Poker Articles

A Bit of Maths: Short Stacked Tournament Strategy - For Beginners
By Paul Samuel
(The UK's answer to Mike Caro or Lassie)

1. Introduction

As discussed in the last article, a lot of inexperienced or passive players suffer in tournaments by waiting for the opportunity to double through when low stacked.

We analysed the concept mathematically and came to the conclusion that by the time you decide you need to double through it is too late and the time when it is favourable, it is too early !

In other words the concept produces a paradox or contradiction.

2. Discussion

You see the good (and good always means aggressive) player will instinctively accelerate his game to maintain a healthy stack size. We said that 17 x SB is a critical point and you watch the good player in such a position. Stealing blinds, re-raising weak calls etc etc.

If you have say 17 x SB, stealing the blinds is still a modest gain in stack but more importantly gives you a free round in which to find a better spot.

The good player will not be seen waiting around to be visibly crippled nor will he diminish his stack size with hopeful calls and unwise peeks at the flop.

Here's the rub :- "The measure of your performance in a tournament is directly proportional to the number of uncontested pots you win"

You see in an uncontested pot, your Aces cant get cracked, your set can be outdrawn to a flush etc etc. You can't lose - that's what uncontested means.

An aggressive player wins a lot more uncontested pots. He's constantly raising and re-raising and betting into scary flops. He gains a lot of chips without a showdown.

3. Analysis

This is more art than science and we are going to use an unusual model. Lets use four base parameters as they apply to a sequence of hands of tournament play related to a particular playing style :-

3.1. Probability of going all in and being called

For each player style we shall estimate the chance that he/she goes all-in and is called.

3.2. Probability of being beat thereafter

Given the above i.e. that the players all-in has been called, what's the chance the player gets beat.

3.3. Probability of calling a bet all-in

For each player style we shall estimate the chance that he/she calls a bet all-in.

3.4. Probability of being beat thereafter

Given the above i.e. that the player has called a bet all-in what's the chance he/she gets beat. Lets work the figures for three playing styles :-

Loose, Tight and strong.

Now here's the bit some of you will love to hate but remember this. These are guesstimates and we can choose any figures we like. Here's my choice :-

Table 1 - Base Probabilities of all-in pots

	Probability of going all in and being called.	Probability of being beat thereafter.	Probability of calling a bet all-in	Probability of being beat thereafter.
Loose	5.00%	35.00%	3.00%	25.00%
Tight	2.50%	25.00%	2.00%	20.00%
Strong	1.00%	30.00%	2.50%	5.00%

This table is in actuality a table of probabilities to determine how and when a type of player exits the comp ! (You've got to be all-in to do that !)

Now we can estimate the probabilities that each player will survive a given number of hands which dealing at 40 hands per hour also gives the equivalent stats based on playing time thus :-

Table 2- Table of Odds

Hands	100	200	300	400	500
Time	2.5hrs	5.0hrs	7.5hrs	10.0hrs	12.5hrs
Loose	19.4:1	416.3:1	8525.1:1
Tight	2.2:1	9.3:1	32.0:1	104.8:1	338.5:1
Strong	0.6:1	1.6:1	3.3:1	6.0:1	10.3:1

Table 2 Continued- Table of Odds

Hands	600	700	800	900	1000
Time	15.0hrs	17.5hrs	20.0hrs	22.5rs	25.0hrs
Loose
Tight	1087.9:1	3491.8:1
Strong	17.3:1	28.8:1	47.4:1	77.6:1	126.6:1

Please note that the red squares represent odds of greater than 9999 : 1.

Ok, its confusing so to illustrate :-

I am estimating that a loose player, because he is loose raises all-in quite a lot but also gets called quite a bit for the same reason. My estimate is 5.00% that he goes all-in and is called. (see row 1 column 1 of the grid) and 35.00% that he is beat thereafter (he's loose remember).

Also as another illustration, we're saying roughly that a strong player is 126.6 : 1 to win the world series (i.e. survive 1000 hands).

4. Summary Conclusion

For all you beginners, it's simple. Learn to become a strong/aggressive player and you will get a lot further.