Listeners to our podcast know I typically end with the line, “Go out and hit a royal flush!” Colin Jones, the owner of blackjackapprenticeship.com, one of the sponsors of our podcast, has numerous podcasts of his own in which he typically ends with, “Keep generating EV!”
Not that I’m planning on changing, but I like Colin’s ending better than mine! It’s far closer to what I believe intelligent gamblers should do.
Continue reading What’s in a Phrase?I received a postcard from the M where they are trying to get new players. The promo was:
The slot club is 0.3% (slightly more, actually, because they give you $3 for $999 coin-in rather than $3 for $1,000 coin-in). 50,000 points is worth $150 of free play — which is way more than the house’s expected win if you’re playing the best machines.
The loosest game is $2 9/6 Jacks or Better. There are two such machines — newly installed — in the high limit room. There is no choice as to the denomination and no telling how long they’ll last. 10x points (which is worth 3%) on top of a video poker game returning 99.54% seemed possibly like a mistake, except that it was limited to $150 max which might be a reasonable cost for a new player.
I don’t actually know if this was a mistake or not. I hooked up with a player friend, “Kevin,” who lives near Aliante — which makes the M geographically undesirable for him. Which is why he didn’t already have a card. I know some non-players for whom I technically could have played the free play, but that’s strongly against the rules there and I’m well known. No thanks. If I had to use a non-player, I would have let them play and talked them through their $105 in free play — which we would probably have played on 25¢ 8/5 Aces Bonus. If they were a non-player, any possible W2G could have been a problem for them.
As it happened, June 1 was a normal free-play pick-up day for me (they have 6 to 7 such days per month). Kevin and I agreed to go in and play the promotion on the first day it was active.
We were certainly not going to ask for clarification as to whether the 10x points included video poker or not. The booth personnel (who are also the cashiers) would likely have said, “I don’t know. Let me make a phone call.” If they did that, it’s possible that signs would have been posted saying “slots only.” If we could arrange it, we didn’t want such signs posted until after we played.
Our deal was, we would play the promotion and also play an additional 850 points which entitled us to a “free” lunch buffet. Other than the amount of my free play, we split everything based on my $850 worth of play and his $5,850. Whether this split was overly generous or not didn’t concern me. Kevin is a friend. And enjoying lunch together was part of the attraction of the “date.”
I often play for a buffet on my free -play pickup days there. There have been incidents where players who only picked up free-play without any additional play were punished for this. As a known professional player, I am hyper-sensitive about creating situations where it would be easy for them to justify restricting me.
The $205 in free play we got between the two of us more than covered the expected loss of playing $5,850 for him and $850 for me. If we got the additional $150, great, but it was still a decent play if we didn’t. (And yes, we could have lost, but the decision beforehand is made based on EV, because you don’t know what your actual result is going to be.)
I had him play $5,850 rather than just $5,000 because the M usually doesn’t allow you to “double dip.” If there’s a gift of the day you can get for 800 points and you also want the free buffet, it takes 1,650 to earn both. We only had one shot at this and if they decided to give us 10x points on only 4,150 points (which would be 5,000-850), that would cost us $28. No thanks.
We didn’t split the $150 on the day we played because I wasn’t certain whether or not we were going to get it. It could be that they “intended” it to say “slots only,” but they didn’t put that in writing. How it would be enforced down the road was an open question.
I hadn’t decided how aggressively to pursue the 10x points if they denied that it applied to video poker. It was “only” $150 (split between two of us) and you need to pick your battles. In a somewhat similar situation at the Silverton I wrote about a few months ago, we were talking about an $8,000 difference between getting the multiple points or not. I’m willing to fight a lot harder for $8,000 than I am for half of $150.
Eight days after we played, I received an email saying that 50,000 points had been placed on my card, so I sent my friend an email saying that I owed him $75 next time we saw each other.
I never had to decide how hard to argue for this. It’s possible that future players will be told “slots only” when they sign up. I don’t know. But this was a case of taking advantage of the situation before they made changes to it. If they keep the promotion “as is,” then whether we did it early or not doesn’t matter. If they restrict it later to slots only, it matters $150 worth. For me it was a no brainer to do it as early as possible.
One of the very first lessons taught by virtually all video poker teachers, including me, involves the game Jacks or Better. We explain how the game pays 25-for-1 for all 4-of-a-kinds, 2-for-1 for two pair, and the difference between the good version and the bad version depends on how much you get for a full house and a flush.
