE; 3-OF-A-KIND; TWO PAIR

RF4 > FL5 and ST5 > any SF4

 

The top line of the strategy lists all hands in that game that are always held when dealt — with no exceptions. This list of hands is not the same for all games. There are games where from AAA44 or AA339 you just hold the aces, but Jacks or Better isn’t one of those games.

The second line lists those cases where a 4-card royal flush or a 4-card straight flush is in the same five cards as a dealt flush or a dealt straight. That is, from A♦ K♦ Q♦ J♦ T♣ you hold just the diamonds, but from Q♦ J♦ T♦ 9♦ 8♣ you hold all five cards.

A key underlying assumption for the strategy cards is that the combinations listed on the first line of the card are mutually exclusive with the combinations listed on the second line of the card. That is, you can’t have 3-of-a-kind and a 4-card royal in the same five cards. It takes at least seven cards to have both combinations.

I suppose technically you could argue the hand A♥ K♥ Q♥ J♥ T♥ is on the first line of the card, and any four cards from that combination are also on the second line of the card — hence the lines are not completely mutually exclusive.  But anyone who has trouble figuring how to play a dealt royal has no chance to understand my writings anyway.

If combinations are mutually exclusive, it doesn’t matter which order you list them in. Liam W. Daily and I recognized that using this underlying assumption allowed us to give completely accurate strategies with fewer rules. And we saw that as a good thing.

When you introduce the concept of Dream Card and you’re considering among alternative fifth cards, we can no longer hold with the assumption of mutual exclusivity while playing that version.

Simply put, the Dancer-Daily strategy card was designed for the “regular” version of Jacks or Better, not the Dream Card version. Since the machine almost always selects the correct Dream Card, you can continue to use the strategy card for the hands where Dream Card is not in effect.

With all that said, while the T♠ would be a much better choice than the Q♣ given the first four cards, the J♠ would be better still, simply because a jack presents three extra chances to end up with a high pair (namely the other three jacks) and a ten gives you no such chances.

Possibly the machine actually gave the correct card and there was a mix-up in the way the situation was presented to me. I assume IGT and videopoker.com can check on that easily enough. But whether there was or wasn’t an error, a discussion on an underlying assumption of the strategy card made this a conversation worth having.

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How Bad Is It to Be Greedy?

I assume you know what it means to be greedy. If I’m right about this assumption, then you’re ahead of me. I’m very confused by what the word means.

I Googled “What is greed?” It came back with the Oxford Dictionary definition, “intense and selfish desire for something, especially wealth, power, or food.” It mentioned that greed was one of the seven deadly sins. And it also quotes Gordon Gekko, the Michael Douglas character in the movie Wall Street who said “Greed is good!”

Still not clear.  When does a desire become intense? I remember back in college that sometimes friends and I would go out seeking pleasant short-term feminine companionship. I would call those desires intense and selfish. Back then, fifty years ago, there was kind of a “boys will be boys” mentality about “cruising for babes.” Today it is considered to be far more predatory than it was then. There are a lot of names you could have called our behavior back then, but I never considered “greedy” to be one of them.

If a student athlete wants to be good enough to someday be drafted into the National Football League, he might undertake the following: he begins his workouts every day at 6 a.m.; he spends hours each week studying game film to improve his own skills and figure out the tendencies of whoever is going to be his college opponent next week; he avoids drugs; he’s the last one to leave practice every day. It’s fair to call this athlete very intense. Although he loves the game, the potential million dollar benefits are certainly a part of working that hard. He may well be looking forward to buying his mother a house, but most of his thoughts about using this money are personal and selfish.

I would call the behavior in the preceding paragraph appropriate actions for somebody with a plan. Laudable behavior. Give that kid a standing ovation for working so hard. The actions, though, meet the Oxford Dictionary definition of “greed” namely “intense and selfish desire for something, especially wealth, power, or food.” I think it’s far better to praise this young man for trying to make something of himself than it is to castigate him for the sin of greed.

I have heard the term greed used in at least four separate gambling contexts recently. Perhaps you didn’t hear of these particular instances, but I’m confident you’ve heard of similar ones.

The first was on a video poker bulletin board where somebody posted a picture of a $1,500 jackpot on a quarter Triple Double Bonus Ultimate X game with the note, “Unfortunately the greed took over and I kept playing and ended up with only $700. I hate when that happens!”

The second followed a story about another Las Vegas casino planning on charging for parking. This comment by a player who was unhappy with the casino’s decision started off with “Greed! Greed! Greed!”

The third was a comment from a quarter player who was mad at all the five dollar players for being greedy and winning all the drawings.

