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'.

[luckyme]

[ QUOTE ]
m 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.

[/ QUOTE ]

I'm not sure why that would convince anyone that it wasn't random. We'd still have some closer to 50 and others 0 if they were playing by flipping coins to bet/call/raise.
Iow, I don't see why that would prove that the leaders are the stronger players. You or I may believe that, but that's by using knowledge outside of those results.

luckyme

[RayBornert]

[ QUOTE ]
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'.

[/ QUOTE ]

thy,

i agree with you to a point.
i cant agree that this issue has little or nothing to do with math.

my assertion is that tournament contests with fewer hands tend toward chance outcomes and tournament contests with more hands tend toward skill outcomes.

i cited the endpoint cases as a means to suggest that the nhands spectrum is continuous and linear.

if those things are true then there is some number of hands where the variance of the game crosses a cusp.

it may be that the problem is so intractable that we cannot know the exact answer; nevertheless, i assert that the cusp is there. i think you can agree with this much.

ray

[thylacine]

[ QUOTE ]
[ QUOTE ]
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'.

[/ QUOTE ]

thy,

i agree with you to a point.
i cant agree that this issue has little or nothing to do with math.

my assertion is that tournament contests with fewer hands tend toward chance outcomes and tournament contests with more hands tend toward skill outcomes.

i cited the endpoint cases as a means to suggest that the nhands spectrum is continuous and linear.

if those things are true then there is some number of hands where the variance of the game crosses a cusp.

it may be that the problem is so intractable that we cannot know the answer; nevertheless, i assert that the cusp is there. i think you can agree with this much.

ray

[/ QUOTE ]

Sure, I understood the OP. I am a mathematician. BTW this has been discussed on the the Poker Theory forum too. The point is that if there is ANY skill whatsoever, then in the long run, it asymptotically approaches what could only reasonably be called 100% skill. So what on earth does `51% skill' mean. The reality is that lawmakers who use this type of language probably have no concept of the issues involved. The real issue is what argument persuades judges and/or politicians, given their knowledge, their biases, and maybe what other games have previously passed or failed the nonsensical `51% skill' criterion.

[keith123]

guys, i think he is only asking how many hands it takes for skill to outweigh luck.

[RayBornert]

[ QUOTE ]
[ QUOTE ]
m 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.

[/ QUOTE ]

I'm not sure why that would convince anyone that it wasn't random. We'd still have some closer to 50 and others 0 if they were playing by flipping coins to bet/call/raise.
Iow, I don't see why that would prove that the leaders are the stronger players. You or I may believe that, but that's by using knowledge outside of those results.

luckyme

[/ QUOTE ]

luck,

what if the 100 table 50 week experiment that involved the 221 hand sngs also included the act of maintaining a database of all server side hand histories (all dealt card info known) such that the participants in the experiment were able to access the db and construct their own statistics in an effort to profile their opponents.

you can assume that the hh's for a given sng would not be available until the conclusion of that sng, however, the hh's preceding that point would be.

this type of experiment is certainly not a coin flip type of proposition.

ray

[thylacine]

[ QUOTE ]
guys, i think he is only asking how many hands it takes for skill to outweigh luck.

[/ QUOTE ]

1. What does this mean? What is a mathematical formulation of what it means for skill to outweigh luck?

2. It is beside the point. If the term `51% skill' is to have a uniquely defined and well-defined meaning, then it must be intrinsic to the game and independent of the number of hands.

[RayBornert]

[ QUOTE ]
guys, i think he is only asking how many hands it takes for skill to outweigh luck.

[/ QUOTE ]

yes. thank you.

that is exactly what i'd like to know such that i'd have a decent chance of winning a court case.

ray

[RayBornert]

[ QUOTE ]
[ QUOTE ]
guys, i think he is only asking how many hands it takes for skill to outweigh luck.

[/ QUOTE ]

1. What does this mean? What is a mathematical formulation of what it means for skill to outweigh luck?

2. It is beside the point. If the term `51% skill' is to have a uniquely defined and well-defined meaning, then it must be intrinsic to the game and independent of the number of hands.

[/ QUOTE ]

thy,

i didn't invent the idea or concept.

the 51% skill test is a legal concept used by states to pass judgement on games of skill versus games of chance.

it might be that there are games that are so intractable that you cannot lab test them to know if there is at least 51% skill involved. nevertheless these types of states are willing to allow games that involve some element of chance as long as the game can be accepted as having more skill than luck.

obviously they are placing the burden of proof on us to provide some evidence that the game we're playing requires more skill than luck.

ray

[thylacine]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
guys, i think he is only asking how many hands it takes for skill to outweigh luck.

