I barely managed to dodge a bullet in a tournament I directed recently. The tournament had a very deep prize fund, meaning that there were prizes for the first forty(!) places. There were also some “under” prizes, which is the source of the complexity.
In the actual tournament, I was fortunate that many of the place prizes had the same value (for example, 9th through 20th $600, 21st through 40th $360). If those place prizes hadn’t been of equal value, I’m not sure I know what the correct prize distribution should be.
So, let’s suppose there’s a six way tie for 10th through 15th places. Suppose the prizes are: 10th place $600, 11th $590, 12th $580, 13th $570, 14th $560, 15th $550. Suppose there is also a top under 1700 prize of $900 which has not yet been awarded to any player in a higher score group. The players and their ratings tied for 10th through 15th are:
Alan 1900
Barbara 1850
Charles 1800
Donna 1650
Edward 1625
Francine 1600
Hmmm…and interesting problem here. I have it as $600 to each of the six players.
Rule 32B3. Ties for more than one prize. If winners for more than one prize tie with each other, all the cash prizes involved shall be summed and divided equally among the tied winners unless any of the tied winners would receive more money by dividing only a particular prize for which others in the tie are ineligible. No player may receive an amount greater from the division of those prizes than the largest prize for which he would be eligible if there were no tie. No more than one cash prize shall go into the pool for each winner.
The highest six prizes that can be brought into the tie are the 10th-14th place prizes ($600, $590, $580, $570, and $560) and the U1700 prize ($900). These sum to $3800. One sixth of that is $633.33. First we look to see if the three U1700 players in the tie would do better by splitting the prize for which others in the tie are not eligible, the $900 under 1700 prize. One third of that is only $300, so they do better by the six way split of the top six prizes. However, the three highest rated players in the tie are over 1700, and so the largest prize for which they would be eligible if there were no tie is $600. Alan, Barbara and Charles cannot win more than this amount. Also, by the first sentence of 32B3 the prizes must be divided equally unless the three U1700 players would do better by splitting the U1700 prize, which they do not. This therefore means that even though Donna, Edward and Francine were eligible for a prize of $900, they also cannot win more than $600 or the six players in the tie would not be splitting the prizes equally. I have it as each of the six players receiving $600 each, with the extra $200 ($33.33 x 6) and the 15th place prize of $550 being sent on to the next lower score group.
1st
10th-15th = $600 each, U1700 = $900
10th-14th and U1700 are awarded to the six players ($3900 total).
$650 (3900/6) > $300 (U1700 split three ways) so all six are added together and divided
$650 is more than the $600 that three of the players could have won for clear 10th, so the three 1700+ players are limited to $600 ($1800 total) and the remaining $2100 is split three ways so that the U1700s get $700 each. This is a modification due to the rule change about such a limit.
2nd
10th to 15th is $600 to $550 dropping $10 per step, U1700 = $900
10th-14th and U1700 are awarded to the six players ($3750 total)
$625 (3750/6) > $300 (U1700 split three ways) so all six are added together and divided.
$625 is more than the $600 that three of the players could have won for clear 10th, so the three 1700+ players are limited to $600 ($1800 total) and the remaining $1950 (including the $900 U1700 prize) is split three ways so that the U1700s get $650 each.
Both splits ensure that the U1700 players combine for at least as much as the U1700 prizes add up to, and that was true even before the most recent change.
Both splits ensure that nobody wins more in a tie than would have been won if all of the other tied players had not scored as well.
3rd
as second with the proposed revision to determining the maximum a player could get with the following additional step added
$625 is more than any of the three 1700+ players could have won for clear 10th ($600) AND it is more than the three could have won if they combined for 10th-12th ($590 each), so the three are limited to $590 each while the three U1700s get $660 each.
The revision would mean that the cap is not based on a player being limited to the largest prize the player could have gotten if everybody else in the tie had scored less, but rather is based on a player being limited to the largest prize the player could have gotten if only players with the same eligibility had remained in the tie and the other tied players had scored less.
Rule 32C6 allows for limited prizes with the amount over the limit being redistributed with the redistribution hierarchy being: within the point group; else within the prize group; else within the section; else within the event.
Oops.
