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入正题：

An equity model is a method for estimating players’ equities, given the current chip stacks. In just a second we’ll introduce the Independent Chip Model, or ICM, the equity model which we’ll be using throughout this book.

Why does equity modelling matter more for SNGs than MTTs?

SNGs and Multi-Table Tournaments, or MTTs, are just different varieties of tournament. Equities could be produced for MTTs using the ICM, although the sums would be much more complicated. However, the differences between cash games and tournaments are more pronounced in SNGs than they are in MTTs, for two reasons:

Harsher bubbles in SNGs

The jump from fourth to third place in an SNG is 20% of the prize pool, a huge change in fortune which often has a dramatic effect on the correct play. No MTT has a bubble with that extreme a jump.

Payout structure

The top 30% of players in SNGs are paid. MTTs typically pay out to only the top 10-15% of finishers, with the top 5% collectively getting about 75% of the prize pool. This makes the MTT prize structure a lot more top-heavy. The more top-heavy a prize structure, the more the tournament should play like a cash game. Winner-take-all tournaments play almost identically to cash games.

Conclusion

In MTTs, equity modelling is both more complex to do mathematically and harder to intuitively approximate at the table, because payout structures differ so widely. Because using an equity model often doesn’t affect the correct play in MTTs, most authors of books about no-limit tournaments have chosen to ignore equity modelling and use simple pot odds calculations.

This won’t do for SNGs. Pot odds calculations often give answers which are wildly wrong, especially on the bubble. Using an equity model like the ICM is essential.

The Independent Chip Model (ICM)

The ICM is an equity model that works well for SNGs. This section describes the method used to calculate equities in the ICM. If you would prefer to think of it as a magic box where you put the current chip stacks in and get equities out, that’s fine – skip to the section on ICM tools.

Suppose in a standard SNG, three players remain - A, B and C – with stacks of 10000, 6000 and 4000 respectively. We assume that all players play with equal skill. The process starts by assigning them a first place finish probability equal simply to the percentage of total chips in play contained in their stack. So:

A: 50%

B: 30%

C: 20%

Now we take each of those possibilites in turn, and mentally eliminate the player from the game, leaving two players. Then we repeat the original process for second place. So taking A first, if we eliminate A from the game, that leaves stacks of 6000 and 4000, with 10000 total chips. That means that along this branch, B finishes second 60% of the time and C 40% of the time. However, we want to know the probability of this finish sequence as a whole. A only finishes first 50% of the time, so to get the overall probability, we need to multiply the B and C second place finishes by 50%, giving:

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