Poker Articles

A Bit of Maths: To add-on or not -part 2
By Paul Samuel
(The UK's answer to Mike Caro or Lassie)

1. Introduction

I was watching WPT2 on challenge TV when the following hand came up. The chip leader on the button called a raise in the final of the no-limit event with an A3 off-suit. To be more specific the JJ had raised early, got one caller and the A3o on the button called.

In my opinion the play was very poor as was evidenced when the JJ lead at the Ace high (and ragged) flop (A72 say), the first caller folded and after a pause the button did too !

What was the point of calling in the first place ? None it seems. Lets reverse engineer this hand.

2. Analysis

In a strong field, you must assume that the original raiser will lead on almost any flop ! If he checks the flop its is either because he has flopped a monster (which is still bad news) or just possibly that the flop is a complete nightmare.

For example :-

Case 1: Flopping a monster such as raising with JJ and a flop of J72 - personally I would probably lead at this flop but a check is ok too

Case 2: A horror flop such as raising with 99 and flopping AKQ - in this case betting into two players could very likely illicit a call or even a raise.

The point is the 'button' cannot count on a friendly 'case 2' scenario. It's so rare !

Without considering position for the moment and allowing that we (the button) will be faced with a bet on the flop, the button will have the following good flops:-

Table 1 - Good flops

The relative probabilities of each flop are:-

Table 2 - Relative Probabilities

By illustration, what we mean by 'relative' is that 'if the button flops something' 79.54% of the time it will be a simple Ace high flop.

Adding a column for absolute probabilities we have:-

Table 3 - Complete Flop Probabilities

What we are saying is that if you must call the raise on the button with A3 then an ace high flop better be good enough to play because most of the time that is as good as it gets !

However, as was evidenced in WPT2 the flat call is in fact poor. Personally I would have passed but if the notion to play the hand is strong I would at least re-raise either before or on the flop.

Lets look at the hands that the raiser may have, say:-

Table 4 - Possible hands for the raiser

Now imagine two scenarios; one where the button raises pre-flop and two where he raises on the flop and split this across three classes of player in increasing degrees of 'tightness':-

(Assume the JJ has a reasonable stack)

Table 5 - Raise analysis

nb. Cells without a 'N' or 'Y' mean in my opinions such a player will not play this hand for a raise pre-flop.

As an example we are saying that with the most aggressive player, 68.35% of the time a re-raise on the flop will lose him !

On average (i.e. for all classes of player) , 43.96% of the time we can lose the JJ with a re-raise pre-flop but 68.11% of the time we can lose him in this way on the flop.

3. Conclusion

In conclusion, play the A3 (for this scenario) in this way in order of preference:-

1) Pass

2) Call the raise pre-flop and re-raise on the flop.

3) Re-Raise pre-flop

The way it was played is just a waste of chips !