The best reasonably common version is 9/6, returning 99.54%. The game in second place is 9-5, 98.45% requiring a similar but not identical strategy.
If you don’t know what I mean by 9/6 and 9/5, compare the two pictures at the bottom of this page. The one on the top is 9/6 and the one on the bottom is 9/5. The key numbers used in naming the games are shown in red.
Under normal circumstances, because of the approximately 1.1% difference in the returns, any player who played 9/5 when 9/6 was available is a player without a clue as to the winning process.
And, yet, for a couple of years ending a few years ago, I personally played millions of dollars of coin-in on a 9/5 game when 9/6 was available. As did many other knowledgeable players. What gives?
It had to do with “theoretical.”
Theoretical is the hold the casino expects to make from players as a whole. If a game is rated with a theoretical of 2%, it means that for every $100,000 coin-in the machine gets, on average the casino expects to hold $2,000.
The 9/6 JoB had a theoretical in this casino of approximately a half percent. For that same $100,000 coin-in, the casino expects to make $500. The “perfect” 9/6 JoB player only loses $460 for that play.
This casino had a policy that if you agreed to earn $5,000 in theoretical, they would give you $3,500 in free play as front money. If they figured the theoretical correctly, this would give them an expected profit of $1,500 on this much play to cover their expenses and profit margin. On the 9/6 JoB, this was no bargain for the player. Your expected loss was $4,460, even if you played perfectly, so while getting $3,500 back was certainly better than nothing, you were still in the hole.
For whatever reason, the 9/5 JoB game was assigned a theoretical of 4%. This meant that it took $125,000 coin-in to generate the $5,000 in theoretical. And playing that much on a 98.45% game meant that you expected to lose a little less than $2,000 on average if you played perfectly.
Losing $2,000 is no fun, of course, but the casino was giving $3,500 to ease your pain. That meant that you had a net expected profit of a little more than $1,500 each time you did it, plus your points were worth something, and there were significant other goodies as well, including a couple of free room nights. We could do this at least once a month, and sometimes twice a month. This was an inadvertent mistake by the casino. We hoped it would be several years before the casino fixed it.
Sometimes I’d lose $8,000 or so “earning” this EV, but other months I would win. Looking at individual months, you could sometimes question whether this was a good deal or not, but over time, it became clear that this was a moneymaker for the players who knew about it and exploited it.
I learned about it from someone who swore me to secrecy. I had to promise not to write about it. I honored that while that situation was still in effect. Now that it’s been over for more than a year, I believe it’s okay to shine a little light on it.
Eventually, the casino figured out that a 4% theoretical for this game was inappropriate and changed it to about 1.6%. Now it costs you almost $5,000 to earn $5,000 in theoretical, and if you get “only” $3,500 back, it’s no bargain. So, knowledgeable players don’t play that game anymore.
I used a 4% figure. Actually, it was slightly different than that and it varied slightly from machine to machine. And it could be “fixed” by the casino at any time. So after we played, we went to talk to a host and asked what our theoretical was. If it was under $5,000 we played some more. We wanted to get the theoretical high enough so that we’d keep getting the offers.
The time it came back as a theoretical of $2,000 for the normal amount of play, players knew that this particular party was over. Disappointing, but all good things end eventually. Calls went all over the player grapevine, and within a few days most of the players who played this promotion were notified.
I’m not mentioning the name of the casino where this took place. There will be many readers of this blog who know whereof I speak. Should any of them choose to comment on this article, please leave the casino name unspoken.
| Royal Flush | 250 | 500 | 750 | 1000 | 4000 |
| Straight Flush | 50 | 100 | 150 | 200 | 250 |
| 4-of-a-Kind | 25 | 50 | 75 | 100 | 125 |
| Full House | 9 | 18 | 27 | 36 | 45 |
| Flush | 6 | 12 | 18 | 24 | 30 |
| Straight | 4 | 8 | 12 | 16 | 20 |
| 3-of-a-Kind | 3 | 6 | 9 | 12 | 15 |
| Two Pair | 2 | 4 | 6 | 8 | 10 |
| Jacks or Better | 1 | 2 | 3 | 4 | 5 |
| Royal Flush | 250 | 500 | 750 | 1000 | 4000 |
| Straight Flush | 50 | 100 | 150 | 200 | 250 |
| 4-of-a-Kind | 25 | 50 | 75 | 100 | 125 |
| Full House | 9 | 18 | 27 | 36 | 45 |
| Flush | 5 | 10 | 15 | 20 | 25 |
| Straight | 4 | 8 | 12 | 16 | 20 |
| 3-of-a-Kind | 3 | 6 | 9 | 12 | 15 |
| Two Pair | 2 | 4 | 6 | 8 | 10 |
| Jacks or Better | 1 | 2 | 3 | 4 | 5 |
Mr. B, a highly successful AP who doesn’t play casino table games, said to me over lunch in a casino coffee shop, “Why don’t they fix everything? If I ran the casino, I would just make it so that no game is beatable!” I’m sure you would try, B! It’s a fair question, but the full answer goes beyond game protection.
