probability

Poker, a Few Facts

  1. at the standard game (before Texas Holdem), there is NO chance for a player to have the Flush Royal and for another to have 4 aces
  2. the probability of the same situation at the TH is so low, that those YouTube videos you can watch are most likely staged.
  3. any two “hands” at the showdown are NOT entirely independent events.
  4. the mere act of folding sends some information about the cards of other players to everybody else
  5. the next card to be shown is NOT independent of the bets (and folds) already made in the game
  6. not every set of five publicly seen cards is equally likely to occur. Aces are a bit rarer then twos.

Some did find those quite hard to understand, but they are all true. Some even apparently stranger facts might be out there, I wonder what they are.

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4 thoughts on “Poker, a Few Facts

  1. msjr says:

    Can we get more detailed explanation of this one, please:

    6. Not every set of five publicly seen cards is equally likely to occur. Aces are a bit rarer then twos.

    • To be precise. The probability for every set of the 5 community cards is the same. However, not every set of them will be equally likely to actually end up on the table. Sometimes, everybody (except the winner) just “folds” before “the river card”.

      Presumably, they have bad hands, with a few aces or kings, let alone pairs. So those high cards are more likely to be in the community cards. But we didn’t see all five, since people folded.

      On the other hand, when everybody has a well equipped hand of private cards, more lower cards are left for the community pack, which then have a higher probability of being on the table at the end of the round..

      Players are egoists. They all rather play with a good hand of two cards, which slightly impoverish the community stack of five cards.

      Or the game ends even before the turn and the river cards are visible.

      Yes, when a big drama is going on, when everybody is waiting for what the final card is going to be … say that the player A is waiting for the fourth ace and the player B is waiting for the fourth 2 – the player B is more likely to get what he is hoping for.

  2. Welcome, as always, msjr!

    I wonder, if poker players are generally aware of this bias toward lower cards AFTER the flop? The flop isn’t biased, the turn and the river are. The river card (the fifth community card) even more than the turn card (the fourth community card).

    It is not only the bias toward lower cards, it is also an inherent bias toward more diverse cards in the community’s 5 cards. The turn card will rather be different from all three flop cards, than normally expected. And the river card will be more likely different from all previous four community cards, than it would be normally expected.

    The fact, that the game hasn’t been folded yet, influences the outcome. Toward the lower cards and toward the greater diversity.

    And also towards the likelihood of straights. But on much more complicated way.

    One could measure the statistical distribution of the river card and from it he could estimate the quality of players. The distribution of the river card would be very random, if all the players are very poor players.

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