In case 2 and 3 it is $3800 instead of $3750 that would be awarded (I summed up 11-15, not 10-14).
So Case 2 would have the three U1700s getting $666.67 each (splitting $2000, not $1950) and case 3 would have the three U1700s getting the $676.67 each you mentioned.
I’m not entirely certain rule 32C6 applies here. My reading is that rule 32C6 refers to a priori restrictions on the amount individual players may win (for example, because the player is unrated or has played fewer than a specified number of rated games). I do not believe it applies to a posteriori prize distribution and reallocation of portions of prizes to lower score groups.
I’m uncomfortable with this prize distribution for two reasons. My primary objection is that it violates what I think is the intent of the penultimate sentence of rule 32B3, although not the letter of the rule. Specifically, that sentence refers to individual players not receiving more from a distribution among tied players than he would win if he were the only player in the score group. However, I think the intent of that change to rule 32B3 is that no subset of players involved in a tie should win more in aggregate than they would if they were the only players in the score group. (I also suspect that, if the rule were worded that way, the reaction of those readers with strong mathematical backgrounds would be “of course” and that of other readers would probably be “say what?”.) The current language of rule 32B3 only considers subsets comprising single players.
With the proposed prize distribution of $600 for each player in the tie, Alan, Barbara, and Charles do collectively win more than they would if Donna, Edward, and Francine were not involved in the tie. If Alan, Barbara, and Charles were the only players in the score group, each would win $590 (an even division of 10th, 11th, and 12th place prizes). While rule 32B3 doesn’t explicitly disallow this, it doesn’t seem right that adding Donna, Edward, and Francine to the score group should increase the prize money paid to Alan, Barbara, and Charles.
Let me put that another way. If we are to pay Alan, Barbara, and Charles $600 each, there would be no way to do so except to pay them the entirety of 10th, 11th, and 12th place plus money taken from other place prizes (presumably 13th). This would seem to violate rule 32B1 (one cash prize per player). Now, to be fair, we violate rule 32B1 all the time, and it is the correct thing to do. For instance, suppose there are two prizes for a small event: 1st $100, top under 2000 $50. Suppose an expert and a class A player tie for the top score. I don’t think any TD would question that the correct prize distribution is $75 to each player, even though the only possible way to pay $75 to the class A player is to award him the entire under 2000 prize plus one quarter of first place. (My conclusion is that rule 32B1 doesn’t say what it really means to say and is written badly.) But, the only cases where I have seen rule 32B1 legitimately broken involve both overall place prizes and restricted (“under”) prizes. I can’t imagine a scenario involving only overall place prizes in which the correct distribution would violate rule 32B1.
My other cause of discomfort with the proposed distribution is that I don’t understand the justification for pushing part of the under 1700 prize down to a lower score group.
(I think the reasoning behind my main objection is the same as Mr. Wiewel stated in the third case in his analysis.)
I’m uncomfortable with this prize distribution myself, but I think it does conform to the letter of rule 32B3. Whether or not the maker(s) of rule 32B3 intended some other meaning that wasn’t adequately expressed in this rule’s wording is something I cannot know. It would not bother me one bit if this whole section was rewritten.
I don’t think rule 32B1 is violated. Six people are splitting six prizes, or parts thereof. How some particular subset of the six come up with the award they come up with is not germane.
Part of the U1700 prize is pushed down the next lower score group because there is nowhere else it can go. It can’t not be awarded, but no one in this score group can get any more than $600 by my reading of the rules, and the extra $200 has to go somewhere.
I don’t understand. Why wouldn’t Donna, Edward, or Francine be awarded the $900 under 1700 prize if he or she were the only player in this score group? Why are they only eligible for a maximum of $600?
I don’t get why any under 1700 money has to be pushed down. Of course I’m not a TD. We have five place prizes and the U-1700; why can’t it all be awarded to those six people? I would have thought the limit for 1700s would be based on what the three of them would get if no higher rateds were involved (2 place prizes plus the U-1700). They won’t get that much, but I thought that was the limit and not just the U-1700 divided by three.
