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How To Play Pocket Fives

The Math Behind Making a Marginal Call

Read the situation below and think about what you would do in this no limit holdem poker situation

The Setup

Blinds are 50/100. You have 2130 in chips. The small blind who has suffered a couple of bad beats an hour ago and hasn't been in a hand since has 510 in chips.

You have pocket fives.

A player in front of you limps in and you smooth call. The small blind goes all in. The guy who limped before you folds.

Do you call or fold?

Analysis

First instincts would say to get out and take the 100 loss, however let's analyse the hand more closely.

Pot odds

There was 150 in the pot before the action had started; with the one limper and your bet there is a further 200 in the pot.

Currently the pot is at 350. Once the small blind goes all in there is 810 in the pot and it's now 410 more to you - so you are currently getting 2-1 on your money if you call.

Concentrate, Here Comes The Science Bit

You have already labelled this guy as a conservative player who had a few bad beats, so therefore he's not on a bluff. Not to mention the fact that he still has enough to see another three rounds of hands before committing all his chips so he doesn't really need to go all in here with a marginal hand.

Here's where we put him on a hand and work out how we'll do against him.

• If he's on a higher pair than our fives then we are a 4.5-1 underdog.
• There are 9 pocket pairs higher than our fives and with 6 ways of making each pair that gives us a total of 54 hands where we are an underdog.
• If he's on two high cards such as AK, AQ, AJ, KQ, KJ, QJ then we are a slight favourite (55-45).
• There are 16 ways to make a hand like AK (12 unsuited and 4 suited) so with these six hands (x 16 ways), there are 96 hands where we are slight favourite.
• This gives us a total of 150 hands he could have.
• We're a 4.5-1 underdog on the 54 pairs so we would expect to win around 10
• Plus we are a slight favourite to win over half of the 96 over cards - so we'd expect to win around 52 of the hands.

Added together that gives us a projection of 62 wins with 88 loses - therefore our 2-1 on our money is a very good call. This is a good investment, not to mention the fact that it will mix up your play showing that you are happy to call an all in (if the odds are there) with something like pocket fives.