Let’s start with the idea of complete game protection. It’s a unicorn. First of all, it’s not even an appropriate objective. Though some casinos actually do have a pathological drive to thwart all APs, that’s just biting off your nose to spite your face. The real goal is profit maximization. The most random shuffle, which would thwart many AP moves, is not as profitable as a much faster shuffle that may occasionally be beaten by a highly skilled AP. Thorough background checks on every person walking into the casino would shut down some APs, but would create a major discouragement to the thousands of degenerates who want to gamble right now! London’s style of casino management is stupid. A zero tolerance policy is not optimal.
Even if a casino wanted to stop every AP, they couldn’t. Casinos have to play the hand they’ve been dealt. Their employee pool consists of people who are less educated and under-incentivized relative to the top APs who are trying to beat the games. Think about it. Casino employees universally believe that the idiot at third base is killing the table by taking the dealer’s bust card. These are people who believe that simply by virtue of a big bankroll and proper money management, a player can beat the games. Ackkk!
If a new casino opens up in Pennsylvania, there are no local employees who have the experience of the long-time Vegas pros who are about to walk in to whack the games. These employees will not know every AP method to beat the games, and it’s not their job to know. Even a Table Games Manager is not a game-protection specialist. A Table Games Manager has to do many things, while APs specialize. There are always new casinos, new employees, new games, new equipment, and new circumstances that make it impossible for a casino to anticipate and thwart every new method of beating a game.
My crew recently found a new game in a casino. The game gave the basic-strategy player an edge of 10.6%, and this was the stingier incarnation (the first gave an edge over 15%). Since the game was new and unique, the casino had no one to turn to for answers or to check the inventor’s math, and the game died a horrible death. Next!
But the real reason that it is difficult to thwart all AP activity is not related to game protection, but rather game design. Suppose that the casinos actually want to provide some entertainment value while they suck every penny from a gambler’s life savings (I said “suppose”!) In that case, they probably want the game to involve some playing decisions. (Obviously, the success of three-reel slots and baccarat shows that playing decisions are not necessarily critical to provide entertainment value. Addictive drugs are entertaining.)
Furthermore, they probably want the game to give the players an edge in the ballpark of -4% (fast games, such as blackjack and Casino War, can make money for the casino even with edges in the -0.5% to -2.5% range). Here’s the key question: Given that there are playing decisions to make within the game, what is the gap between the typical gambler’s edge and the expert player’s edge?
If the game involves tricky consequential decisions, then the expert player’s edge might be 20% higher than the gambler’s edge. But if the casino wants the masses to be playing at -4%, then it means the expert is now at +16%. If we were to make the payouts stingier, to put an expert at breakeven, then the gambler would be at -20%. At that level, the gambler probably gets gutted too quickly, and the game won’t be popular. The zero-tolerance policy to thwart the expert makes the game unpalatable to the thousands of regular gamblers.
You’ve got to give the fish some play for their money. Fantasy sports websites started to see this problem. The pros were gutting the fish so efficiently that the fish lost interest, and the regulators started questioning the equity of it all.
So the key in game design is to offer a set of decisions where the range from the smart to the stupid is not too extreme, or to offer decisions that provide entertainment, but which are completely inconsequential in the game, and which are meaningless in terms of EV. For instance, in Rock, Paper, Scissors, the player has a choice, but a meaningless one if measured by EV. Likewise, choosing Banker vs. Player in baccarat is a relatively inconsequential decision, but one which receives more human scrutiny each day than the debate over climate change.
This column is written primarily for beginners and low-intermediate players. Readers more advanced than that should give it a once-over as well. There’s a chart here you’ve likely never seen before.
