Saturday, April 9, 2011

A logical approach to the skill vs. luck structure of cash games vs. tournaments

In a ruling that, from a practical standpoint, is completely backwards, the Supreme Court in Sweden essentially decided that tournament poker is skill and cash game poker is luck.

Now, there may be more nuance in the ruling than that one article provides. But, if I recall correctly, this is not the first jurisdiction or court ruling that has found tournament poker to be "predominantly skill" or "not gambling" while finding the opposite for cash game poker.

I've even encountered poker players who believe either of these.

After all, the structure of tournament poker strongly resembles that of tournaments in other games that are commonly-accepted as games of skill and are rarely treated as gambling, while cash game poker looks a lot like "table games" in a casino, to the untrained eye.

Perhaps we can even sympathize with those who have made these decisions; perhaps they recognize that skill will always predominate over chance in the long run in any game, and that tournament poker "locks players in" to playing multiple hands of poker. Meanwhile, cash game poker lets players leave after one hand, which might give some gamblers the opportunity to take a quick risk on a hand of poker, just as they might do on the spin of a roulette wheel.

I have a reasoned argument as to why it cannot be the case that all tournaments "are skill" ("are not gambling") while cash games "are luck" ("are gambling").

A logical argument

Assume that it is somehow sensible or consistent that all tournaments are skill while all cash games are luck.

Then a 6-handed, winner-take-all tournament with a $200 entry fee, $200 in starting chips, and fixed (nonincreasing) $1/$2 blinds is skill.

Consider the following modifications to the rules of the tournament:

1) Players can buy in for less than the full amount if they wish, and they receive a proportional amount of chips; since the tournament is winner-take-all, and since each player's winning chances are equal to the ratio of their chips to total chips in play when all players are equally skilled, no inherent strategic advantage is given by this option (modulo short-stack advantages).

2) Players can rebuy when they lose all their chips or whenever they want to add on back up to the maximum.

3) If a player leaves the game by going broke or cashing out, a different player can take the seat and buy in just as the previous player could have rebought.

4) Players can "buy out" of the tournament at any time for their fair share of chip equity, equal to the ratio of their stack to the remaining prize pool. Ignoring the position of the button, again, since the tournament is winner-take-all, this is equal to the expected payoff for the player when he or she is at an equal skill level to his or her opponents, therefore this modification affords no in-game strategic advantage.

Making all four of these changes to the tournament makes it equivalent to a $1/$2 cash game.

So, which of these extra rules changed the fundamental "skill" or "gambling" nature of the game?

Do any of these changes make the game less skillful, or more luck-based?

#1 doesn't reduce skill. While shorter-stacked poker involves less complicated decisions, the level of stack-depth skill at work in any poker game with varying stack sizes will always be at least that of the same poker game if all stack sizes were at the minimum. An appropriate minimum buyin requirement can ensure that this level of skill is suitable.

#2 doesn't reduce skill. It's just a way for players to reenter the game. Notably, it allows a skilled player to continue to participate in the game, even if some bit of "bad luck" caused him to lose a big hand. In the right context, this would only increase skill relative to luck.

#3 doesn't reduce skill, same as above.

#4 doesn't reduce skill. It's just a way for players to leave the game early on any given night. The skill is still exercised over whatever number of hands they chose to play. I get that #4 is the one that Sweden and others might feel does change the skill vs. luck nature of the game, but even if the luck doesn't "even out" until a "long run" is reached, it's important to recognize:
  • If, say, we determine that 1,000 hands is the point where "skill predominates" in a certain poker game, there's no logical or practical difference between that player playing 1,000 hands in one night, or by playing those 1,000 hands in several sessions over the course of his life.
  • Almost every type of poker player will play sufficiently many hands in their life, even casual players.
(And I'm not even bothering to consider the fact that, by any measure, the amount of time in a cash game where "skill predominates" is going to be much, much less than the same necessary amount of time in tournament poker, as any actual poker player knowledgeable of the "LOL donkaments" creed is aware.)

So, with all due respect to naïve judges' attempts to implement an approach to skill vs. luck that recognizes that the duration of play affects the influence of luck on outcomes, a duration-based legal classification has logical as well as practical issues.

