[VHRanger]

All Poker AIs developped as yet approaches Nash Equilibrium -- it's just a "perfect" strategy that wins by default because it makes no mistakes. Since you make mistakes against the AI strategy, and the sum of the game of poker is 0, you lose by default.

No poker bots yet I know of have developed "exploitative" strategies, where they deviate from the Nash Equilibrium strategy to exploit opponent mistakes.

Back when I played professionally (2012-2016, poker AIs being relevant in 2015/16) the standard was to use a bot to study the best default strategies and use expert human judgement to deviate from it against bad opponents.

[clolege]

Nash equilibriums exist when bluffing is involved?

It seems like it would introduce a level of predictability that would make it easier to know when the opponent is bluffing.

[aidenn0]

They absolutely do. Since it's world cup time I'll use a contrived soccer example.

A penalty kick where the kicker can kick left or kick right. The goalie has to jump one direction, if they jump the wrong direction a goal is scored. Both people know that this kicker is great at kicking to the left side of the goal but rather "meh" at kicking to the right, so if the kicker kicks to the left and the goalie jumps left, there's still a 20% chance of scoring, but if the kicker kicks to the right and the goalie jumps right, there's only a 5% chance of scoring.

There is a Nash equilibrium for the kicker, and it can't be "always kick left" because then the goalie would "always jump left" which would give the kicker an advantage if it kicked right.

Similarly the Nash equilibrium for poker can't be to always fold a weak hand, because that's leaving money on the table because then the opponents will always fold against a raise, which would mean the player could get easy money by raising with a weak hand.

[eru]

> Nash equilibriums exist when bluffing is involved?

In some sense that's the whole point of Nash equilibria.

[aetherane]

A strategy can involve probability, like bluff 30% of time.

[tonystarch]

Bluffing isn’t really something one needs to compensate for. Bluffing as a game rule simply means that all hands or values may be max or min values, but the idea is that if you are making bets based on the mathematics of your hand itself this isn’t so pertinent.