You’re playing Double Double Bonus, receiving 45 for a full house. How much you get for the flush is irrelevant to this discussion. If you get only 40 for the full house in the game you typically play, you’re permitting yourself to play such a bad game that no amount of advice from me is going to help you be a winning player.
You’re dealt K♠ K♥ 6♣ 6♦ 5♠. You’re debating holding just the kings or holding the two pair. You’ve read from people like me that holding two pair is correct by a mile, but it’s counterintuitive to you. After all, you get the same “even money” for a pair of kings as you do for two pair and if you hold the kings you might get lucky and receive four kings. So why not go for it?
Let’s talk dollars and sense. Assume you’re playing dollar single line DDB, five coins at a time. Holding two pair, you have the following possibilities — and the value of those possibilities.
The frequency numbers from the chart may be found in Video Poker for Winners or other quality software. The dollar figures aren’t generally seen, although you do get the sum of them, shown in green. And notice I didn’t include columns for straights, flushes, straight flushes, or royal flushes simply because you can’t get one of those when you start out by holding a pair or two pair.
Let’s take the line corresponding to KK66. You have 47 possible draws, which is the normal number when you’re drawing one card from a 52-card pack and you’ve already looked at a five-card deal. You’ll end up with two pair 43 times and a full house four times. You can probably do this much in your head if you start with figuring how many full houses you can get. After all, the only time you’re going to get a full house is when you draw one of the two remaining kings or one of the two remaining sixes. In all other cases, you’re going to end up with the same two pair with which you started.
What’s new in this chart, shown in blue, is how much each of these hands is worth. The two-pair final hand contributes $4.57 to your total EV and the full house adds $3.83. Rather than give a definition for how I figured out those numbers, I’ll show you the calculations: $3.83 = (4 * $45 / 47). $4.57 = (43 * $5 / 47). The $45 and $5 in the formulas are the amounts you receive from a full house and two pair respectively in this game.
In the line corresponding to holding the kings, there are now 16,215 possible draws. For most of us, including me, there are way too many possibilities to figure this stuff out in our heads, or even with paper and pencil, with a high degree of confidence. Fortunately, software to do this for us is very fast, accurate, and inexpensive.
The number that really pops out at me on this line is the 69¢ that the chance at a 4-of-a-kind is worth. Yes, the quad is worth $250 when you get it, and that’s the number beginning players focus on, but you only get it a little less than one chance in 360. Multiply it out and it comes to 69¢.
Also, note that the chance for a full house is 47¢ when you hold a pair, compared to the $3.83 it’s worth when you hold two pair.
It’s easy to think of possibilities — like you COULD get a four-of-a-kind. It’s much harder to think of probabilities — which means how often does it happen percentage-wise. It’s even harder to multiply out the VALUE of the hands which means the probability multiplied by the pay schedule.
Players sometimes confuse this hand with A♠ A♥ 6♣ 6♦ 5♠. To put this into the above chart we need to add another column for four aces with a kicker. If we do that, we’ll find all the numbers in the chart stay the same, except the value of the four aces without a kicker is worth $1.63 and the value of four aces with a kicker is worth $1.48. Adding those together gives us $3.11 — compared to the 69¢ the kings were worth. This makes holding the aces worth more than holding two pair, aces up.
The strategy for this part of the game is AA > Two Pair > KK, QQ, JJ. If you can read the strategy and just follow it no-questions-asked, then you don’t need columns like this one. If you ever wonder “why,” and haven’t figured out the answer to this particular question, maybe this column will be useful to you.
As for me, I’m always wondering “why?” Once I figure that out (which I normally can do in video poker — not so much in certain other parts of life), it makes it much easier to keep strategies memorized.
“EV” stands for expected value, which is a type of weighted average. The exact definition I’ll leave to the probability and statistics textbooks. As cut and dried as the definition is in the math books, there’s plenty of wiggle room in the way it’s applied to video poker.
Before we discuss this wiggle room, let’s talk about how EV is most properly used. EV gives you a “best guess” of how a situation will turn out — on average — if you play it out zillions of times. It’s not a guarantee at all of how things will turn out this time. If you’re flipping a fair coin 100 times, the EV is for 50 heads to show up. But sometimes only 40 heads will appear, and equally often 60. In actuality, ending up with exactly 50 heads out of 100 trials is an underdog to happen. If you’re betting on heads, you may well be upset that the actual result this time didn’t match up with the EV.
