In my opinion, every imperfect information game where there is the possibility of bluffing lacks a perfect (or winning) strategy, for the simple reason that knowing your opponent's strategy will let you beat him easily (even if his strategy isn't 100% deterministic).

So why do the guys that developed 'Cepheus' claim that they made a program playing poker with a perfect strategy, claiming that their AI 'is guaranteed to not lose money in the long run' ?

I'm pretty sure I can create a strategy winning versus Cepheus, because I know its strategy.

Where am I wrong ?

  • 2
    $\begingroup$ the media did not report this very well, but basically cepheus computes nearly perfect statistics of the game (or statistics within an extremely small error), which is very complex and requires nearly supercomputing level resources to calculate. the real game involves a lot of other factors such as noticing patterns in opponents play. the point is that even if you did know Cepheus's entire code, you could only tie it at best over many games. $\endgroup$
    – vzn
    Commented Sep 7, 2015 at 1:23
  • $\begingroup$ I could get only a draw in front of him on the long term ? this is what I don't understand : if I know how he bluffs (or doesn't), I can bluff him more, and better, so that I should be able to beat him on the long term ? and we agree, we talk about real-life poker with limited money and betting. $\endgroup$
    – reuns
    Commented Sep 7, 2015 at 1:29
  • $\begingroup$ @vzn for me, poker would be like the prisoner dilemma : if you know your opponent's strategy, you can easily beat him. $\endgroup$
    – reuns
    Commented Sep 7, 2015 at 2:40
  • $\begingroup$ try thinking about it this way. with perfect strategy the game becomes like a coin flip. can you consistently win at coin flipping also, even knowing your opponents "strategy"? $\endgroup$
    – vzn
    Commented Sep 7, 2015 at 2:42
  • $\begingroup$ no sure, that's why I mentioned bluffing in my post. the probability your opponent is bluffing at a given moment is unknown, but the more you approximate it well, the more you can counter-bluff and win. $\endgroup$
    – reuns
    Commented Sep 7, 2015 at 3:18

1 Answer 1


Nash proved that every zero-sum game has a perfect strategy called a Nash equilibrium. This is a possibly randomized strategy for both players such that given that one player follows the strategy, it doesn't pay the other player to deviate from her strategy. As an example, consider the game rock, paper, scissors. One Nash equilibrium here has both players choosing their signal randomly. If one player does that, there is no point for the other player to follow any other strategy (though it doesn't hurt).

Since Poker is a symmetric zero-sum game (both players are treated the same by the game), the value of the game is zero, and any Nash equilibrium on average results in zero expected profit for both players. According to Wikipedia, Cepheus is an approximation to such a strategy. As such, Cepehus' strategy may be randomized.

What about bluffing? Let's consider a variant of rock, paper, scissors in which players can bluff. Say each player writes their choice on a piece of paper, and then there is some structured dialog in which players announce their choice and offer the other player to capitulate. The random strategy is still perfect, in that if one player follows it, it doesn't pay for the other player to deviate from it.

While Cepehus (if it were perfect) shouldn't lose on the long run, it is not guaranteed to be a good strategy in practice, since it only promises you a small negative expected profit. Perhaps when playing against good human players it will just break even on average. That doesn't mean that humans are any better than it, just that they're not any worse. Another possibility is that while in theory the only guarantee is that it breaks even, in practice it wins against sub-optimal humans. This is an empirical question that the developers are testing right now through their website.

  • $\begingroup$ in that case, I solved poker too, before them : just don't play. that's a Nash equilibrium too. :) anyway, thank you, I think it is the idea of Nash equilibrium for bluff games that is difficult : it is quite obvious for the bluffing version of rock paper scissors, but not for poker. $\endgroup$
    – reuns
    Commented Sep 7, 2015 at 6:29
  • $\begingroup$ @reuns The rules of poker don't allow you to stay out (you might have to pay the blind). $\endgroup$ Commented Sep 7, 2015 at 6:35

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