The fourth was about a player who hit three royal flushes in two weeks at a casino after which the casino kicked him out. The comment from another player was, “Serves him right for being so greedy!”

These examples do not follow the Oxford Dictionary definition.  The first case resulted from normal swings in a game with sky-high variance. If the swings went up, the person would have felt intelligent, skillful, and proud. When the swings went down, the player blamed greed. To me, it’s a case of the player either not understanding the normal swings of the game or being a bad loser.

In the second and third example, we have somebody else taking actions that cause our lives to be a little more expensive. Since they did it to us, then they are greedy! I see the world as a bunch of moving parts where each person is trying to do what’s best for himself. I do not expect anybody else to roll over and play dead in order for me to succeed. If they block me going to the left, I go to the right. As our outgoing first lady said recently, “If they go low, we go high.” I do not see this as greed on their part. Or on my part for adjusting to what they are doing.

In the fourth example, the player was greedy because he hit three royals? I don’t know anybody who knows for sure when he’s going to hit his next royal, let alone his next three. Royals happen in their own good time. It is possible you’re going to hit three royals tomorrow. It’s possible it’s going to be months and months before you hit that many.

The player who hits three royal flushes in a short period of time is fortunate. But greedy? Like he did it on purpose just to spite the casino? I might well have some unkind words about a slot director who thinks getting royals quickly is a sign of great skill, but calling the player greedy? I don’t get it.

What would I call greedy? Well, if there was only so much food for, say, four people, then taking more than a fourth of it before others have had a chance to eat would be greedy. If some food was left over at the end, then that’s fair game. Or perhaps two roommates were both trying to get ready to go and they had a deal that 15 minutes in the bathroom at a time was all you got. Someone who took more than that is greedy, in my opinion.

What these examples have in common is that there’s a fixed amount of something and sharing is the name of the game. In this context, greed is refusing to share. In a game situation, where players compete against each other, refusing to share is often the sensible thing to do.

If you think of the world as a closed system and everybody from all lands are brothers, then you can come up with some sense of greed. In this context, you’ll see “green” philosophies, which basically try to save the environment for everybody. Within that context, people who refuse to save the environment are greedy.

But you’re not going to get universal agreement on this. I can easily support a “take nothing but pictures, leave nothing but footprints” philosophy when visiting a national forest. Whether we should shut down a lumber industry to save an endangered species of owl is a topic of spirited emotions on both sides.

If you cannot or will not see the world as a closed system and you believe it is “every man for himself,” then greed isn’t well defined, at least to me. Or perhaps, Gordon Gekko’s “Greed is good!” makes sense. I do not see the world that way, but I’ll be damned if I can figure out exactly where the lines of demarcation go.

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Where I Grew Up

Someone pointed me to an article in a West Hollywood publication about the Cavendish West. I was surprised to find that I was quoted in the article as the author never spoke to me. He did, however, paraphrase some things I’ve said on the radio show.

The Cavendish West is the place where I learned many lessons about gambling — from about 1975 – 1991. Although I did play a bit of contract bridge there for money, I was never a winning player at that game. My game of choice was backgammon, where I was successful — for a time.

In the mid-1970s, when backgammon was a sexy game, was played in discos, and was written about in popular magazines, I was sufficiently above average that I did quite well financially. Eventually the game passed out of favor and the Cavendish was left with only the good pros beating up on the not-so-good pros. I fell into the higher end of the lower category — and eventually, around 1980, I had to go out and get a job to support myself. It was awful.

I wrote a “Lessons from the Cavendish West” chapter in my Million Dollar Video Poker autobiography, but today I want to primarily address other things.

At the Cavendish, there were a LOT of good players. You could sit and watch them play, and so long as you were quiet you were generally allowed to look on. As Yogi Berra said, “You can observe a lot just by watching.” You could take notes and see how the big boys did things.

Sometimes they’d take three or so minutes to make a play and you could see what they finally did, but you had no idea of what their thought process was. For me, just watching was pretty boring. Playing was a lot more fun than watching. Still is. I basically had a free backgammon university education available to me, but instead chose to go and play backgammon against somebody over whom I had little or no edge. That led to a form of gambler’s ruin.

Today I hope I’m smarter than that. Video poker opportunities are less plentiful and less lucrative than they used to be. Studying, scouting, and waiting for the good ones are all part of succeeding these days. It’s easy to predict a day will come that I’ll be playing two hours a week or less. I’m preparing for that day. Perhaps you should too. Those who continue to play even though they are not the favorite will continue to lose.

