Bad Beats - Myths and Mathematical Regularities

One of the most discussed topics in the poker community is bad beats. Let's start with a...

 

... definition:

A "bad beat" (thus, a hand which you lost in a very unlucky way) – is when a player with a hand that is very likely to win (as a rule with a probability of winning significantly greater than 80%) still loses in the end.

  • Here's an example:

Player A has :Ah:Ad. Player B has :Ac:Kh. Both players go all-in before the flop. The probability of player A winning the hand is just under 93% before the flop. In other words, the pair of aces will win in 93 out of 100 cases.

Let's assume the flop is :7c:Jh:Js.

Now player A is even a 98% favourite to win with his aces. Player B needs the next two cards to be a ten and a queen (to make a straight), two kings for a full house, or the two remaining jacks for a split pot (which would then be quads with an ace kicker). If the next card is not a face card or a ten, player B can no longer win the hand.

The turn is the :Kc.

The aces remain a clear favourite to win, at 95.5%. But the probability has been reduced somewhat, as one of the two remaining kings would now complete player B's full house.

And indeed the river brings another :Kd. Ouch! So player B really has won the hand after all. Witchcraft?...