Poker Articles

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

1. Introduction

I am so rushed this month. Really late with this article and dithering over what to write about. Running three businesses, playing poker, six kids, blah blah blah.

Do you like the new pic. OK I confess the other one was taken over 20 years ago so I thought I would come clean.

The number of times you judiciously see a flop is very important in Hold'em. I mean, before the flop you know 2/7th of your hand and on the flop you have 5/7th of the story !

A lot of people discuss the merits of the various starting pairs and this is what we shall do today.

2. Discussion

The question I asked myself in proceeding with this analysis is what constitutes a good (or at least reasonable) flop for a pair. I came up with the following categories :-

2.1. Set

Lets say you hold 99 and the flop comes 9JA you still have to rate this hand. If someone has flopped a flush you still have a draw and not a bad one.

So I allow that if your card falls - it's a good flop.

2.2. Quads

Nuff Said

2.3. No overcards and no opposing 3 flush

As an example if you hold 66 and the flop is 224; we class this as a good flop but if you hold KK and the flop comes 976 this is classed as a bad flop.
See the category below as it is a special case for smallish pairs (22-JJ) where any 3 flush is considered poor.

2.4. No over cards and no 3 flush

As an example if you hold 66 and the flop is 224; we class this as a good flop.

2.5. One over card, not AK & no 3 flush

We are saying here that if you hold 99 and the flop is 27Q this is still a good flop whereas if the flop were 27K, because of the popularity of the Ace and King this flop would be poor. Also 27Q would be a poor flop for 99.

2.6. Two or more over cards, nut straight draw & no 3 flush

If you hold 99 and the flop comes 8TJ, we are going to class this as good (ish)!

3. Analysis

Straight into the famous table :-

Table 1 - Probabilities of Hitting a good flop

Hand	Set	Quads	No over cards and no opposing 3 flush	No over cards and no 3 flush	One over card, not AK & no 3 flush	Two or more over cards, nut straight draw & no 3 flush	P
AA	11.51%	0.24%	86.00%	-	0.00%	0.00%	97.76%
KK	11.51%	0.24%	65.89%	-	0.00%	0.00%	77.64%
QQ	11.51%	0.24%	49.18%	-	0.00%	0.31%	61.24%
JJ	11.51%	0.24%	-	34.71%	12.12%	0.61%	59.20%
TT	11.51%	0.24%	-	24.16%	19.10%	0.31%	55.33%
99	11.51%	0.24%	-	16.00%	21.86%	0.31%	49.92%
88	11.51%	0.24%	-	9.92%	21.31%	0.31%	43.29%
77	11.51%	0.24%	-	5.61%	18.37%	0.31%	36.04%
66	11.51%	0.24%	-	2.78%	13.96%	0.31%	28.80%
55	11.51%	0.24%	-	1.10%	9.00%	0.31%	22.16%
44	11.51%	0.24%	-	0.29%	4.41%	0.31%	16.76%
33	11.51%	0.24%	-	0.02%	0.00%	0.31%	12.08%
22	11.51%	0.24%	-	0.00%	0.00%	0.31%	12.06%

The 'P' column is simply the probability of seeing a good flop for the pair in question. For example a 99 yields a decent flop 49.92% of the time.

4. Summary Conclusion

Generally and taking no particular special circumstances into account :-

1. With 99-AA raise to get heads up; otherwise look for a multiway pot.
2. Play pairs similarly as colour grouped above. For example play TT,JJ and QQ the same before the flop. When the flop is flopped it will yield roughly the same number of good results for any of these pairs.
3. Consider 99 to be the middle pair !