Poker Articles

A Bit of Maths: Weak Tournament Play from the Small Blind, by YT
By Paul Samuel
(The UK's answer to Mike Caro or Lassie)

1. Introduction

I hope you are reading my lessons in Poker School on-line.

I wish I had taken a bit more notice of them last week in the £20 rebuy comp at Luton.

It's the old uncontested pot thing again; I've discussed this concept several times. Its so important in pot limit and no limit hold'em. In fact the concept is more important in no limit hold'em than any other game.

So, what did I do ?

J9 in the SB with the blinds at 100, 200 and my stack at around 1200. UTG limps and drags in another caller from a middle seat. The button cant resist and I flat call. The BB checks ! It's a 5 way pot and no one has a massive stack.

The flop comes J high (J62 say) and I move all-in. The QJ under the gun calls immediately and I exit the comp under a cloud the size of Greater London.

Instinctively I felt that I played very weakly. Lets look a bit closer.

2 Discussion & Analysis

Be careful of retrospective wisdom. It is often wrong but my strong feeling in this case was that I should have moved them in before the flop. Ok if someone had limped early (and realistically the UTG was the likely candidate) with a monster I would be caught but considering the stack sizes I was up against (no one with big chips) it would be reasonable to have expected a big hand to declare itself pre-flop with a raise.

The question is can we evaluate the chance that a pre-flop raise would have won me the pot there and then. If this is true then of course this is the preferred result. I mean we would have made a 800 profit, a 66% increase - good enough and still in the comp.

Lets look at a table of hands that people will typically limp with in this situation :-

Table 1 - Hands to limp with

A9o

A8o

A7

A8-A9s

A2-A6s

KQ

KJ

KT

K9

K8s

QJ

QT

Q9s

JT

J9

88

77

22-55

56-9Ts

Now the hands highlighted in red are important !

These are the hands that I consider to be those that a player might call my pre-flop allin raise with. This takes into account this particular case where no one had mounds of chips.

Now bearing in mind the following table is not absolutely correct mathematically, look at this :-

Table 2- Chance of the preflop raise being called.

	1 Plyrs	2 Plyrs	3 Plyrs	4 Plyrs
0 calls	74.90%	56.09%	42.01%	31.46%
1 calls	25.10%	37.60%	42.25%	42.19%
2 calls		6.30%	14.16%	21.21%
3 calls			1.58%	4.74%
4 calls				0.40%
Any Call	25.10%	43.91%	57.99%	68.54%

It's a good approximation and in particular we are interested in the last column because that is the situation under discussion. The last column tells us the probability of our preflop all-in being called with four opponents.

For example, there is a 68.54% chance we will be called by one or more players in this exact situation !

But...

The only call which ends up being a bad one for us is the KJ and this only occurs 26.67% out of all possible calls !

Even with two callers, the chance of one of them being a KOJAK is 46.22% ! We still are slight favourites for our top pair to be good once the cards are down !

Lets skip to the summary, I am sure many of you have already !

2 Summary Conclusion

Its clear that I should have moved all-in before the flop.

31.46% of the time I would win it there and then.

42.19% of the time I will get one caller but there's only a 26.67% chance that he is calling with a KJ and the other calling hands are all good for me once the flop is flopped.

Even if I get two callers, which according to our estimates occurs 21.21% of the time, there is less than a half chance (46.22% actually) that I have caught an unlucky KJ !

In this actual case, the QJ would have folded pre-flop to my all-in bet and history shows there would have been no other callers.

I would have still been in the comp with a stack increased to 2000.

Bad play by me.

Its these fine decisions that make the difference between success and failure in poker.

In my last article in the poker school I described how I split joint 2nd in a recent comp with almost no luck and no hands. I just consistently made good decisions with poor cards.

Let the example here be a warning to us all especially YT !