Classifying cash game poker as "luck" because it is possible to play it for a very short amount of time per day would be the same as deeming chess as "skill" under normal conditions, but "luck" when the same game of chess is broken up over several days and played a few moves at a time.

Do any of these changes make the game more "gambling"?

#1 doesn't introduce any "gambling". Certainly, giving players the option to play for less than the nominal amount can only reduce the amount of "gambling", by any definition.

#2 doesn't introduce any "gambling". In an environment where all tournaments are "not gambling", a player who has lost in a tournament could very easily enter a new tournament right away, if he were inclined. There's no difference between letting him do that on some table across the room and letting him do that at the same table he started at.

#3 doesn't introduce any "gambling", it just changes the particular players that might be participating at any time.

#4 doesn't introduce any "gambling". Again, this option can only reduce the amount of "gambling", and it does so in an incredibly significant way, especially in big tournaments.

In fact, the effects of #4 are so huge that I would argue that, from any sensible perspective, tournament poker has to be more "gambling" than the equivalent cash game. The primary difference between the two is that tournament poker forces its players to continue taking risks with their money rather than giving them the option to leave when they would like to, and certainly most tournaments will end with the remaining players taking on much more risk than they would be comfortable with, or rationally interested in.

For example, in a $1/$2 cash game, a player can leave if he triples up his stack and doesn't want to risk losing $600. In the equivalent $200-buyin tournament (think the Sunday Million), he can't leave with his $600-equivalent stack, nor any higher stack. If he makes the final table, he will be effectively taking risks for tens of thousands of dollars on every hand.

In almost any multi-table tournament with a reasonable field size, very few of the players who choose to play the tournament are actually well-equipped to rationally tolerate the financial risk they will have to endure if they make it to the end of the tournament and no deal is made. Utility annihilation, etc.


It cannot be logically consistent for all tournaments to be "skill" or "not gambling" while all cash games are otherwise. The differences between the two types of poker are largely practical, in that cash game poker accommodates players' personal schedules and personal risk tolerances much better than tournament poker. As far as game design goes, the additional game flexibility options of the cash game allow for a broader audience to participate, spending time on the game as it is convenient for them. This effect has to be an economic benefit to society from any perspective.

Any factor of cash games that might intuitively seem like enabling "luck" or "gambling" would also exist in tournaments of a certain blind structure, or a series of such tournaments.

Would Sweden really hope to provide regulations over tournament stack/blind structure? After all, it would be easy to define a tournament structure with very large blinds that would be over in fewer hands than any cash game.

Would Sweden also hope to regulate over deal-making in tournaments? After all, if a group of players join a winner-take-all tournament with the intent of chopping the prize pool with a chip-proportional deal after a certain amount of time, that's identical to a cash game.

There's an analogy to finance and investing here. Perhaps a government might decide that it doesn't want its citizens taking any short-term financial risk (a la playing only a few hands of a cash game), and thus only allows long-term investment by letting individuals only deal in instruments whose payoffs are far enough into the future. Consider a bond that pays out $100 in 365 days. Perhaps the current interest rates are such that the value of that bond today is $95. But if somebody buys that bond now, and the interest rates change such that the value increases to $98 the next day, he can't really be stopped from selling that bond to another person and locking up his quick $3 win -- the exact same $3 short-term payoff he could have had by speculating in interest rate futures. Generally, any short-term payoff can be derived synthetically by trading in longer-term payoffs, and settling tournaments early via deal-making achieves the exact same result in poker.

Would Sweden presumably approve of a cash game variant where players were artificially "locked in" to playing a certain number of hours or hands before they could leave? If so, then we're back to the silliness of the example of a game of chess being "skill", but the same game of chess being "luck" when played a few moves at a time and over the course of several days.

From a practical standpoint, looking at the ruling from any of these three natural conclusions should highlight the logical absurdity of the ruling in a manner which I would hope and expect to be apparent to everybody, regardless of knowledge or experience with poker.


  1. I just learned that Minnesota has an interesting approach to circumventing an apparent ban on NL cash game play (but not on tournaments):

    So, basically, it looks like they were only comfortable making change #2.

  2. Tournament has bigger luck factor than cash games, is a higher variance game. I mean Jamie Gold manage to win wsop, thats the proof ;p .Cash game brings Justice


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