# How Short Should You Go?

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I’ve been thinking about the various short stack versus deep stack no-limit arguments lately, and I came up with a question that I wanted to ask you guys.

You’re playing a series of 6-handed winner-takes-all no-limit tournaments. The blinds start at $50-$100, and all your opponents start with $10,000 in chips each time. They all play fairly well, but none of them is a real standout. You play fairly well too, perhaps a bit better than them. You’ve been boning up on your short stack strategies lately, so you can be counted on to play fairly well with stacks of all sizes. The tournament structure is slow and doesn’t include antes at any level.

Which of these scenarios would be worth the most money to you?

- One entry into this tournament series with a starting stack of $10,000
- Five entries into this tournament series with starting stacks of $2,000 each time
- Twenty entries into this tournament series with starting stacks of $500 each time
- One hundred entries into this tournament series with starting stacks of $100 each time

In other words, you get $10,000 total in each scenario, but in the first scenario you get it all in one big shot, whereas in the other scenarios it’s broken up into chunks that you play over a series of tournaments. Every tournament has the same prize.

Note that I’m not talking about winrates, just which of these scenarios is worth the maximum in dollars. If you want to talk about winrate, you can rank them for winrates too, though I would suggest assuming that the next tournament starts for you immediately after you bust from the previous one.

I’ll post my thoughts in the next post, but I don’t think I have it completely worked out.

Tags: no-limit-holdem, poker, poker-tournaments, Short Stack Strategy

As I see it, there are two parts to this problem. One part is strictly math probabilities (which I can say a little about) and the other requires a lot of poker experience and judgement.

The basic math problem is, given that your probability of winning a tournament is P, what is the probability of winning 1 out of “n” tournaments? (You have four values of n, these are 1, 5, 20, 100)

Your chance of losing one tourney is (1-P). Therefore your chance of losing all n tourneys is (1-P)^n (that’s 1-P raised to the “n” power). So finally your chance of winning at least one out of n is 1-(1-P)^n. Multiply that by the prize and that’s your equity in the tourney, if it’s a “winner take all”.

If there are multiple prizes then you have to work out the same kind of formula for each prize, with different P values representing the probability of winning each prize. It’s a whole lot easier if you assume that it’s a “winner take all” tourney so you don’t have to do that.

That’s the easy part. Now you have to estimate P for the four cases of n. I assume that being short stacked is supposed to make your decisions easier, thereby having a positive effect on P. But then you have a shorter stack which has a negative effect. Whoever can work that out knows a heck of a lot more about poker than I do.