If one doesn’t attempt to parse out the meaning of the rule book and just thinks from general principles, does anyone come up with anything other than the over 1700’s splitting 10-11-12 and the U1700’s splitting 13-14 and the U1700 money? Clearly the six players jointly have a right to that combination of prizes, so it’s just a question of how it gets divided up, and the above gives the over 1700’s exactly what they would get if the other three players weren’t in the tie. If we agree on what’s correct, then it becomes a question of figuring out how to describe that for the rule book.
This was my first thought, but then I’m having difficulty justifying allocating 13th and 14th places to the under 1700s. After all, if only the under 1700s were in the score group, wouldn’t they divide the under 1700 prize and 10th and 11th place prizes equally? Why should the 10th, 11th, and 12th place prizes be allocated to the players over 1700? Granted, that maximizes the money those players win. Couldn’t an argument be made for combining 10th through 14th places, dividing by five (the average of 10th through 14th places), and allocating three of those five shares to the players over 1700 and dividing the remaining two shares plus the under 1700 prize among the other three?
Each of them would be awarded the $900 U1700 prize if he or she was the only player in the score group, and the last sentence of 32B3 sets their maximum available prize here at $900. However, the first sentence of 32B3 states that the prizes to be summed must be divided equally unless the three U1700 players would do better by splitting the U1700 prize among themselves than taking a 1/6th share of the six prizes to be divided. Clearly that condition does not apply here. The second sentence of 32B3 effectively sets the prize limit for the three Class A players at $600, and since the prizes must be divided equally, that re-sets the limit for the three Class B players at $600 as well. I don’t say that I like this whole mess, but I don’t see any other way to divide these prizes that doesn’t violate part of 32B3.
That would mean the three 1700+ each get 1/5 of 10th + 1/5 of 11th + 1/5 of 12th + 1/5 of 13th + 1/5 of 14th (five fifths of prizes = 1 prize each) while the three U1700s each get 1/5 of 10th + 1/5 of 11th + 1/5 of 12th + 1/5 of 13th + 1/5 of 14th + 1/3 of U1700 (five fifths plus 1/3 = 1.333 prizes each).
Tom Doan’s suggestion would have the three 1700+ each getting 1/3 of 10th + 1/3 of 11th + 1/3 of 12th (three thirds = 1 prize) with the three U1700s each getting 1/3 of 13th + 1/3 of 14th + 1/3 of U1700 (three thirds = 1 prize).
I thought the logic behind the original change was that the U1700s shouldn’t get less money than they would have gotten if the 1700+ players in the tie has each scored a 1/2 point more. Tom’s suggestion follows that logic.
I’m not sure to which change Mr. Wiewel refers. If it is the relatively recent change to rule 32B3 (the next to last sentence), isn’t the intent of that change to set a maximum, not a minimum, of how much each player should receive in case of a tie? Also, why should consideration be limited to what would happen if the 1700+ players in the tie each scored 1/2 point more? What if those players scored 1/2 point less?
I am a Bear of Very Little Brain, and I have never been able to wrap my mind around the “summing fractional prizes” logic as it applies to rule 32B1. After all, in the straightforward example I presented (1st $100, top U2000 $50, and a tie between an expert and a class A player), the correct prize distribution clearly has the class A player receiving 1.25 prizes. The only sense I can make of 32B1 in this case is to apply it to what goes into the pot to be divided according to rule 32B3.
I admit to being stubborn, but I’m just looking for the justification for assigning 10th, 11th, and 12th prizes to be divided among Alan, Barbara, and Charles.
I’m a little confused why all of the examples listed in the replies only use 6 prizes and not 7. I must be missing the obvious. In the replies only 10th-14th place plus U1700 prizes are pooled together. What happened to the 15th place prize?
Here’s what I get:
10th - 15th place money: $3,450
U1700 money: $900
Total: $4,350 potentially divided among 6 players.
Alice, Barbara, and Charles get $600 each (limited to 600 per 10th place prize)
Donna, Edward, Francine get $850 each (remaining $2550 / 3 which is less than $900 U1700 limit)
Does this seem reasonable or am I completely off-base?
It seems to be a serious mistake to divide seven prizes among six tied players. That, I think, is the actual meaning of rule 32B1 (one cash prize per player). The fifteenth place prize should be distributed in the next lower score group.
