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I found this article to be very interesting but I would really like to get a clarification from the author.
In order to understand the math, I tried to plug in numbers from a trivial theoretical case. I tried to apply the math to a Heads Up game with no fee and a 50% win rate. Since there is no expected profit from this situation I would expect the math to calculate F* as 0. Here's how the math turned out: Assume 1000 games, 500 wins. Payout is 2 for 1'st place. <font class="small">Code:</font><hr /><pre>b = 2 * 500 / 500 = 2 p = 0.5 q = 0.5 F* = (2 * 0.5 - 0.5) / 2 = 0.25</pre><hr /> This is obviously wrong. I believe the problem is that b needs to be calculated differently. In the article, b is calculated in terms of earning rather than profit. I believe b should be calculated like this: <font class="small">Code:</font><hr /><pre>b = (2 - 1) * 500 / 500 = 1<font class="small">Code:</font><hr /><pre> The "-1" subtracts the tourney cost from the earnings resulting in profit. Now we get: <font class="small">Code:</font><hr /><pre>F* = (1 * 0.5 - 0.5) / 1 = 0</pre><hr /> Which is what I would expect. If I use this approach on the authors example: <font class="small">Code:</font><hr /><pre>(210 * (4.2 - 1)) + (238 * (2.5 - 1)) + (152 * (1.68 - 1)) / 600 = 1.89</pre><hr /> This will in turn result in: <font class="small">Code:</font><hr /><pre>F* = (1.89 * .40) - .60 / 1.89 = 8%</pre><hr /> Am I missing something? |
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