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A Bit of UFA Maths

UFA

Introduction

Whilst losing my money on Paradise Poker recently, I found myself considering an interesting problem. In the UK, we play mostly pot limit and it is clear that pot limit hold’em and limit hold’em are two completely different games.

One difference in limit hold’em is playing out of the same blind. Clearly in a multi-way pot, there is a temptation to call with trash from the small blind. Who wants to go through the agony of throwing away a 38 offsuit and the flop coming down A88? It happens all the time to me. Of course, in my case, the big blind is always slow playing AA.

Anyway, there is the introduction. Let’s get on with the analysis.

Calling from the small blind.

Firstly, we must make some assumptions about what constitutes a good result and calculate the probabilities of achieving this.

We shall define two broad styles of play, loose and NOT loose (i.e. tight).

Lets say a loose player is a player who will consider certain additional flops as good and doesn’t care if there is a subsequent raise.

The tight player will regard a subsequent raise as a bad result. As a base, we shall consider the probability of a subsequent raise to be 10.00%.

Let’s consider two hand types, 27 and 56, and look at the suited and non-suited cases against our loose/tight players.

2.1. 27 offsuit for the loose player.

The loose player considers a positive result to be flopping a set, a full house or two pair and doesn’t care whether there is a subsequent raise.

See how this trash hand requires pot odds that CANNOT be met? 26.17 to 1 would require 12 additional limpers to give the required pot odds.

2.2. 27 offsuit for the tight player.

The tight player as stated, considers a subsequent raise to be a bad result and as you can see he requires even worse pot odds of 29.19 to 1. Pas Possible!

2.3. 27 suited for a loose player

You can see what I’m trying to do here. I’m saying that a loose UFA player considers flopping a four flush as being a good result! For me (as a rule) that’s loose.

Even given this latitude, he requires pot odds of 5.17 to 1 to justify his cavalier attitude. He needs two limpers after the big blind to justify the call. Of course, this can happen.

2.4. 27 suited for a tight player.

The tight player excludes the four flush, thus…

27 suited-loose

He needs 11 limpers after the BB to achieve the 23.28 to 1 pot odds required. NO WAY rocky.

2.5. 56 suited for the loose player

56 suited-loose

Clearly the pot odds are (even without a limper) at least 3 : 1 (for the extra half bet) so for the loose player the call is always justified for this hand.

2.6. 56 suited for the tight player

56 suited-loose

We’ve dropped the four flush and four straights for the tight player. This means we need 8 additional limpers. Throw ’em away Sylvester!

2.7. 56 offsuit for the loose player

56 offsuit-loose

The pot odds are too large. 12 other limpers cannot be.

2.8. 56 offsuit for tight players

56 offsuit-loose

Here we have our additional 10% factor for the case where there is a subsequent raise. This makes the case even worse. 14 limpers required. Get a bigger table.

Summary of Results

You must admit it’s quite interesting. For the more conservative player, even the suited 56 appears to be unplayable out of the small blind (according to our definition).

Ok, I know many thousands or even millions of loyal readers will be sending me friendly messages about all the considerations I have not made, but…

It’s still food for thought. I have a feeling that erring on the side of caution will save me a lot of money.