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?“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.
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.
