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I was thinking about this topic: Quantifying the amount of luck required to win a tournament And I wondered if there is a way to quantify the relation between skill and final place.

It's seems hard to me to find a way to quantify skill, and how skill influence chips count/win rate/classement.

My idea is to eliminate the influence of skill in chips count/win rate/classement. The model where everyone has the same starting stack and different skill won't give anything. So why not consider a model where everyone has the same skill but different starting stack ?

As skill is not quantifiable, the relation between skill in the first model and stack in the second one is difficult to establish. But maybe we can just make supposition about the distribution of skill/stack.

Can we assume skill is a gaussian distributed variable ? (I don't think so) Can we assume starting stack in the second model would be proportionnal to skill in the first one ? (I don't think so, because of the dynamic of the game). This would lead to a gaussian distributed starting stack in the second model.

Not bothering with the 2 precedent no, can we assume a gaussian distributed starting stack ?

Concerning the simulation, if everyone has the same skill can we assume the gain/loss on each hand to be gaussian ?

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Actually, if you ask anyone who knows poker, (s)he'll tell you that poker is a game of skill. Yes, it can be quite hard to quantify, but it's the most important factor to consider if you're wondering who's going to win in a poker game... –  Radu Murzea Apr 11 '13 at 17:26
    
I am not trying to ignore skill, i am trying to build an equivalent model in terms of starting stack... –  lmorin Apr 12 '13 at 8:55
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2 Answers

Am I misunderstanding your question? If we are to assume that all players in a tournament have the same skill level, then the probability at a given time of a player winning the tournmanet is equal to the number of chips he has over the total number of chips in play, at that time. So varying the stacks simply would increase/decrease the liklihood of winning for each player according to that formula. I don't know if we really learn anything from that.

I like your play on words for this question title, but I believe that quantifying the amount of skill required to win a tournament and the amount of luck required to win a tournament are independent and unrelated calculations. I think quantifying skill is the easier of the two, because over (a long) time if you consistently place higher than the expected amount, then you are better than average skillwise. The further away from the expected number, the higher your skill level.

It's more difficult to quantify luck because you can't use your place in the tournment to gauge this. You'd have to track every hand to know how lucky you got.

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No, you can't replace a player's skill level with a variable stack of chips; simply because even if all players have equal skill, they will certainly play their sized stack appropriately (small stack playing conservative, cheap leader aggressive, etc.). Similarly, you cannot turn the "luck" factor into a chip amount either.

In my opinion, the most logical way of calculating it would be a simpler equation regarding the basics:

Player Skill (better players generally finish above worse players)

Player Focus (the "in the zone" feeling while playing)

Luck (hitting the river, etc)

If you have a poker game with hand selected players that all have about equal skill, then poker really turns from a game of skill into a game of luck. Fishies keep the sharks satisfied, sharks don't want to keep passing their money back and forth on the table against other sharks.

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Welcome to the site. A good first answer IMHO. An upvote. –  Tom Au Apr 22 '13 at 23:11
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