Luck Variance Factor

[saw7988]

This question is similar to a recent post about which games require the most skill, but I wanted to gear it more specifically.

The luck/skill ratio is an important factor for me in choosing my games. Who wants to win at a game that's all luck? No one brags about being good at War, do they? Obviously poker is not as luck-based as War, and many people also say that it's 100% skill in the long run.

I know some scenarios and some games have more luck variance to them than others though. For example, I've read that tournaments have more luck than cash games for a few reasons: you get 1 bad beat and you're done, and also then end of tournaments require a good amount of luck; there's so many all-ins and coin flip situations. I've also read that omaha had less luck variance than hold 'em.

If anyone has any more specifics, opinions, or corrections about them, I'd like to know.

[MikeBandy]

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This question is similar to a recent post about which games require the most skill,

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some scenarios and some games have more luck variance to them than others

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This has also been previously discussed, but I hope 2+2ers won’t mind revisiting the topic. I for one will be interested in what they have to say.

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I've also read that omaha had less luck variance than hold 'em.

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On the one hand, I know of a small Native-American-owned casino. This one’s in the boondocks (where I live). Anyway, they stopped spreading Omaha in 2002, because many players complained that the same few people consistently won. This wasn’t true in hold ‘em. This tells me that, at least in the low limits, there are numerous bad players in Omaha, and there’s money to be won.

On the other hand, Mason Malmuth has made some comments to the effect that there’s more variance in Omaha than in hold ‘em (because there are so many opportunities to draw out in Omaha.) However, I believe he was referring to middle and high limits, where there would be few bad players. Those statements were made a few years ago, and I don’t know whether his opinion has changed (or perhaps the situation has changed).

[DrVanNostrin]

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...many people also say that it's 100% skill in the long run.

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It is. A pretty basic rule of statistics:

L = k/(n^1/2)

-where L is the amount of the degree of accuracy of the results (or in the case of poker luck). If there is a lot of luck involved the accuracy of the results are low; it would be very easy for a winning player who made the correct play to lose. Example: for political polls the margin of error is determined by the sample size. If the sample size is greater there will be less error. It would be likely that a poll said the wrong canidate was ahead if the margin of error was greater.

-k is a constant. In a high varience game k would be greater. Also if one canidate was a heavy favorite in a race k would be greater than if it was close.

-n is the number of hands you play. Or in the case of a tourneys the number of tourneys you play. For a political poll n would be the number of people surveyed.

Long story short, as n approaches infinity L will approach zero.

[ohnonotthat]

Omaha hi-only (limit) does have a high varience - higher than limit holdem and higher than low/middle limit stud. (Hi-limit stud typically has a very large ante and features wild swings).

Omaha/8 does not. This is a very stabile game against weak opposition; against clueless opposition the swings are tiny and few in number.

I'm not sure whether P-L Omaha or O/8 are more or less stabile than the limit versions of these games; standard wisdom says there should be fewer swings - P-L & N-L holdem are relatively tame games - but I've played very little big bet Omaha so it's a little hard for me to say.

Use the "search" feature to find more on this topic.

[MikeBandy]

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...many people also say that it's 100% skill in the long run.

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It is. A pretty basic rule of statistics:

L = k/(n^1/2)

<snip>

Long story short, as n approaches infinity L will approach zero.

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It appears to me that the statement, “As n approaches infinity L will approach zero” is correct. However, it’d be true whether you’re talking about poker or war (the card game). Presumably, poker and war would have different values of k, though.

[DrVanNostrin]

Good point. I'm not sure how to justify it but clearly k for war would be such that L is always infinity. That would make 'k' infinity as well. I'm confident with this answer, but not as clear on the justification. If anyone could offer a good explaination or correction I'd be interested.

[MiloDanglers]

i'm guessing that formula doesnt work on games of pure chance i.e. flipping a coin.

[Kenneth Sloan]

Even for War - as n goes to infinity L goes to zero. It's just that the EV for War is 0.

[Jatal]

I believe the only real luck factor in poker are how the cards are dealt. The rest is skill only.

You can however make the luck factor smaller or bigger.

If you choose a game where there are less % of showdowns, then there should be less of a luck factor since you don't always have to rely on your cards. For example Omaha "should" induce more showdowns than holdem since more cards involved in the game.

Another way to reduce the luck factor is to choose a game where you can play many hands, or rather play to win money many times. For example cash games where you win/lose money each hand.

In tournaments you have to play more hands to get to the money i.e. it takes longer. Also if you get to the money and want to place better so you win more money you don't have that many hands to make your moves on. You can't wait too long to get good hands since the blinds increase and you are out when you lose your stack. If you choose the right tournaments the reward are good though.

Don't confuse luck factor with earning money though. The game with the smallest luck factor does not necessarily mean best ROI. For example in higher stakes hold'em (cash games) there "should" be less of a luck factor since fewer players go to showdown but you are also most likely playing against more skillful players so it's probably harder to win money.


I don't think you should choose your game based on the luck factor. I think it's more important to choose based on bankroll, ROI and skill factor (and many other things). Regardless of which game you play you have to have knowlage about the probabilitys of how the cards are dealt (i.e have knowlage about the luck factor) so you know how much you can bet, call and so on. The money are made when you play against players who are less skillful than you are.

[Jimbo]

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Obviously poker is not as luck-based as War, and many people also say that it's 100% skill in the long run.


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In theory I would agree but in practice i don't believe you will live long enough to find the proverbial "long run".