Poker, politics, philosophy

when EV is not EV

30th-Jun-2006 07:54 am

Jacqueline has an interesting claim (written by someone else) that your EV in video poker goes down if you only play a few hands.

Medium-Risk Strategy - 25c 10-play NSUD at Caesars Palace
To achieve $18,000 coin-in, you play 1,440 deals of 10 hands each, or 14,400 total hands. Given that a royal flush occurs, on average, every 43,456 hands in NSUD, chances are you won't hit a royal flush. Since the royal flush accounts for 1.84% of the total game return in NSUD, you're really playing a 97.9% game, not a 99.7% game.

This doesn't make any sense at all. The EV of the bet doesn't change just because you are likely to miss -- EV takes likelihood of occurences into account already.

In the high risk case, it's true that you are more likely to end up with a loss than in the other cases -- but in return, if you do hit one of the unlikely but good hands, you'll have a bigger win than you would expect. Those two probabilities, the more likely loss versus the bigger win, exactly balance out, so that you end up at the same EV. (Isn't math great that way?)

Here's an example. We roll a 6-sided die. On a 6 I pay you $10, and on anything else you pay me $1. Each roll of the die is worth $5 to you.

CLCJim seems to be claiming that if we only played this game once, that since the 6 is unlikely we can discount it, so your EV is actually -$1. But this is obviously very silly: you would want to play this game even if I were only willing to play it once, even though you will probably lose. This is because if you win you win $10, which is much higher than your expectation of $5.

Video poker is just like that. You may not hit the royal if you don't play for very long, but in return when you do hit it you don't have all those losses that piled up first, so you end up way ahead.

As a sidenote, it's amazing to me how many "professional gamblers" don't understand the very basic statistics and math behind their job.

Tags:poker

Comments

30th-Jun-2006 03:09 pm (UTC)

jacqueline1776

I don't think he's claiming that. EV is EV is EV. I read his post as pointing out that in the short term variance is going to affect your results more than long term EV, so don't be surprised if you lose a lot of money, and that he included some specific examples of what sort of results you can expect if you don't make those big payoff hands.

30th-Jun-2006 03:19 pm (UTC)

dmorr

I read "what sort of results you can expect" as being roughly synonymous with "expectation".

Also, "you're really playing a 97.9% game, not a 99.7% game" is a pretty clear statement that is just flat out wrong. Regardless of short term variance, if you're playing a 99.7% game you're playing a 99.7% game.

It's possible that he is really talking about the most likely outcome (which I think is your reading), but he keeps saying "expected loss" which has an actual meaning, and if he's using it to mean what it really does mean, then he is incorrect.

If he really does mean "most likely outcome", then he probably should have said that instead of using terms that mean something else like "expected loss." I suspect, though, that he really does mean expected loss and just doesn't understand why your expected loss per hand doesn't change with the number of hands you play.

30th-Jun-2006 03:38 pm (UTC)

jacqueline1776

Heh, maybe I read him too generously then. I just assume that everyone who is knowledgeable enough to be reading and posting in those sorts of forums understands that EV is EV is EV and thus I read everything he wrote through that filter.

30th-Jun-2006 04:22 pm (UTC)

dmorr

Heh, sadly you'd be surprised.

30th-Jun-2006 06:29 pm (UTC)

evwhore

it's amazing to me how many "professional gamblers" don't understand the very basic statistics and math behind their job

I once got into a protracted argument on one of the VP mailing lists with someone who should have known better, explaining why "royal pays double with game ticket 3 hours after Wranglers games" was a good promotion for VP players. His argument was along the lines of "You really think you can just order up a royal and have it happen during a 3 hour period?"

30th-Jun-2006 08:34 pm (UTC)

fich

Many people confuse the average result with the distribution of results.

High carding for fun and profit, anyone?

30th-Jun-2006 09:28 pm (UTC)

dmorr

Ooh, good idea.

Maybe I should go ask them about the monty hall problem, and then offer to actually play the game against them.

1st-Jul-2006 10:31 am (UTC)

michaelsullivan

If the payoff for an extremely rare event is very large relative to bankroll (i.e. much more than the current bankroll), then assuming it won't happen often gives you a good zero order approximation of dollar equivalent expected log utility.

Expected log utility is suprisingly good at explaining some "irrational" behaviors, and it's a good idea to do a quickie analysis when somebody's behavior arond rare huge payoffs looks way too risk averse. I've determined, for instance, that playing in the WSOP main event is probably a kelly mistake for anyone with a moderate bankroll (less than a few million) and less than a full buy-in of EV. Obviously there are other factors that may make it worth playing, but I'm not sure most poker players realize that their expected log utility in huge big buy-in tourneys looks pretty tiny compared to their dollar EV.

Note, I agree in this case that guy is using the mathematical language, so it's not completely excusable that he doesn't know what he's talking about, even though I could read it like Jacqueline did if I wanted to be charitable.

4th-Jul-2006 09:51 am (UTC) - EEV: Expected expected value?

Anonymous

The funny part is that I doubt the people playing the game would care about the difference between 97.9% and 99.7%... What he seems to be saying is that if you play the lottery, you're playing a 0% game. If people don't care about shaving off 100% from the EEV, I doubt that 1.8% is going to matter much in their decision.

5th-Jul-2006 06:15 am (UTC)

sabyl

As a sidenote, it's amazing to me how many "professional gamblers" don't understand the very basic statistics and math behind their job.

David, I have been surprised by this too. And I still could learn a lot more about statistics, so I am always amazed when I run into pro gamblers who have a lesser understanding than I do.

To achieve $18,000 coin-in, you play 1,440 deals of 10 hands each, or 14,400 total hands. Given that a royal flush occurs, on average, every 43,456 hands in NSUD, chances are you won't hit a royal flush. Since the royal flush accounts for 1.84% of the total game return in NSUD, you're really playing a 97.9% game, not a 99.7% game.

This isn't a function of EV. I sometimes like to look at the EV of a VP game without the royal and other lare hits (deuces for example in NSUD) to get an idea of how much I might lose in between those hits. But that is more to help me decide how much risk I am willing to take in relation to my bankroll. But your chance of hitting a royal is the same on hand #1, as on hand #1000, as on hand # 45000. Right now I have gone ~160k hands without a single line royal (I play mostly single line), but I would have expected to receive about 4 by now. Now it doesn't mean I more likely to hit tomorrow because I am due. Everything is independent. In contrast, Steve and I hit two royals within an hour of each other twice in the same day back in January. Here we did not play enough hands to expect one royal by the author's calculation, but we it 4. I think people tend to forget that in video poker, each hand is truly independent of the others. The machine has no idea how many hands you are going to play and your EV is the same percentage whether you play one hand or 1 million hands. Your variance is higher with one hand, but the EV is the same.

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