Poker Articles

A Bit of Maths: Playing the Weak Ace
By Paul Samuel
(The UK's answer to Mike Caro or Lassie)

1. First thanks to Barbara Yoon

Article 15 had a slight Mathematical error. Only a little one but in Maths 'near' doesn't count. The above lady pointed out the error and although her corrected answer was also slightly incorrect it still inspired the corrected version :-

Table 1 - Probabilities of facing JJ or better (against the blinds when you have 22 on the button)

2. Introduction

This may form a series of articles. Its an important subject.

How many times have you folded your weak Ace (correctly) only to hit the flop and win a virtual pot?

Many times if you play poker!

As a rule those weak aces are trash. Really! We cannot analyse every variation but we can look at the cold stats for hitting the flop.

This is a truly cool article and at the end the maths will give a clear test question you can ask yourself when playing these 'trash' hands.

Let's go.

3. Playing the Weak Ace

Lets start with a suited A2. Say A2. How often are we tempted to take a peek at the flop with this hand?

Too many I feel.

Let's look at all the flops where we hit something and categorise each hit as either a good hit ('N') a trap hit ('Y') or a either/or hit ('B'). (Sorry about the notation it just grew on me like a wart).

Here's the breakdown:-

Table 2 - Hit flops for suited Ace

Lets pick a few rows to explain.

We say (row 1) that if you hit two pair and the flop is not suited like A 2 7 . You have hit a good flop.

If the flop is we say you have hit A 2 7, albeit a trap flop.

Now consider row 3. (4 flush {no pair}), like K 8 3 . We are calling this a 'B' or borderline flop. Yes you have the nut flush draw but this only comes about 1/3rd of the time and you may lose the lot drawing against a pair of kings.

The 'N' column is the number of distinct ways such a flop can be drawn and the 'P' column is the probability that it happens.

Now let's see what all this gives us:-

Table 3 - Summary of A2 suited

If we tip our marginal ('B') hand as favourable then we are a 2.91 : 1 dog to hot a good one. If we decide that our marginal flops are traps then we are a 26.07 : 1 dog to hit a good flop.

THIS IS THE RUB.

Before you play this hand ask yourself, "Are the marginal flops good or bad for me?" or in this example:-

"If I flop a 4 flush or top pair, am I happy?"

If the answer is 'No' then you are a massive 26.07 : 1 underdog to hit your flop. Throw it in the muck, the pot odds cannot be that good.

Now for an A2 offsuit we have (and I'll be quick)

Table 4 - Stats for A2o