OK, that makes sense. I’ve done some cash prizes, but nothing nearly this complex, which is why I make sure to read every thread along these lines. 40 place prizes… was this the Millionaire Open?
As as aside, if the U1700 prize amount was lower than the 15th place prize, would the U1700 prize than get dropped down instead? Using your example, let’s say it was $500. Then each of the 6 players would just get $575 and some other U1700 player would get the $500 or fraction thereof based on other ties. Correct?
1700+ vs U1700
If the 1700+ players scored a half point less than the prizes to be awarded to the U1700s would be 10th, 11th and U1700 ($2090 split three ways). If the 1700+ players scored a half point more then the prizes awarded to the U1700s would be 13th, 14th and U1700 ($2030 split three ways). In the six way tie if the U1700s are given 11th, 13th and U1700 they would split the $2060 you are trying for while getting three prizes for three players. The way you calculated it you would be awarding three players five fifths each of five prizes (three total) and three players [after restating the calculations to account for three people splitting the last two fifths of each prize instead of two people splitting the last two fifths of each prize] 2/15th [not 3/15th] each of five prizes plus 1/3 each of the U1700 prize. That 3/15 → 2/15 change does make it a total of 10/15+1/3=one prize for each of the three U1700s. Thus you can come up with a new ADM that does what you want without violating the one prize per player limit.
Straightforward example
The straightforward example has both players getting 1/2 of 1st and 1/2 of U2000 (two halves equals one prize). It only looks like one player getting 3/4 of 1st and the other getting 1/4 of first plus all of U2000. The mathematics of the split is performed as 1/2 plus 1/2 = 1 for both players, not 3/4 and 5/4. The same mathematics supports 1st=100, U2000=20 (60 each for one prize each instead of 3/5 vs 7/5), 1st=100, 2nd=50 (75 each for one prize each instead of 3/4 vs 5/4), 1st=100, U2000=80 (90 each for one prize each instead of 9/10 vs 11/10)
The six prizes to be summed must be divided equally. The three players in the tie rated over 1700 cannot win more than $600 each. Therefore no one in the tie can win more than $600. Since the sum of the six prizes to be divided is at least $3600 ($600 x 6) each player in the tie is awarded $600. The remaining money is awarded to the next lower score group.
If I am misunderstanding something I would appreciate being shown the error of my ways. You are the OP here. How do you think these prizes should be distributed?
I’ll offer my opinion about this since it’s of great interest to me, but since I’m a moderator I don’t want to get into an extended argument about it. My apologies in advance if I don’t reply to objections.
I agree with Tom Doan’s distribution. Ignoring the most recent amendment to rule 32B3 for the moment, the three players rated over 1700 are entitled to an equal distribution of the most valuable prizes for which they are collectively eligible (A) or to an equal distribution of all the prizes (B).
A: Over 1700 get ($600+$590+$580)/3 = $590 each; under 1700 get ($900+$570+$560)/3 = $676.67
B: Every player gets ($900+$600+$590+$580+$570+$560)/6 = $633.34
Since the under 1700 players do better under A than under B, that’s how the prizes are distributed.
I think this distribution is the fairest and is valid under the rules as written, although it requires some reading between the lines. 32B3 says “If winners of different prizes tie with each other, all the cash prizes shall be summed and divided equally among the tied players unless any of the winners would receive more money by winning or dividing only a particular prize for which others in the tie are ineligible.” Reading between the lines, “a particular prize” in this instance needs to be interpreted as “particular prizes” for which the players rated over 1700 are ineligible. We’ve had this argument before. As I see it, the players rated over 1700 are eligible for only three prizes, the most valuable of which are $600, $590 and $580. If they split those prizes they’re not eligible for the $570 and $560 prizes, so those prizes can go into the pool for the players rated under 1700.
In an attempt to make the rule clearer, the delegates added an additional sentence to 32B3: “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.” This seemed reasonable when we were considering a prize distribution where only one player in the tie was ineligible for an under prize, but it doesn’t really help here. Taken literally, it means that none of the players rated over 1700 can win more than $600, so my B above should be:
B: over 1700 win $600 each; under 1700 win ($900+$600+$590+$580+$570+$560-$600-$600-$600)/3 = $666.67
Since $666.67 is less than $676.67, A is still the correct distribution.
I think the intent of the ADM is that the players rated over 1700 shouldn’t be able to win more than they would have if the players rated under 1700 weren’t in the tie, which means that they can’t win more than $590 each, confirming that A is the correct distribution.
Here is my suggested rewording of 32B3:
According to the first sentence of 32B3, all six prizes have to be shared equally unless any of the winners (in this case the players rated under 1700) would receive more by winning or dividing only a particular prize for which others in the tie (the players rated over 1700) are ineligible. The players rated over 1700 aren’t ineligible for the 10th-12th prizes, so they can’t be deprived of those prizes unless there is an equal division of all the prizes, including the $900 under 1700 prize.
Scott, I think the mistake you’re making is that you’re applying the $600 prize limit (really should be $590 as I see it) to every player in the tie, not just to the players rated over 1700. The equal division should come before applying the prize limit, not after.
Consider this simple scenario:
Prizes: 1st $100, 2nd $50. Unrated players can’t win more than $60.
Alice (rated 1500) and Bill (unrated) tie for first. According to the rules, they divide the prize money equally. Following your logic above, since Bill can’t win more than $60 Alice also wins $60. So what happens to the remaining $30? You’re saying (in effect) that the $30 goes to the players in the next score group. Even if the $60-$60 distribution were correct, according to rule 32C6 the $30 should go to players in “the point group in which the limit was awarded”, meaning it goes to Alice. Alice wins $90 and Bill wins $60.