Other factors that were drummed into me concerned sleep management and substance abuse. During certain periods in the 1980s, I worked 50+ hours a week in IT departments and then tried playing and/or studying 40 hours a week of backgammon. Both careers suffered — as did my social life. Today I can’t stay alert and play more than 6-8 hours at a time, although if I get a good four hours of sleep I can put in another session of that length. However much EV I calculate a play is worth, that calculation presumes an insignificant number of errors. If I play long enough, I make many more errors than I calculated and lose all my edge.

The Cavendish was housed in an office building and one flight up was a small roof that covered a portion of the building. Players frequently smoked marijuana or other substances on the roof and getting an invitation to join them was fairly easy. I didn’t do that very often, but when I did, my results suffered greatly. I am not someone who can smoke a joint and then concentrate on playing the way I need to in order to succeed.

Because of our last election, recreational marijuana is about to be legalized in Nevada. That’s fine for those of you who want that, but for me it’s poison. I’ll stay away. It’s possible that someday I’ll be in sufficient pain that I will take marijuana to help deal with it, but I’ll give up gambling for as long as I’m consuming.

The end of the article tells of the last days of the Cavendish, when voters of the then recently incorporated West Hollywood decided they didn’t want the club in their city. Previously, West Hollywood was a part of the City of Los Angeles. It was said around the club in the 70s and 80s that the mother of the DA (or was it the chief of police?) regularly played gin rummy at the Cavendish, so the club was safe from being raided. That was probably true, but I don’t know which public official, which mother, or even which jurisdiction this applied to. I was just happy that I could play there.

The Cavendish died a couple of years before I moved to Las Vegas. I was sad to see it go, although by that time it was just a time-killer for me. There were relatively few backgammon players at the end and, although I could get into a game where I was a slight favorite (I was a MUCH better player at that time than I was back in 1980 when I had to leave and go get a job), the house rake absorbed most of my edge. Still, it was a pleasant diversion one or two nights a week and I liked that.

When I got to Vegas, there was a backgammon club here. I briefly considered staying active in the backgammon scene, but I already knew I couldn’t support myself playing backgammon in Los Angeles and had heard it was tougher in Las Vegas. No thanks. I decided to stick to games I thought I could beat.

If you read the article, you’ll see a picture of a backgammon board at the top. This is a folding board, sold at toy stores with toy store dice. This is NOT what we used at the Cavendish. In a reply that I sent in response to the article, I explained what the differences are.

The picture is also missing the most important part of the game — i.e. the doubling cube. Without a doubling cube, backgammon is just a game. With a doubling cube, backgammon is a great gambling game.

I suspect my many thousands of hours at the Cavendish helped make me a better gambler today. After you’ve been through many many dozens of winning streaks and losing streaks, it’s easier to keep your balance when you’re in another one.

At the time, especially when I was losing and had to go and get a job, I thought I had “wasted” several years of my life. Today I believe I couldn’t have gotten to where I am today without going through that first. Among other things, the Cavendish introduced me to Richard Munchkin and for that I’m very grateful.

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Do You Have What it Takes?

Bonnie and I recently cruised the Mexican Riviera on NCL, courtesy of Penn National — in particular M Resort. We’ve vacationed several times on the same cruise line courtesy of Harrah’s/Caesars, but this time it was from somewhere else.

I packed a lot of M logo shirts — of which I have dozens. Perhaps two or three times per week, M offers free gifts — such as shirts or alcohol, sometimes higher-end stuff. I rarely go down to pick up these gifts. It’s ten miles away; it causes another trip which can lower my mailer; and how much do I need another T-shirt anyway? A few times a year, however, they have a “Warehouse Blowout” event on a Sunday, where they “give away” unclaimed items. Depending on your tier level, you get one, two, or three tickets for free and you can earn another four tickets for play that day. If you do “play up” for extra tickets, you also qualify for a free Sunday lunch buffet — which is a quality meal at this casino.

Once inside, you spend your tickets on whatever you like — keeping in mind that the pickings are pretty slim (leftover alcohol rarely finds its way to these events). Often neither Bonnie nor I can find stuff we can’t live without, so T-shirts and polo shirts (for which you get two shirts for one ticket) are our default. More than once I’ve brought home eight or ten shirts.

On the ship, a senior couple, “Marge” and “Ed,” recognized the shirt I was wearing and told me they lived in Henderson, which is in the greater Vegas area. They played Double Double Bonus and told me the casino they played at, Emerald Island, had the 9/6 version on a 100-coin penny machine — a level at which they were comfortable. “We’re retired, you know, the casino is close to home, and they give us free food.”

“That’s fine,” I told them. “The game is costing you a penny a hand on average, assuming you play well, offset by whatever food they give you. It sounds like low-cost entertainment.”

“What do you mean ‘play well?’” Marge asked. “It’s pretty much common sense.”

