Thursday, December 06, 2007

Cash Value Of Tournament Chips

After reading KODs excellent post on the matter, I thought I would put some hard numbers behind the concept of "Cash Value of Tournament Chips". First off, I love the pure economics argument that because you can't simply cash out your MTT chips for their face value, they can't be worth face value. Its amazing what you can prove using economics alone. So I wanted to look at a couple of examples and put a cash value on MTT chips. The two examples will be a single table S&G and the 50/50 tournament on Full Tilt.

Example #1: $10+1, 9-Player S&G, 1500 starting chips.

You pay $11 for 1500 in chips.
Initial cost = $11/T1500 = $0.007333

So $1 in MTT chips is worth less than one cent when the thing starts.

If you accumulate all of the chips and win the S&G you will win $45

End Value of chips $45/T13500
Final Value of all chips = $0.00333333

A couple of things to notice right away is that the rake of an MTT comes right out of the value of the chips, and the chips will always be worth less at the end than what you paid for them initially.

Example #2 50/50: $50+5 buy-in, 1000 entries, T2000, $10,000 for 1st

Initial Cost of Chips $55/T2000 = $0.0275
Final Value of Chips $10,000/T2,000,000 = $0.005

So as you can see the value of the MTT chips will be less in the end when you win the MTT than what you paid for the chips. So as KOD points out, taking a coinflip early on in an MTT or a S&G is a -EV move for those who coinflip, and +EV for the others at the table who do not. Doubling your chip stack does not double your cash amount because MTT chips lose their value over time.

There is a huge problem with this argument. Do you guys see it? This argument ignores all of the positions that win cash in an MTT or S&G after they have lost all of their chips. All the non-first cash finishers, got paid cash and had zero tournament chips after busting out. Since they won cash without any chips, the value of the chips to them is actually infinite. If you combine the infinite value of chips for the bustouts with the reduced value for the winner, the chip values really do not change over time in an MTT. You take a hit in the beginning based on the rake, but that's it. Doubling-up early effectively doubles your projected cash amount in an MTT. Think about the Sit and Go example with "average play" from everyone at the table. Basically average play means that the blinds are getting distributed around the table in general. So when you double your stack to T3000 early you now have the average stack for when 1/2 of the field is gone. Assuming that you can maintain that stack until the point where the other 1/2 is actually gone, you really did just double your chances. I think the greater point that KOD was getting at is that MTTs are not very fair to the winner, in that they are not winner take all, even though the winner gets all the chips. So the winner of an MTT or S&G really does not get all of the EV they are entitled to by the plays that they made. However, this is offset perfectly by the people who were eliminated and still won cash.

So whats the moral here? Play for second place is as +EV as it gets in MTTs!



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