[/ QUOTE ]

1. What does this mean? What is a mathematical formulation of what it means for skill to outweigh luck?

2. It is beside the point. If the term `51% skill' is to have a uniquely defined and well-defined meaning, then it must be intrinsic to the game and independent of the number of hands.

[/ QUOTE ]



thy,

i didn't invent the idea or concept.

the 51% skill test is a legal concept used by states to pass judgement on games of skill versus games of chance.

it might be that there are games that are so intractable that you cannot lab test them to know if there is at least 51% skill involved. nevertheless these types of states are willing to allow games that involve some element of chance as long as the game can be accepted as having more skill than luck.

obviously they are placing the burden of proof on us to provide some evidence that the game we're playing requires more skill than luck.

ray

[/ QUOTE ]

AAAAAAARRRRRRRRRRRGGGGGGGGGGGGHHHHHHHHHHHHHHH!!!!! !!!!!! I give up. Phrases such as "the game we're playing requires more skill than luck" is meaningless non-sensical gibberish and therefore falls into the realm of politics and law, rather than mathematics and poker. I fully undestand all your points. Please understand my points.

[RayBornert]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
guys, i think he is only asking how many hands it takes for skill to outweigh luck.

[/ QUOTE ]

1. What does this mean? What is a mathematical formulation of what it means for skill to outweigh luck?

2. It is beside the point. If the term `51% skill' is to have a uniquely defined and well-defined meaning, then it must be intrinsic to the game and independent of the number of hands.

[/ QUOTE ]



thy,

i didn't invent the idea or concept.

the 51% skill test is a legal concept used by states to pass judgement on games of skill versus games of chance.

it might be that there are games that are so intractable that you cannot lab test them to know if there is at least 51% skill involved. nevertheless these types of states are willing to allow games that involve some element of chance as long as the game can be accepted as having more skill than luck.

obviously they are placing the burden of proof on us to provide some evidence that the game we're playing requires more skill than luck.

ray

[/ QUOTE ]

AAAAAAARRRRRRRRRRRGGGGGGGGGGGGHHHHHHHHHHHHHHH!!!!! !!!!!! I give up. Phrases such as "the game we're playing requires more skill than luck" is meaningless non-sensical gibberish and therefore falls into the realm of politics and law, rather than mathematics and poker. I fully undestand all your points. Please understand my points.

[/ QUOTE ]

thy,

i'm not trying to be frustrating here. i am trying to find some working definition for an online game of texas holdem that a state court would bless as a game of skill.

i totally agree with you that politics are involved.

i'm just trying to take a stab at a working definition of a skill-based holdem contest.

if you want to move to my state and run for elected office and change the political constraints then do it. i'm not motivated to do that.

i'm hunting for a solution within the existing political framework.

ray

[soon2bepro]

But what if not all players play with a complete lack of skill?

In any game of skill with no inside luck (outside luck is irrelevant), the best player wins tournament (the best player is the one who played the best during the tournament). This doesn't happen in poker. If you put the best 100 players to play a hold'em limit tournament, the result will probably be decided mostly by chance. Even if they play 100 such tournaments, the overall result will be mostly guided by chance.

In your example, you make the bad players have no skill at all, but when they have a dot of common sense, you need to play more hands against them to get a clear edge.

In any case, I don't know how to calculate this, I was just trying to point out what I said above.

[madnak]

Your definition would not exist based on any kind of rigorous mathematical framework, at least not at its base. You'd probably want to use some common assumptions or something along those lines, and use the math to work from there.

Legal distinctions are frequently very arbitrary from a rational standpoint, and rely on cultural assumptions and subjective judgment calls. It's not always quite so bad as "I know it when I see it," but it's frequently not far off.

Thus, the standard for evaluating a measure of "the amount of skill involved" is its intuitive appeal and palatability, rather than its logical consistency. Sad but true.

[RayBornert]

[ QUOTE ]
But what if not all players play with a complete lack of skill?

In any game of skill with no inside luck (outside luck is irrelevant), the best player wins tournament (the best player is the one who played the best during the tournament). This doesn't happen in poker. If you put the best 100 players to play a hold'em limit tournament, the result will probably be decided mostly by chance. Even if they play 100 such tournaments, the overall result will be mostly guided by chance.

In your example, you make the bad players have no skill at all, but when they have a dot of common sense, you need to play more hands against them to get a clear edge.

In any case, I don't know how to calculate this, I was just trying to point out what I said above.

