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Vegas Super Jackpot Entry Round

Posted By: Chuck Bower
Date: Tuesday, 31 March 2009, at 4:39 p.m.

In Response To: Vegas Super Jackpot Entry Round (David Rockwell)

OK, let's say you have $2k to 'invest' and your goal is to have the maximum amount (expectation-wise) after this Masters' event. Now let's make some assumptions:

0) there is no alternate investment method for any part of your $2k (like poker, blackjack, chouettes...).

1) you can enter either the round of 32 or the round of 16, but not both.

2) the round of 16 bracket will be full.

3) it costs twice as much to enter the round of 16 as the round of 32.

4) the rake is 5% (i.e. 95% return).

5) you have the same probability to win any match. (Obviously this isn't true but unless you want to do a serious simulation or a lot of handwaving, you have to make some simplifications. This assumption is about as simple as it gets but the answer, as you will see, has some meaning.)

Define the variables: F = full entry fee for round of 16. E = expectation when in the round of 16. (Note: E > 0, even if you're hopeless. However, E not necessarily > F for a typical player.) p = probability of winning each match you play.

It is correct to enter the round of 16 (as opposed to the round of 32) if the following equality holds:

E > p*E + F/2.

(RH side of inequality is expectation after entering round of 32 plus the half entry fee -- which you still have in your pocket.)

Note that assumptions 4 & 5 lead to: E = 0.95*p^4*(16*F).

Now if you turn the above INequality into an equality and combine the two equations you can solve for the breakeven value of p, although it's a 'quintic' equation (highest power of p is a 5), not easily solved (AFAIK). With a calculator, however, you can do a bit of iteration to find p.

Doing that I get 50.87% as the breakeven (uniform) MWC. So if you win more than that it is correct to enter the round of 16 as opposed to the round of 32. That number is (surprisingly, to me) small. Compare it to what is required to make up the rake if entering the round of 16 [solve 0.95*p^4*16 = 1]: 50.65%. So there is a small zone (between 50.65% and 50.87% MWC) where you have an edge by entering the round of 16 but are better off entering the round of 32. (Again, NEVER lose track of the assumptions made in reaching your conclusion.)

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