A rock-paper-scissors game in poker

In Texas Holdem, the best starting hand is pocket aces. This hand is favored against any other starting hand, and it’s almost always a simple decision to play this hand pre-flop and play it aggressively.

With other starting hands, it’s a more complicated decision. The odds of winning depend on what you think the other player has. Pocket kings are great against pocket queens, for instance, but they are in bad shape against pocket aces.

The odds get even more interesting for other starting hands. Below is a clip from Daniel Negraneu on High Stakes Poker explaining a type of rock-paper-scissors game for poker starting hands.

The hands involved are pocket twos, jack-ten suited, and ace king. Here is the clip:

Link to youtube video: Did you know? with Daniel Negraneu

To verify, I used a poker odds calculator here to find out that:

–jack-ten suited is favored to beat pocket twos (something like 52.97 to 45.58, with 1.45 percent tie)

–ace-king is favored to beat jack-ten suited (something like 61.02 to 38.50, with 0.48 percent tie)

–pocket twos are favored to beat ace-king (something like 49.96 to 49.37, with 0.67 percent tie)

Just as rock beats scissors, which beats paper, which beats rock, we have the following with the poker hands: jack-ten suited beats pocket twos, which beats ace-king, which in turn beats jack-ten suited!

This example again highlights how poker is more than a game of odds. It is a game of reading opponents and adjusting strategies accordingly as game theory dictates.



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  • http://www.franchise-info.ca michael webster

    Presh;

    I bet that even a Stanford graduate wasn’t taught about how to evaluate the rationality of preferences which are stochastically intransitive: A is probabilistically preferred to B which is probabilistically preferred to C which is probabilistically preferred to A.

    How would you have played Daniel’s bet?

  • Jake

    I agree with Mr. Webster. I’d love to hear what you’d do in practice.

    LTR*

    *long time reader

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  • Sauron

    The thing I notice here is that the probabilities are vastly different. If I’m holding AK I have a relatively huge advantage over J-10 suited, but a very small disadvantage for the pocket 2s. Ignoring the other vast possibilities for a moment, this suggests that, playing the odds, I can get away with the AK most often, regardless of whether I can read the other people or not.

    Maybe I’m missing the precise point here, but I feel this is important too.

  • Mauricio

    One key difference between this poker example and rock-paper-scissors is not being able to choose which hand is being given in poker, and being able to choose between rock, paper and scissor.

    In other words, the hand in poker alone is not part of the players strategy set.

    A better analogy would be:
    Raising with weak hand (bluffing), raising with strong hand, not raising with weak hand, and not raising with strong hand (slow play). And for the other player, folding, calling, and raising.

    Bluffing beats folding. Folding beats raising with strong hand, raising with strong hand beats calling, calling beats bluffing.

    Slow play beats raising, raising beats not raising with weak hand, not raising with weak hand beats calling, calling beats slow play.

    Of course this is only a model, real poker has many levels of raises, many different hands for all players, many rounds, and usually more than 2 players.

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