The correct way of awarding the prizes is first to split the money equally, $75 each to Alice and Bill, and then apply the prize limit just to Bill. Bill wins $60 and the remaining $15 goes to Alice, giving her $90.
The prizes that get carried into the pool are 10th-14th and the under prize. The place prizes should be treated as five identical prizes of $580 each (the average), because each of the players is as entitled to 10th as they are to 14th.
D, E, and F are the only players eligible for the class prize, and are thus the only players entitled to have the prize averaged into their share.
Thus, A, B, and C take $580 (the average place prize). D, E, and F take $686.67 (the average of the class prize and two average place prizes).
There is none. D, E, and F have as much right to an equal share of 10th-14th money as A, B, and C do. That they also have an exclusive right to share the under prize does not change this.
It might be possible to write a rule that would produce that result (and I agree that it isn’t unreasonable on its face). However, the general idea has been that you average actual prizes within score groups and subsets of score groups, not shares of prizes. Here you divide 3800 by six, unless some subgroup could do better by letting the others have first dibs on prizes. That subgroup here is the U1700’s, who can give up the specific 10th, 11th and 12th prizes (which are summed and divided among the A-B-C’s) since they do better with the specific 13th, 14th and the U1700 money (which are summed and divided among them).
Suppose that there was also an undistributed $700 under prize for which B-F are eligible and A is not. If we keep prizes intact, it’s fairly easy to see that you would give 10th to A, $700+11th to B and C, and $900+12th+13th to D-F. If I had 30 minutes, I might be able to figure out how to extend your share calculation to this situation.
Bob - Thanks for this post, and for your work here. I understand that being a moderator you can’t reply as you might like to. I think you are basically right here in that I was in error in not applying the prize limit after the equal division. I still am not entirely sure if 32C6 applies to players not listed a priori as prize limited, but 32C6 doesn’t actually say that this rule is only for such players, so maybe it does. I do have some quibbles, however.
The prize limit for the players rated over 1700 must be $600 for each of them. The relevant sentence of 32B3 is, “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.” If there were no tie, if this score group consisted of only one player, and that player was rated over 1700, then that player could win $600. That argument is valid for each of the three players rated over 1700.
You cannot give the three players rated over 1700 the top three place prizes here ($600, $590, and $580), and then give the three players rated under 1700 the two place prizes next in line ($570, and $560). The players rated under 1700 have just as valid a claim on the top three place prizes as do the players rated over 1700.
The first sentence of 32B3 is, “If winners of different prizes tie with each other, all the cash prizes involved shall be summed and divided equally among the tied winners unless any of the winners would receive more money by winning or dividing only a particular prize for which others in the tie are ineligible.” This means you cannot restrict the $900 U1700 prize to be divided only among the three players rated U1700. You could do that only if they were splitting that prize alone, and leaving the place prizes to be divided by the players rated over 1700. If the U1700 prize was enough so that a three way division of it would yield more to each of the players rated under 1700 than he or she could get by receiving a 1/6th share of the top six prizes, then you could do that. It isn’t, and you can’t. It goes into the pot to be divided equally among all the players in the tie.
The total of the top five place prizes plus the class prize is $3800. Absent any restrictions the award for each player would then be $633.33. However, the three players rated over 1700 each have a limit of $600, so that is their award. The $100 taken from them thereby is distributed between the three other players in the tie, who each get $666.66.
OK. It didn’t take 30 minutes, but there are some tricky spots.
D-F are entitled to a full share of the $900. They are also entitled to 3/5 of the 5-way split of $700. They would also be entitled to half of the 10-14th prizes, but that would take them over the 3-prize share, so they can get only 7/5 of a share of the $585 average. That’s a 3-way split of 2139 vs 2050 above. B,C would get 2/5 of 700, and 8/5 shares of the $585 average from 10-14. Note that B,C aren’t actually entitled to that large of share of the place money (they’re only two out of a six way split of four prizes), but apparently it needs to go there after the limit to D-F. That gives them a split of $1216 vs $1290 above. A gets one share of the place money, so $585 vs $600 above.
I’m not sure how I would even describe how to do that calculation in general. As ugly as that is, it would likely be even worse if you couldn’t rely on the fact that each player gets a full prize share (thus making it easy to figure out the share limit on the overall prizes for D-F). If it were seven players somehow splitting five prizes, yikes!
That’s just wrong. If the U1700’s had a lower score, then the 1700+ would only split $600+$590+$580. They can’t make more money as a result of additional players (the U1700’s) being in the tie.
Yes they can. The additional players in the tie bring in additional prizes. In this specific case we have the odd situation where one of the prizes these additional players bring in is a class prize larger than the place prizes the 1700+ rated players were eligible for. I’m not saying your way doesn’t make sense. I’m saying that the rules as written don’t support it.
That requires a tortured reading of the rules as written. It clearly can’t be right for players to win more by having additional players join them in a tie (coming from below).
There’s nothing “tortured” about it. That’s what the rules say. The crux of the problem here is that the U1700 prize is larger than the place prizes, but not large enough that the U1700 rated players could just split it among themselves and leave all the place prices to the over 1700 rated players.
Or maybe I am wrong here after all. I’m certainly willing to listen, if you can cite the rule that I am misapplying. If all you can argue is that “this way must be wrong”, then you need to take this matter up with the Delegates.