The definition of EV is about “how many times something happens.” In video poker, we often turn this into a percentage. For example, 9/6 Jacks or Better has a well-known probability of returning 99.544% when played perfectly. That means if we play $100,000 through a 9/6 JoB machine, our average ending balance will be $99,544, meaning the casino keeps $456 from our play. This will be true whether we play for nickels, quarters, dollars, or larger stakes. This will be true whether we are playing single line, Triple Play . . . or Hundred Play.
It is common among video poker players, but not universal, to add the return on the game with the slot club return and call the result EV. That is, if you’re playing 9/6 JoB at the South Point on double point days, the EV is 99.544% +2(.300%) = 100.144%. Adding the slot club return is reasonably certain, as almost always you know what it’s going to be before you play.
Adding mailers is a bit iffier, if that’s a word. If you know you are going to get mailers worth $80 for $40,000 coin-in, you can go ahead and add another 0.20% to the EV. But we are rarely that certain — or rather, the ones who are certain are frequently mistaken. Slot clubs change their parameters for mailers all the time, and usually these parameters are unpublished. You can get a feel for what the rules are if you talk to enough players, but it’s normally the case that players don’t keep good enough records to be useful.
Someone can accurately tell you that their mailer is $25 a week. But if you want to know how much they won or lost each month over the last six months, including how much was played during promotions and on which machines, that information is tougher to come by. And, at some casinos, how many times did the player come into the casino? And what “discretionary” comps were issued to this player? Some or all of this information is used by at least some casinos to determine your mailer. And most casinos don’t publish the formula they use.
Still other players (including me) add an estimate for the value of the current promotion into the EV calculation. I wouldn’t be playing at all at any casinos if it wasn’t for their promotions. (Yes, I could play 100% games for low stakes in Las Vegas for less than $10 per hour. And there’s money to be made playing video poker progressives. If that’s your thing, welcome to it. For me, no thanks.)
I was playing $1 9/6 JoB Spin Poker on a recent double point day at the South Point, when there was another promotion going on as well. There are higher-EV games there, but only for lower stakes. With good enough promotions, playing $2 single line ($10 per hand) 99.728% NSU Deuces Wild sometimes just isn’t as good as the 99.544% ($45 per hand) game.
Another player was playing $1 9/5 White Hot Aces on the same Spin Poker machine. I asked him why he chose that game instead of JoB and he responded “Higher EV.” Really? Not in my book.
The WHA game returns 99.572% which is certainly a tad higher than the 99.544% you get from JoB. But every time you get dealt a quad, the Jacks or Better game returns “only” $1,125 which, importantly, is less than W2G range. Getting two or more quad 2s, 3s, or 4s, or even one set of aces, generates additional W2Gs.
For professional players who get LOTS of W2Gs, these are not particularly terrible things. We have learned how to “write off” a high percentage of them. Still, at this casino, on a double point day, it takes more than five minutes per W2G for a slot attendant to arrive and reset the machine. On a promotion that is worth, say, $36 an hour, not playing for five minutes costs you $3. Are you planning on tipping when you get paid for your W2G? If you typically tip $5, that’s $8 out of every W2G. That more than eliminates the difference in EV from the game itself.
You pretty much get the same number of royals in the two games, but you get more straight flushes in WHA. Why? Two reasons. First of all, you get paid $400 per straight flush rather than $250 so it only takes three to get a W2G rather than five. Also, the strategy calls for you to go for straight flushes more in WHA. For example, from a hand like 3♠ 4♥ 5♥ 6♥ 7♥, you hold five cards in JoB and only four in WHA. When you do catch a straight flush on the draw, usually you get three of them — and hence a W2G.
Instead of EV, I use a form of “expected dollars per hour,” which includes how many hands per hour I can play and at what stakes. Are my calculations different from those of other players? Maybe. Part of the calculation includes an estimate for the current promotion, and personal estimates differ. But for figuring out whether I should be playing at Casino A or B, I find the calculation very useful.
Using stereotypes to say “women are this way and men are that way” in today’s political climate is a formula guaranteed to generate multiple negative comments. Rightfully so. There is very little interesting where you can say that every female (or every male) is a certain way. There are always exceptions.
With that said, there are also tendencies that appear to be there. A tendency doesn’t mean a certainty. For example, I can correctly say that in general men tend to be taller than women. And that’s true on average — but we recognize there are some taller and shorter examples of each sex.
