Poker Articles

A Bit of Maths:
Flopping A Set
By Paul Samuel
(The UK's answer to Mike Caro or Lassie)

1. Introduction

   I had been playing in Finland & England (on and off) and the other night I was having a pre- tournament dinner in Luton when 'M' asked my table's opinion on the following. I apologise if some details are hazy, but the principle is what is of interest.

   M: 'I was playing in a pot limit hold'em comp and had just sat down at a new table when I found myself with 4 4 in the BB. A mid-position player raised and I called for the remaining bet. The flop came down T 9 4. I checked and so did he.

   The next card was a second heart. I bet and he thought for a long time and called. The A came on the river. I bet all-in and he thought for ages and called with two raggy hearts, making his little flush.'

   The standard procedure when flopping a set is to lead out. Let see...

2. Flopping a set

   Clearly with this drawing flop, and given that you have no information about your opponent, your only purpose in checking this flop can be to set yourself up for a check-raise. M's opponent can have anything, and let's face it - he did!

   Let's list possible groupings of hands the opposition may have :-

   1. Killer Hands
      Simply TT or 99.

   2. Betting (and raising) Hands
      Hands such as AA or T9 where he will bet to your check or quite likely move all in to your bet.

   3. Steal (and folding) Hands
      Hand such as AK (not clubs) where he may well bet to your check but will fold to your bet.

   4. Strong Drawing hands
      Hands such as KQ.

   5. Weak Drawing Hands
      Hands such as Q8.

   6. Back Door & Trash
      Everything excluding the above!

   Now it seems to me that the purpose of checking the flop is to induce a bet that we would discourage by leading out.

   In the absence of any information, we must assume that our opponent is a good player and will only make an 'unfortunate' bet with hands that fall into the following categories :-

   • Steal (and folding) Hands

   • Weak Drawing Hands

   In all other cases, whether we bet or not makes no difference! Think about it!

   Now let's count the hands...

   Table 1 - Hand count

   

   Table 2 - Summary probabilities

   

   We see that the two cases here where our check is likely to induce a semi-steal occur 44.68% of the time.

   In any other case, it either makes no difference or we are giving an unnecessary free card! I can't actually draw a conclusion from this. After all, this was a competition and the idea is to win. The opponent had more chips than 'M'. 'M' also had substantial chips, so I feel he should have bet. An expectation of less than half just isn't good enough when you are in good chip position.

   He didn't need to gamble!

   Thanks for your attention,

   Paul Samuel