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BGonline.org Forums
Are Advanced Round Entries Fair?
Posted By: Steve Mellen In Response To: Are Advanced Round Entries Fair? (Bob Glass)
Date: Wednesday, 31 March 2010, at 9:26 p.m.
Let's say he spends $8,000 to enter the semifinals instead. 70% of the time he will win the semifinals and have equity of $22,400 as you calculate, so his equity is $15,680. That's $7,680 in profit, which is actually more than the $6,400 in profit he gets by entering straight into the finals... and of course his ROI is much higher in my scenario than in yours, because he's basically doubling his money.
Back it up another step. If he pays $4,000 to enter the quarterfinals, his equity is 70% * $15,680 or $10,976. Now he's getting close to tripling his money.
If he pays $2,000 to enter the second round, his equity is 70% * $10,976 or $7,683. That's almost 4 times his entry fee.
If he just enters the first round like a normal person, he's paying $1,000 for 70% * $7,683 in equity, which is $5,378... more than 5 times his entry fee. Of course we could have calculated his starting equity in a more straightforward way by saying that he has to win 5 straight matches to claim first prize, and (70% * 70% * 70% * 70% * 70%) * 32,000 = $5,378.
So he actually gets much less bang for the buck by skipping ahead to the final round. This makes a lot of sense, since he needs to actually play backgammon for his skill as a superstar to matter. To illustrate the point, let's imagine a super-super-superstar who wins 99.999% of his matches. Why would he ever pay extra to enter an advanced round, when he's virtually guaranteed to win first prize even if he starts in the first round?
Bottom line is that the option to enter an advanced round is actually beneficial to the inferior players, not the superstars.
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