What brings this up is something that happened to a friend of mine, Reuben, who is also a competent video poker professional. He was playing at a casino whose name he doesn’t want me to publish, and playing a game that is still around. He said that if I wrote about it, I could call it $5 Multi Strike — just to give it a name — but in fact it was a different game.
He was playing two machines at a time — which happened to be the only two $5 Multi Strike machines in the casino. He believed that the game plus the slot club plus whatever promotions were going on gave him enough of an advantage to justify him being there.
He rarely played two machines at a time. It often announces “I am a pro” to a casino which tends to reduce your longevity there. But in this particular casino, he had run unlucky and to date was a big loser — even though he had always played games with positive EV. Since he figured this casino wouldn’t make him as a pro, he could play more aggressively than he otherwise would.
After playing a while, a woman he had never seen before came up and asked if these were the only two high-denom Multi Strike machines in the casino. Instead of his usual “I don’t know,” which is generally the smart answer in cases like this, he told her that yes, he believed they were.
The woman then asked, “How long do you intend to play?” Reuben said he hadn’t really decided yet. It depended on how much he lost and how quickly. Which was nonsense, of course. Reuben was planning on playing until midnight, which was when the promotion ended. She looked at the machines longingly for a while and then left.
Reuben speculated that she was waiting for him to offer her a machine. After all, in Reuben’s experience, women tend to be more empathic and less direct in their requests. Had it been his wife instead of a stranger, his wife would have expected him to realize that she wanted a machine — and hence, given one to her because it was the polite thing to do.
Still, keeping both machines was the desired goal and if this lady wanted a machine, she was, at a minimum, going to have to explicitly ask for one. Whether Reuben would have said yes or no wasn’t a certainty. He would have made a decision when necessary — but not before. There are often extenuating circumstances one way or the other.
Reuben considered the possibility that the woman would go to the slot shift boss and complain that she couldn’t get a machine and one guy was hogging both of them. He didn’t want that to happen, although it was largely out of his control. He preferred to be a “low maintenance” player. It doesn’t take too many incidents for some casino employees to conclude this player is “always” causing trouble. If he developed that unwanted reputation, close calls down the road (such as whether to pay him in a sticky button situation — or whether to allow him to remain even after he starts winning) might not go his way.
If the slot shift boss came over and asked for a machine for the woman, Reuben’s answer would have been an immediate, “Of course.” He likely would have added, “All she needed to do was to ask me, but she never did.” The last four words were absolutely true. The first nine — maybe. But the slot shift boss couldn’t know that.
It’s possible the woman believed she shouldn’t have to ask. She possibly believed even a guy should have been able to understand she wanted a machine. It could seem to her to be common courtesy that should prompt Reuben to give up a machine. That definitely was Reuben’s best guess as to what his wife would believe were she the one wanting a machine.
One thing that Reuben felt was a bit of a safety cushion this time was that the slot shift boss was a man. Right or wrong, he believed a male shift boss would be more sympathetic to “she never actually asked” than a woman shift boss would. Reuben’s actions would likely have been the same with any boss, but he would expect the aftermath to be gentler on him when the boss was a male.
Could Reuben’s stereotypes and assumptions based on them have been way off? Of course. No player or boss acts exactly like you expect him or her to.
Is he smart to use such stereotypes and assumptions in his decisions? Absolutely. You are frequently called on to make decisions based on incomplete information, and sometimes stereotypes give you some extra information that is useful.
Would Reuben be called prejudiced or sexist if he verbalized his thought processes? That too. You can’t please everybody, and people will use whatever ammunition against you that you give them. Often, it’s better to make your decisions quietly and not discuss why you made them.
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.
I planned on playing for six hours at the Palms from shortly after midnight until about 6:00 a.m. on the early morning of Wednesday, April 27. It was a double point day— I also earned points for gift cards, a small amount of value for the weekly drawing, plus my play kept the mailers and other benefits coming. There were only two machines that I wanted to play, both containing $1 Ten Play Deuces Wild Ultimate X, and I expected other players to want the same machines on that day. So I went at hours when other players preferred to sleep. And this time, at least, one machine was available. Continue reading Identifying a Pattern
A handful of times in my career, a boss has sat down at our table while my BP and I were playing a target game. Many players have never experienced that scenario, and completely panic when it happens for the first time. They’re not even sure what to make of it, but I’ll tell you. Continue reading The Boss Just Sat at Our Table with Game On: What Now?
