Isn’t the result exactly the same? 1st and 2nd are obvious. D E F split the $2000 U-2400 money because that’s how they get the most, renouncing 3rd place. C gets 3rd. 4th goes into the pot for the next lowest score group. You don’t have to be a TD to figure this one out! (Hopefully I didn’t just make an idiot of myself).
Prizes with disjoint eligibility sets (X, A, B, etc.) rather than nested (open and Uxxxx) can give very easily give rise to really unfortunate prize distributions such as higher rated players with lower scores getting more money than lower rated players with higher scores.
Well, this is a slightly modified version of a topic that was discussed in this very forum August, 2012. Back then, three NTDs (one of whom is easily the most experienced director in the country and one of whom is a Special Referee and also very experienced) and an ANTD (also very experienced) came up with three(!) different prize distributions.
Doesn’t rule 32B3 say that the correct distribution is to add the four prizes (3rd, 4th, and the two U2400 prizes) and divide evenly, so that C, D, E, and F all receive $700? The alternative in 32B3 is to check whether the three players under 2400 would receive more by splitting just the U2400 prize money and renouncing the place prizes. They would not, as that would only be $666.67 each.
In fact, the three prize distributions were:
C, D, E, and F each receive $700.
C receives $500, and D, E, and F each receive $766.67.
C receives $400, and D, E, and F each receive $800.
(The third distribution is the one offered by the special referee and is reached by awarding C half of third place and half of fourth place, and dividing the rest of the prize money evenly among D, E, and F.)
In rules committee discussion, it was suggested the correct prize distribution is clear (in fact, I think the word “obvious” was used) because of the “one prize per player” rule. But I claim that rule is not as clear as one might hope. In the example that started this thread (2nd place $600, U1800 $500), a player under 1800 who was tied with a player over 1800 correctly received $550, which was the under 1800 prize money of $500 plus an additional $50 taken from second place. Doesn’t that contradict the “one prize per player” rule? That leads to the inference that “at most one prize per player” refers to the prizes that are put into the pool to be divided among the tied players, not to the payout resulting from the division.
The following seems to be a general principle which gets you to the right place:
Each group of players (which could be just one player) is entitled to an equal share of the maximum prize money for which someone in that group is eligible after allowing other players at or above them in score to take the maximum prize money for which they (jointly) are eligible. All determinations of joint prize money for any group allow at most one prize per player.
Thus starting from the top, each score group collectively gets the maximum for which someone in the group is eligible, then within that score group, look at whether any player or group of players can do better by letting the others pick first. If not, they get the average. If someone can do better, take the subgroup with the maximum average payout, take their prizes out of the mix and repeat with other subgroups until no one does better. At that point, give everyone else the average of what’s left for the score group.
This avoids trying to specifically allocate shares of prizes to individual players. The tendency is to share equally because there is no other “fair” way to allocate the pot if no one does better on their own.
Regarding the one prize per player counterexample (open and U1800), the U1800 did not get any more money than the highest prize he qualified for (the $600 second place) so he did not exceed one prize. Otherwise any split of 1st and 2nd could be contended because each player received more than the amount of one of the prizes (2nd).
I’m kind of hoping the “obvious” split was 1x$500 and 3x$766.67. If not then I am confused. If it is then I’d still guess that the confusion involved among even ANTD/NTD TDs means it’s not particularly obvious.
I think the problem with that was that the rulebook in 32B3 uses the word “ineligible” when that’s not what really is meant. C is “eligible” for both the 3rd and 4th place money, but obviously can’t take both of them, so the 4th place money should go into the D,E,F group which gives you the (I believe clearly correct from general principles) $500 for C + 3 way split of $2300 for D,E,F.
The second one is the easy one. The 5.0 takes the 3rd place money without question. It’s the first where the unfortunate wording in the rule book causes confusion.