HIGH CARD BEATS A PAIR!

Last month we asked our Facebook Fans to answer the following question. From worst to best, what is the ranking of hands in 3-card poker?

  • 3 of a kind – straight – flush
  • Flush – straight – 3 of a kind
  • Straight – 3 of a kind – flush
  • 3 of a kind – flush – straight

The correct answer to this is “Flush – straight – 3 of a kind”, and of the 68 of you that answered, just 11 were correct, as can be seen here.

The vast majority (52 of those who responded) answered : Three of a Kind, Straight, Flush. This is hardly surprising as it follows typical hand rankings you’d find in any game of poker, such as Texas hold’em.

Three Playing Cards Blog 7mar12Alas, this is wrong, and at least one member of staff in the IFP office took some convincing, with all kinds of algebra, then simple pictures, scribbled on the back on an envelope to explain why.

The reason these rankings change is because the ranking of a hand is based on its probability.

For example, in five-card poker there are 10 possible straights, (A-5, 2-6, 2-7 etc…) with a possibility of four suits for each card making 10 x 45 – 40 = 10,200 possible straights. For a Flush there are four possible suits with five cards of that suit to be chosen from a total of 13. So, there are 4 x 1287 – 40 = 5,108 possible flushes.

It is therefore more than twice as likely that you will be dealt a straight as a flush – the straight is thus a less valuable hand when ranked.

This system gets interesting when looking at Texas Hold’em and other seven card games (two hole cards and five community cards). Here there is a 43.8% chance of getting a pair, while not hitting at all and making your hand a “high card” only is 17.4%. So strictly speaking, following the rules, high card should beat a pair.