Where is the chance/skill cusp for Hold'em?

[RayBornert]

Where is the chance/skill cusp for Hold'em?

Assume for a moment that a state court here in the U.S. is hearing a case wherein you are asking the court to define their official chance/skill cusp for poker in general and more specifically Hold'em.

The context presented is one where a table of differentiated players have paid an entry fee and will compete with each other in a single table LIMIT tournament for a prize based upon performance after a given number of hands - for now you can assume that the contest is a winner-take-all proposition with zero rake for the operator. You may also assume that the blinds do not increase for the duration of the contest.

You can also assume that you're in a state that applies the predominance test which requires that the contest have at least 51% skill involved in the outcome in order to be released from the gaming regulations.

The question you're attempting to settle is the minimum number of hands required in order for the contest in question to be a game of skill and not chance.

You begin your argument by citing the extreme cases:

Hands=1 :
You present a simple proof that shows that no player can do any better than than to play a "no-fold" strategy while hoping for lucky common cards. You submit to the court that a contest of a single hand is 100% chance.

Hands=Infinity :
You present an intuitive argument to show that a contest with an infinite number of hands is a 100% skill.
the +ev players increase winnings in a random upward walk
the -ev players decrease winnings in a random downward walk

Hands=X :
You then move on to the core question presented to the court where you are asking that the state accept your number X as the official cusp where the contest officially crosses from > 0.50 chance to > 0.50 skill.

What is the lowest value of X you'd favor?

a) more than 2652
b) 2652
c) 1326
d) 663
e) 221
f) less than 221

discuss ...

[arahant]

Obviously, you need to give the starting stacks and blinds. In fact, I would say this is far more important than the number of hands.

This is also easier to define in a ring game. With a tournament, other players misfortune can impact one's results.

Even so, the terms 'luck' and 'skill' still seemed poorly defined. I guess I would set the number of hands such that:
Given 10 'typical' players, the player with the highest win rate (at SNG's, not ring) will win the tournament 51% of the time.

Of course, since the number of hands will end up being huge, we can actually just make this the player with the best ring game results, but then you need to factor in the differences in play based on number of players.

eh...impossible, but food for thought.

[RayBornert]

[ QUOTE ]
Obviously, you need to give the starting stacks and blinds. In fact, I would say this is far more important than the number of hands.

This is also easier to define in a ring game. With a tournament, other players misfortune can impact one's results.

Even so, the terms 'luck' and 'skill' still seemed poorly defined. I guess I would set the number of hands such that:
Given 10 'typical' players, the player with the highest win rate (at SNG's, not ring) will win the tournament 51% of the time.

Of course, since the number of hands will end up being huge, we can actually just make this the player with the best ring game results, but then you need to factor in the differences in play based on number of players.

eh...impossible, but food for thought.

[/ QUOTE ]

ara,

assume that the blinds do not change for the entire X number of hands.

assume one of the following:
a) bankrolls begin at zero and are allowed to go negative.
b) bankrolls begin large enough such that players cannot go negative.

in other words the proposition is to measure the earnings of the players over a fixed number of hands - the winner of the tournament is based on who won the most from their opponents who are also attempting to win the most.

the premise here is that there is some number of hands (X) such that winning the most for the number of hands against opponents attempting the same involves more skill than chance.

if we can find that number X then we can host this type of game inside the united state without fear of prosecution for violating gaming law.

ray

[alphatmw]

winning fifty [censored] one percent of the time?

[luckyme]

the 9 oppenent actions are determined by a dice roll. each turn , whether to fold or call or raise.
10th player is allowed to do what he wants, Chris Ferguson perhaps.

100 hands should be plenty to make the point.

luckyme

[RayBornert]

[ QUOTE ]
winning fifty [censored] one percent of the time?

[/ QUOTE ]

alpha,

that's not how states measure a given game.

they pass judgement on a given definition of the game based on whether or not there is more skill involved than luck in order to win the contest - all based on how that contest is defined.

were looking for some number of hands (X) such that there is more skill than luck in order to out perform your opponents.

winning 51% of the time would not be a good criteria for a 10 chair sng - that's probably impossible.

ray

[RayBornert]

[ QUOTE ]
the 9 oppenent actions are determined by a dice roll. each turn , whether to fold or call or raise.
10th player is allowed to do what he wants, Chris Ferguson perhaps.

100 hands should be plenty to make the point.

luckyme

[/ QUOTE ]

yes.

this is intuitively apparent to those of us that know holdem; however, you couldn't use this as an example unless this was going to be the game you really intended to play - you'd have to specifically include the dice rolling random players into your definition of the contest itself in order to make your point.

the counter example here is where 10 non-differentiated players compete for X number of hands. the game is then pure chance - e.g. 10 players that never fold, always call, and never raise.

or if chris plays his 9 clones then every chair has equal chances.

ray

[arahant]

[ QUOTE ]

winning 51% of the time would not be a good criteria for a 10 chair sng - that's probably impossible.


[/ QUOTE ]
Well yeah...I would say that that is one reason why it's considered gambling!

It's clearly a game of skill, and I don't think you need to change the game to make it become 'non-gambling'. Golf is considered a game of skill, and no one is going to try and ban things like match-play where the results are quite variable. For that matter, I'm sure they could hold a '1 shot tournament' and no one would complain.

Heck, sudden-death overtime explicitly includes a luck component, and that's not illegal.

All you really need to show is that for a large number of hands, certain players will do well and others won't. You can show this with hand histories alone.

Edit: Is there such a thing as a game that is X% luck? I guess a game where the worse player would lose every time, but then we tack on a random variable such that he is now allowed to win X%/2? Of course, this means that in a 50% skill game, the better player would win 75% of the time, not 50...

[RayBornert]

[ QUOTE ]
[ QUOTE ]

winning 51% of the time would not be a good criteria for a 10 chair sng - that's probably impossible.


[/ QUOTE ]
Well yeah...I would say that that is one reason why it's considered gambling!

It's clearly a game of skill, and I don't think you need to change the game to make it become 'non-gambling'. Golf is considered a game of skill, and no one is going to try and ban things like match-play where the results are quite variable. For that matter, I'm sure they could hold a '1 shot tournament' and no one would complain.

Heck, sudden-death overtime explicitly includes a luck component, and that's not illegal.

All you really need to show is that for a large number of hands, certain players will do well and others won't. You can show this with hand histories alone.

[/ QUOTE ]

ara,

totally agree with you here. analyzing hand histories is very useful but we still need to select a number and stand behind it.

neither one of us is going to pick X to be 1 or 2 or 3 ... etc.

im willing to say that if you selected 1k players and got them to meet in a cardroom every weekend to play a 221 hand limit sng (as described above) at a total of 100 tables where the seating was random, that at the end of a year of weekends the stronger players would be closer to 50 wins and the weaker players would be closer to 0 wins.

ray

[thylacine]

This has very little to do with mathematics and poker, and has everything to do with politics and law.

There is simply not a uniquely and meaningfully defined concept of `51% skill'.