3 ms·

Is 6-handed a significantly harder game or is it just (from the computer's point of view) just like playing 5 single games of heads-up?

whiskers08xmt 10y ago
It is much more difficult, as interactions between all of the players usually have to be modeled.
snarf21 10y ago
I would argue that it is significantly harder. In heads up, you can call a bet and see the flop and go from there. In a full table, calling early means you may have to fold to a raise. There is also a much more complicated analysis of the possibility that you are beat. Lots of times I may be in a hand and think I have the original raiser beat but when two other people call before me, the odds are much less that I have all of them beat. I still think the hardest part of poker is the grind. The computer doesn't get bored or tired and play hands it doesn't have a reason too just because they are stuck in a dead streak. Taking a mostly conservative style, you'd expect the computer to out perform over time. It would be curious to know what percentage of the time the players bluffed the AI successfully and vice versa.
xapata 10y ago
No, the actions of players are not independent. For example, if 3 are in the hand and the 1st to act bets the 2nd is less likely to call because of the risk of the 3rd raising. Or was the 2nd only calling instead of raising because they expected the 3rd to raise based on recent aggression?!
splonk 10y ago
It's a significantly harder game. Computing a Nash equilibrium in a 2-player game is relatively straightforward in technique (albeit very computationally expensive in the case of poker). There's several factors that make even 3-player games much more complicated than 2-players. An additional player requires some sort of modeling of the interaction between players, which may not be feasible. For example, Player A may have multiple co-optimal strategies with respect to his own EV, but that affects the EVs for players B and C differently. Player A can choose arbitrarily between these strategies at any frequency, but players B and C can't predict this choice at all. On top of that, Nash equilibrium requires that each player acts independently in their best interest. Teams can be modeled as a single player if necessary, but shifting alliances over the course of a series of hands can't be easily. And on the pure computational complexity side, the state space explodes when you can have more than one opponent in a hand simultaneously. Combinations of players in a hand scales as n!, not n.

whiskers08xmt 10y ago

It is much more difficult, as interactions between all of the players usually have to be modeled.

snarf21 10y ago

I would argue that it is significantly harder. In heads up, you can call a bet and see the flop and go from there. In a full table, calling early means you may have to fold to a raise. There is also a much more complicated analysis of the possibility that you are beat. Lots of times I may be in a hand and think I have the original raiser beat but when two other people call before me, the odds are much less that I have all of them beat. I still think the hardest part of poker is the grind. The computer doesn't get bored or tired and play hands it doesn't have a reason too just because they are stuck in a dead streak. Taking a mostly conservative style, you'd expect the computer to out perform over time. It would be curious to know what percentage of the time the players bluffed the AI successfully and vice versa.

xapata 10y ago

No, the actions of players are not independent. For example, if 3 are in the hand and the 1st to act bets the 2nd is less likely to call because of the risk of the 3rd raising. Or was the 2nd only calling instead of raising because they expected the 3rd to raise based on recent aggression?!

splonk 10y ago

It's a significantly harder game. Computing a Nash equilibrium in a 2-player game is relatively straightforward in technique (albeit very computationally expensive in the case of poker). There's several factors that make even 3-player games much more complicated than 2-players. An additional player requires some sort of modeling of the interaction between players, which may not be feasible. For example, Player A may have multiple co-optimal strategies with respect to his own EV, but that affects the EVs for players B and C differently. Player A can choose arbitrarily between these strategies at any frequency, but players B and C can't predict this choice at all. On top of that, Nash equilibrium requires that each player acts independently in their best interest. Teams can be modeled as a single player if necessary, but shifting alliances over the course of a series of hands can't be easily. And on the pure computational complexity side, the state space explodes when you can have more than one opponent in a hand simultaneously. Combinations of players in a hand scales as n!, not n.