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Poker Life: Transitivity in Poker

Thu, Apr 27, 3:58pm by Poker Guru

In mathematics there are something called transitive relations. One classic example is that if A > B and B > C then A > C. Poker is a complex game and some things are transitive and some are not. One example of transitivity is the hand ranking. If hand A beats hand B and hand B beats hand C, then hand A must beat hand C. Am I boring you already? Sorry, it is the math geek in me. I promise it will get more interesting.

Transitive relations are pretty intuitive but let us look at some examples of relations that are not transitive. One classic poker example is that in an all-in situation pre-flop AK is a favourite against JT, JT is a favourite against pocket deuces but AK is not a favourite against pocket deuces. Have you seen this example before? If not, I am sure it is a little mind-boggling.

AK is a 62-63% favourite against JT (depending on the suits), JT is 51-54% favourite against 22, and 22 is a 51-53% favourite against AK. Do you have any practical use for this knowledge at the poker table? Not really.

You can use it to make some money from your friends though. Put the above three hands on the table, ask one of your friends to pick the hand he likes the best and then you pick the hand which is a favourite over your friend’s pick and bet him 20 dollars you will win. Then you deal a flop, turn and river and hopefully win the bet. At least you will be the favourite.

Warning: Do not do it three-ways though. In a three-way all-in situation with the above hands AK is the favourite.

How about players? If player A is better than player B and player B is better than player C, does that mean that player A will beat player C? Not necessarily. Poker is a very complex game, and player C’s style may not fit player A. Of course, if player A is Phil Ivey, player B is you or me, and player C is a beginner, then the relations are definitely transitive.

If player A is good at adapting to different playing styles he should be able to beat both player B and C. But suppose player A and B play in the same regular home game, and player A is the strongest player in that group. Then there is no reason for player A to change his style—he has found a style that works well in that game. Against a random group of players, player B might still be the stronger player.

You do not need to be good to make money from poker. Just make sure that you are better than the players you play against.


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