Poker Articles

A Bit of Maths: Playing for a Pair
By Paul Samuel
(The UK's answer to Mike Caro or Lassie)

1. Introduction

Happy Christmas to one and all, I wish you all the best of fortune in particular at the poker table except in the case where I am a participant. I mean this quite sincerely, that's why I never apologise to someone when I outdraw them; I just make that famous wry Samuel number 7 expression that says. "Next time you will be doing that to me".

This has nothing to do with this article, nothing at all. This is a quick and curious article I have had on the back burner for a while. In playing poker especially on the internet or in low limit games anywhere you will often see people play trash hands in order to see the flop.

In particular I mean unconnected cards such as K2!

Lets put these hands in perspective. You can expand the concept and adjust your thinking accordingly. Or not!

2. Discussion & Analysis

Lets consider the range of hands 52 to K2.

Firstly what do you expect to hit if anything at all ?

Well 67.57% of the time you will flop, 'No Pair' and be done with the hand. (Ok, I know in the case of a 52 you have straight potential but for the sake of this article lets ignore this).

In all we have (a table) :-

Table 1 - Probabilties of hitting the flop

You can see that if we hit its most likely we will hit a pair and since pairing the deuce is not that exciting, lets focus on pairing the high card as our most likely good result. This will happen 14.48% of the time.

Now listen up!

I have mentioned the following concept here and will especially press the point on poker school on-line. I will impress this point again and again.

When you decide to see a flop. That is when you commit to play 2 cards you must understand the most likely positive result and when this result occurs continue your commitment to your hand!

For example, if you are a persistent 'suited card' aficionado, when you flop a 4 flush you must consider this flop a good flop and back up your conviction. Its no good at this point wimping out because your scared your opponent has a better hand. You are played poor cards in order to get reasonably lucky, not to get 'winning the lottery' type luck. If you play any 2 cards to hit 2 pair or better look at the previous table and if that doesn't put you off, give up poker and hit the roulette table.

Now coming back to the range of hands in question.

The most likely decent flop for you will be pairing the high card. Pairing middle or low is a classic trap situation (especially I imagine in limit). In this case its tempting to call a bet just to see if you can hit on the turn. The old "In for a penny, In for a pound" (as my dieting Granny used to say on her third doughnut). You can lose a lot of money drawing to that second pair or trips but now you are into protecting your investment!

Here's the table :-

Table 2 - Probabilities by Quality of Pair

To illustrate the table, if you play a 72 and pair the high card, 49.21% of the time you will have hit the second pair.

Furthermore, given that your high card pairs (our most likely good result), J2-K2 will generally flop top pair ! As expected the J is on the cusp. 72 to T2 will more than likely hit 2nd pair or bottom pair and quite likely turn you into a cash cow.

3. Summary Conclusion

The conclusion is simple, if you have to play trash unconnected cards (i.e. Big, littles) try and hold at least a Queen. If you must a Jack. The Doyle Brunson (T2) is best left to Doyle Brunson and 9's and lower are best left to the bin.

Me, I rarely play these cards anyway but if I do I will be playing the player and position. I won't sit down in a cash game and immediately start limping with such trash. I hope you enjoyed this year of articles. I've enjoyed writing them. Have a great New Year.