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Early vs late round byes, some math for single elim
Posted By: neilkaz
Date: Tuesday, 29 October 2013, at 6:29 p.m.
In Response To: Early vs late round byes (Matt CohnGeier)
OK lets assume a single elim. 24 player event like Masters. If a 32 player draw is used, there will be 8 byes. Those players getting a bye will have a 1/16 chance to win the T whereas those not getting a bye have a 1/32 chance. Of course, initially everyone had a 1/24 chance prior to the draw for byes.
Lets assume there's a $1000 entry fee and 100% return and a typical 4,2,1,1 payout. The equity of the players getting the bye is $1500 and the equity of those not getting the bye is $750 so in this case the rd 1 bye is worth $750.
Now lets look at the method I much prefer where the 24 players are broken down into three 8 player brackets with no byes. Now everyone's equity at the start is $1000 and all 24 players get to sit down and start playing with no waiting around for 8 of them.
We'll pay the final 3 in a typical 4,2,1 ratio and draw the bye sending one of them to the finals. There are 7 shares of the $24K pot at stake and the equity for the player getting the bye is 3 shares, whereas the equity of the two nonbyes is 2 shares. This late bye is worth 1/7 of $24K! Or about $3420 !!
This late bye to the finals in this format is worth more than 4.5 times as much as a rd 1 bye.
Now consider the above fact and we see why we don't worry about compensation for a rd 1 bye, but most definitely should compensate for the very valuable bye to the finals when a format playing down to 3 equal players is used.
It is totally fair and equitable and a much better solution to handle a bracket of 24 players and playing down to the final 3 and then compensating for the bye to the finals than it is to give byes at the start using a bracket of 32. Now there's only 1 bye given and that player can either go to bed early or play a side event since the finals are typically the next day. This sure seems better than having 8 players with double the equity of the other 16 waitng around for the rd 1 matches to finish.
Some progressive directors realize this and have standardized this method.

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