“Every hand has a mathematically correct play. Let me ask you some basic ones,” I said. “How would you play A♠ Q♥ J♣ 7♦ 4♣?” I knew the correct choice was QJ, but many DDB players hold just the ace. Occasionally some players without a clue hold AQJ.

“I’d throw them all away,” Marge announced.

Whoa! This shows a fundamental misunderstanding of how the game is played. I wasn’t sure how to tell her that without insulting her.

“No,” I told her. “That’s not close. Sorry.”

“How do you know?” she asked.

“Computer programs tell you how to play every hand. Over time I’ve learned correct plays,” I told her.

“I’ve never heard of that,” Ed said.

“Do you guys own a PC?” I asked. They did. My computer, with Video Poker for Winners installed, was in my cabin. I was willing to spend a few minutes showing them — but if they hadn’t owned a computer there was no hope that they’d remember enough hints to make a difference.

When we got to my cabin, I let the computer deal hands just to see where they were. I had it set on “Advanced” so the hands were tougher than average. I didn’t do this to be mean — it’s just that they are more interesting. Having the computer ask them if they know how to play Q♥ Q♣ 7♦ 7♠ 7♥ is a waste of their time and mine.

One hand was K♠ Q♥ J♣ 9♣ 7♣. This is not a beginner level hand. Not all players would correctly play KQJ9. Some would hold KQJ and other hold J97. But not Ed and Marge.

“I’d hold king jack,” Ed told me. “Holding queens is always unlucky.”

“And I’d throw them all away,” Marge chimed in.

These were both awful decisions

Next was K♦T♦7♦ 6♠ 3♥. Ed held the KT and Marge held the K. Both wrong, but at least reasonable. They didn’t come close on three of the next five hands we tried.

There are some people who just aren’t smart enough to play intelligent video poker. I concluded I was talking to two of them. I didn’t suggest they buy the Winner’s Guide for the game because I think it would have been incomprehensibly difficult for them.

I did suggest they get the software. I told them that if they practiced a couple of hours a week before they played, and attempted to play like the computer recommended, they would save more than a thousand dollars a year.

Marge was doubtful. “I’ve seen people use strategy cards, including some with your name on them,” she told me. “They don’t do any better than anybody else.”

I asked Marge if she knew for sure how well she and Ed were doing gambling-wise this year. She didn’t. “Keeping records is too much like work. We’re retired, you know.”

I wanted to ask her how she could possibly know that somebody else was doing better or worse than she was if she didn’t even know how well she was doing? Surely, she had no strong knowledge of how the other person was doing either.

But I didn’t. I did tell them that strategy cards worked well if you practiced with them and used them regularly.

I also told her that I’d be teaching beginner DDB at the South Point, probably in January. I invited them and promised it would help them a lot. Although the DDB class is for beginners, they would probably still find it too difficult.

They left with a “we’ll think about it.” (I know what that means! It means I should assume 10-1 odds against them showing up for class.)

Playing video poker intelligently isn’t for everybody. It takes a certain level of the right kind of intelligence. Not everybody has a chance to succeed.

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Legal Musings: “Making a Bet After the Outcome is Known”

With all the casino cheating going on these days (see my previous two-part post), casinos have stepped up their game. Not only do they cheat you by not paying when you win, but they strengthen the move by enlisting the local district attorney to extort you. The way it works is that the casino doesn’t pay. Simultaneously, they get the DA to intimidate the players by filing charges relating to the game, or threatening to file charges. A law-abiding AP is terrified by criminal charges, so it’s a no-brainer to accept the implicit deal — virtually always available — to have the DA drop the charges, and let the casino keep the money. Continue reading Legal Musings: “Making a Bet After the Outcome is Known”

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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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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

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You Have to Work it Out Yourself

I get dozens of video poker emails a month from people I’ve never met. Often the emails are similar to the following:

“I play Double Double Bonus. From a hand like KK773, I hold the kings and a friend tells me to hold two pair. Which is right?”

I typically answer that it’s correct to hold two pair — and the answer would be easy to obtain using video poker software or by consulting a strategy card or Winner’s Guide. If they wish to get better at video poker, they need to be able to check these things out themselves. Continue reading You Have to Work it Out Yourself

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Is it Guaranteed?

I recently published an article on quitting when you’re ahead which may be found here. The article referred to a particular $100,000 royal flush I hit at Dotty’s and why circumstances at that establishment led me to quit gambling there for a few months after the jackpot. Some of the follow-up comments about the article were, to me, very strange and irrelevant. I wouldn’t call them stupid questions. I would call the questioners uninformed. Continue reading Is it Guaranteed?