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Are Advanced Round Entries Fair?

Posted By: joe freedman
Date: Wednesday, 31 March 2010, at 10:23 p.m.

In Response To: Are Advanced Round Entries Fair? (Steve Mellen)

Steve is right, as usual (if not always). It is clearly in the interest of a WEAKER player to buy into a later round. For the sake of simplicity, suppose Mr. Fish, who wins approximately 40% of his matches, has the option of paying $1 to enter the first round of a field of 8, $2 to skip to the field of 4, and $4 to skip to the finals.

In case 1, Fish's chance to win the tournament = .4 x .4 .4 = .064 When he wins, he will receive $8, so he has paid $1 for an equity of .064 * $8, or $0.512. So he gives up appx 49% of his entry fee by entering in the first round (compared to not entering at all).

In case 2, Fish's chance to with the tournament = 4. x .4 = .016. By buying into Round 2, he increases his winning chance by a factor of 4, while paying only double. When he wins, he again receives $8 (including his entry fee), so he has paid $2 for an equity of .16 * $8, or $1.28. So he gives up appx 36% of his entry fee by entering in the second round (compared to not entering at all). Of course, in absolute dollar terms, he would do better to enter in Round 1. But he would also do better to simply give the Tournament director 25 cents and skip the event.

In case 3, Fish's chance to with the tournament = 0.4. By buying into Round 3, he increases his winning chance by a factor of 16, while paying only quadruple. When he wins, he again receives $8 (including his entry fee), so he has paid $4 for an equity of .4 * $8, or $3.20. So he gives up 20% of his entry fee by entering in the third round (compared to not entering at all). Of course, in absolute dollar terms, he would do better to enter in Round 1. But he would also do better to simply give the Tournament director 25 cents and skip the event.

Fish's best strategy would be to buy the Championship, which would guarantee 100% return, less the rake (which has not been considered above, but should affect all scenarios equally, I think).

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