Wednesday, September 26, 2012

20 thoughts on skill vs. chance in poker, part 17: Why does poker need randomness?

<-- Part 16: Does duplicate poker have higher skill relative to chance?

Some competitive games other than poker have randomness that would ideally be removed and could be removed without changing the strategy and appeal of the game. The toy game example of rando chess, traditional chess with a random component tacked onto the end, is probably a worse game than traditional chess for both casual and competitive play; if rando chess were the game that was invented and popularized first, it would likely be replaced by traditional chess rather quickly. Similarly, physical sports affected by factors such as wind and weather might end up being better, more engaging games in a world where these games were not influenced by these external factors and where raw individual physical prowess and game strategy were the only factors in the outcomes.

Poker, however, could not practically remain the same game if the random deal of the cards were removed.

Consider the number of different situations that could take place in a game of poker. This number accounts for every possible decision point for every combination of holecards, boardcards, and betting lines. Even for as simple of a game as Heads-Up Limit Holdem, this number looks to be about 290 quadrillion — I'm not going to double-check this, but the point is, it's big. Let's design a way to play Heads-Up Limit Holdem without its intrinsic random components and call it deterministic poker. Playing deterministic poker would involve each player sitting down and specifying the decisions they would make in each of these 290 quadrillion game situations. After the players (and their ancestors) finished writing out this full strategy specification, a supercomputer could compare the players' strategies against each other and decide the winner by playing through each of these situations. Alternatively, each of the 290 quadrillion game situations could be played through in sequence by the players. Neither of these are particularly efficient, but, with a long enough amount of time and infinite human longevity, the game of poker could indeed be played fully deterministically. There's certainly no intrinsic randomness in deterministic poker, and it would never be treated as gambling.

Instead, in the real world, the game of poker ends up being essentially the same game as deterministic poker (with the added bonus of being realistic to play through) by having its players play through a randomly-chosen subset of these 290 quadrillion game situations for whatever period of time they find comfortable. Poker and deterministic poker are equal in expectation for the players and admit the same strategies and skills. Just as rando chess and chess have the same strategies and would eventually produce the same ranking of their players, poker and deterministic poker are, in this sense, the same game. The same is true for other strategy games with intrinsic random components, such as bridge, backgammon, Scrabble, and Magic: the Gathering. The game trees for these games are too large to play through in one sitting or in one lifetime, but, by randomly shuffling between these game situations, the depth of strategic diversity of these games can be obtained and enjoyed in a reasonable amount of time.

Thus is the miracle of randomization, enabling an activity that could not exist without it, and yet most of our society fears this type of uncertainty. In poker, since the variances are always finite, risk management principles can allow a player to control and ultimately ignore the effects of the intrinsic random components of the game. From this perspective, the presence of the intrinsic random components in real poker does not make the game meaningfully different from deterministic poker.

This is in stark contrast to other games which are commonly treated as gambling. One-player casino games without randomness would just be machines or tables that a customer could walk up to and, after specifying a full strategy for any potential strategic inputs, immediately be handed some smaller portion of his or her bet back. Casinos would be much less popular in this world.

Poker without its intrinsic random components would still be a strategically-rich and compelling game.

Games of chance without their intrinsic random components would be nothing.

Part 18: The relationship between level of stakes and degree of chance -->

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