News: Quick MTT bubble math
Dara O’Kearney with a ‘gorilla math’ method for working out how strong you need to be to call an all-in on the bubble.
Those of you who read my first book will be familiar with the term “gorilla maths” to describe a simplified version of complicated maths that can be done at the table as an approximation for satellites.
In regular tournaments ICM is a complicated calculation of how many times a player comes 1st, how many times they come 2nd when another player comes 1st, and so on. In a satellite ICM is practically a calculation of how often all the players can mincash, so it is much easier to simplify satellite math.
Having said that, I am now going to explain a gorilla maths method for determining ranges on the bubble of a regular tournament.
Say we have a 500 runner tournament that pays 60 players, and the mincash is 2 buy-ins.
That means with 60 players left, everyone in the field is guaranteed a 2 buy-in mincash (120 buy-ins in total shared between 60 players), and their “share” of the remaining prize pool (380 buy-ins total yet to be won) is in direct proportion to their share of the chips. This is a simplification. Usually the big stacks have a slightly smaller share of the pool than their chips, and the smaller stacks a bigger share, but it’s close, and we are not computers that can calculate exactly so we just want a decent approximation.
So the equity of someone who gets through the bubble with a starting stack can be calculated as:
- 2 buy-ins (the guaranteed min cash)
- Plus One 500th of the other 380 buy-ins (.76 buy-ins)
Total 2.76 buy-ins.
The equity of a player with 2x starting stack using the same method is equal to 3.52 buy-ins.
That means if a player with starting stack gets it in on the bubble they are risking 2.76 in buy-ins in equity to gain .76.
2.76/(2.76+0.76) = 78%
So he needs to be 78% favourite roughly. Here’s the equity of strong hands versus different ranges:
Against any 2 cards
- AKs 67%
- AKo 65
- AA 85
- KK 82
- QQ 80
- JJ 77
So even Jacks not a get in here on the bubble despite being up against a 100% range.
Against top 20% of hands
- AKs 64%
- AKo 62%
- AA 86%
- KK 72%
- QQ 69%
- JJ 66%
Here we need Aces!
It’s not perfect but we roughly get to the same outcome that a solver gives us in these spots. Try it out for yourself and let me know how you get on.
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