[/ QUOTE ]

what if the contest is changed to headsup? everything else stays the same. an entire match could be played in about 1-2 hours online.

ray

[RayBornert]

[ QUOTE ]
Your definition would not exist based on any kind of rigorous mathematical framework, at least not at its base. You'd probably want to use some common assumptions or something along those lines, and use the math to work from there.

Legal distinctions are frequently very arbitrary from a rational standpoint, and rely on cultural assumptions and subjective judgment calls. It's not always quite so bad as "I know it when I see it," but it's frequently not far off.

Thus, the standard for evaluating a measure of "the amount of skill involved" is its intuitive appeal and palatability, rather than its logical consistency. Sad but true.

[/ QUOTE ]

mad,

same question. what if the X=221 and the contest whas headsup?

if the game is mostly luck then we'd each win the sng about half the time. but if you're much better than i am then you'd win much more often.

ray

[Torgeir23]

wouldn't the best way to 'legalize' poker, or to get politicians to view poker as a game of skill, be to draw parallels to the stock and options market and show how the two forms of 'gambling' aren't that different? Too drunk and high to draw any parallels right now

[RayBornert]

[ QUOTE ]
wouldn't the best way to 'legalize' poker, or to get politicians to view poker as a game of skill, be to draw parallels to the stock and options market and show how the two forms of 'gambling' aren't that different? Too drunk and high to draw any parallels right now

[/ QUOTE ]

i'd say that for 3 or more chairs then the stock market parallel begins to be appropriate.

for headsup, chess is a better comparison.

ray

[FortunaMaximus]

[ QUOTE ]
[ QUOTE ]
wouldn't the best way to 'legalize' poker, or to get politicians to view poker as a game of skill, be to draw parallels to the stock and options market and show how the two forms of 'gambling' aren't that different? Too drunk and high to draw any parallels right now

[/ QUOTE ]

i'd say that for 3 or more chairs then the stock market parallel begins to be appropriate.

for headsup, chess is a better comparison.

ray

[/ QUOTE ]

No. There is still plenty of luck involved in HU matches. Not as much, admittedly, as 6max or FR, but it is still an element.

HU still should be comparable to the stock market analogy, because your edge comes from volume and consistent overall positive ROI. Tournaments might well be described as a finite chaotic system.

[Torgeir23]

How then about the options and futures market? Couldn't u view your hand as a call option on the pot. You are basically betting on the flop turning in your favour. I really can't see how poker differs from the new innovations in financial markets, like weather options for example. It is allowed to bet on the weather now and it's organised on exchanges. How does that differ from, in a gambling perspective, from poker.

[RayBornert]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
wouldn't the best way to 'legalize' poker, or to get politicians to view poker as a game of skill, be to draw parallels to the stock and options market and show how the two forms of 'gambling' aren't that different? Too drunk and high to draw any parallels right now

[/ QUOTE ]

i'd say that for 3 or more chairs then the stock market parallel begins to be appropriate.

for headsup, chess is a better comparison.

ray

[/ QUOTE ]

No. There is still plenty of luck involved in HU matches. Not as much, admittedly, as 6max or FR, but it is still an element.

HU still should be comparable to the stock market analogy, because your edge comes from volume and consistent overall positive ROI. Tournaments might well be described as a finite chaotic system.

[/ QUOTE ]

fortuna,

just wanna make sure that you know that the theoretical match being discussed here is:

221 hands of limit holdem played headsup with no change in stakes. if you already knew this then please ignore this reminder.

ray

[FortunaMaximus]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
wouldn't the best way to 'legalize' poker, or to get politicians to view poker as a game of skill, be to draw parallels to the stock and options market and show how the two forms of 'gambling' aren't that different? Too drunk and high to draw any parallels right now

[/ QUOTE ]

i'd say that for 3 or more chairs then the stock market parallel begins to be appropriate.

for headsup, chess is a better comparison.

ray

[/ QUOTE ]

No. There is still plenty of luck involved in HU matches. Not as much, admittedly, as 6max or FR, but it is still an element.

HU still should be comparable to the stock market analogy, because your edge comes from volume and consistent overall positive ROI. Tournaments might well be described as a finite chaotic system.

[/ QUOTE ]

fortuna,

just wanna make sure that you know that the theoretical match being discussed here is:

221 hands of limit holdem played headsup with no change in stakes. if you already knew this then please ignore this reminder.

ray

[/ QUOTE ]

Wouldn't this be swayed slightly by uneven distribution of equal starting hands across such a narrow range? If not, then I suppose there's nothing random in poker.

Must've been distracted by that stoned and drunk lobbyist up there and put it in that context. That's not a strong enough argument to present before a court.

If it isn't strong enough for the court, surely it isn't strong enough for a formal proof of logic...