Yet Another Prize Distribution Question

Running Chess Tournaments
1

This concerns the distribution of prizes when some players are prize-limited and there is more than one “flight” of prizes. The correct method for dealing with players who are limited when there is only one prize schedule I think has been figured out (there are several mathematically equivalent ways to do that). Unfortunately, it’s not so clear when there are different eligibility sets. Take the following:

Prize Fund
Overall
1000
500
300
200
100

U1400
600
300

Results
5.5 A (U1400), B (subject to limit)
5.0 C (U1400), D (subject to limit), E, F
4.5 G (U1400),H

Without limits, A and B split 1000+600, C,D,E and F split 500+300+300+200 and G and H split 100.

With a 600 limit

A and B can still split 1000+600 with A getting 1000 and B 600. The rest is as before.

With a 500 limit

There are two distinct ways to handle this depending upon the source of the 1500 that A and B will split:

  1. They can split 1st and 2nd (A = 1000, B=500) which means that C gets the 600 U1400 prize and D, E and F split the 300+200+100, and G gets the 300 2nd place U1400 money, or

  2. They can continued to “split” the 1000+600, with the extra 100 being added to the 2nd overall money. C, D, E and F would split the (now) 600(augmented 2nd place)+300+300+200 and G and H would split 100.

To me, (b) is more principled (as much as possible you do the normal calculations, and flow unused money down). However, suppose now that the limit is 0. (As in the CCA on-line tournaments where people who did not do the extra monitoring were ineligible for prizes). The “obvious” way to handle that (basically ignore the ineligible players) is (a). A gets 1000, B nothing. C gets 600, D nothing, E and F split 500+300. G gets 300, H 200, with 100 left over for the next score group.

(b) applied to that situation would have A gets 1000. Extra 600 flows to 2nd place (take 500 to make it 1000—can’t go above the 1000) and 3rd (from 300 to 400). C, D, E and F would bring in 300 (U1400, 2nd), 1000 (now 2nd), 400 (now 3rd) and 200 (4th). D can’t take any, so C, E and F split 1700 (567 each), leaving 200. 5th place gets upped to 200 (can’t go above 200), and “6th” to 100. G and H will split 200+100.

Note that in (b), six players “take” seven prizes, which seems to be a fundamental error. However, it really is eight players taking six prizes, two just get calculated at zero. If the limit were $1 instead of $0, then you would have effectively the same calculation.

Where there is just one set of prizes, (a) and (b) are basically the same—whether you float players down until they hit the right spot given their limit or flow unused money down end up being mathematically equivalent. They aren’t, and in fact, can be quite different, when there are multiple flights of money.

2

The way I handle limits (when a simple split would exceed the limit) is to find the smallest amount greater than or equal to the player’s limit and then include that as the prize the player would pull in, with the excess going to the next prize in line. That is similar to your A, except that three $0-limited players would then each (in succession) pull in the bottom $100 prize, take the $0 out, and put the $100 balance into the next prize - allowing 9 players to take 9 prizes (5th place, 6th place and 7th place at $0) with the $100 left over as the new 8th place prize for the seventh eligible player. Note that two tied limited players would bring in the two prizes that combine for at least as much as what they earned (i.e. if the limit was $800 and both A and B were limited then they could still pull in $1600 and split it without leaving anything to push down to the next prize).

A $300-limited U1400 that tied for first or was clear first would pull in the 3rd place overall $300 and a $350-limited U1400 clear first would take $350 out of 2nd place’s $500 and put the remainder into 3rd place to increase it from $300 to $450 (taking the lowest dollar amount at least as large as the limit means that the next prize in line will not be increased to be larger than the prize selected).

A $1000, $500, $300, $100, $100, $100 and U2000 $300, $200, $100 prize fund (I’ve seen multiple identical prizes at some big tournaments) would have a $75-limited player take from the lowest dollar amount prize ($100) from the highest ranking group such prizes are in (6th overall, not 3rd U2000).

3

Wouldn’t a simpler way to think of that is for the $0-limited players to pull in the “6th place” $0?

4

True.

For $1 limited players it becomes 5th, 6th and 7th each being $1 with 8th being the left over $97.

5

I think clearly stating the principles would help. I generally agree with you that (b) seems more principled, but something that doesn’t seem to be stated anywhere is that a player who is limited brings the full prize to the pool but is then limited only their share of the prize. This occurs even if the pool is a pool of 1.

Additionally, the list published is in reverse order. It’s given as:

  1. Within the event.
  2. Within the section in which the limit was awarded.
  3. Within the prize group (e.g. place, class or under) in which the limit was awarded.
  4. Within the point group in which the limit was awarded.

But should be:
1. Point Group: Within the point group in which the limit was awarded.
2. Prize Group: Within the prize group (e.g. place, class or under) in which the limit was awarded.
3. Section: Within the section in which the limit was awarded.
4. Event: Within the event.

Since the priority of where the payment should be 1-4 in the latter.

Stating it this way makes it clear that all prize amounts should be paid in the event, and could be applied generally, even overruling 32C2.

Indeed, based-ons could be defined by the same groups.

6

A concern is that somebody would point to that and say that the excess of the 4-1 prize of the Class B prize would use number 1 to say that the excess should go to the 4-1 Class A players instead of the 3.5-1.5 Class B players.

The full rule is below (I added a potential modification in red).

32C6. Limited Prizes: In general, when a player is allowed to enter a given event or section, that player is eligible
for the prizes in that section. However, when a player (e.g. an unrated in a lower section) receives a limited prize,
the distribution of the remaining prize is to follow the following priority list.
The total dollar amount of all cash prizes announced or computed by “based on” shall be paid using as many of the following, in sequence:

  1. Within the event.
  2. Within the section in which the limit was awarded.
  3. Within the prize group (e.g. place, class or under) in which the limit was awarded.
  4. Within the point group in which the limit was awarded.
7

I must be missing something. I don’t see how that’s possible.

8

For example:

The remainder of the prize must be paid to players in the World Open.
If there are enough players, it must also be paid in the Open section.
If there are enough players, it must be paid to players U2300.
If there are enough players, it must be paid to players who scored 5/9.

At some point, those possibilities will run out. If all the players in the Open section under 2300 with 5 points have been paid then presumably we only satisfy the first three and pay a 4.5.

Alex Relyea

9

Example:
U2300 prizes are 1000-500-300 with a three-way tie and one limited player with a provisional rating.
If the player has a limit of 400 then $400 goes to him and the other two get $700 (still less than splitting just 1st and 2nd) - satisfies all four conditions
If the player has a limit of 200 then $200 goes to him, the other two get $750 (split of 1st and 2nd) and $100 goes to the next U2300 score group - satisfies the first three conditions
If there was an extremely low turnout for some reason and there is no other U2300 then the $100 becomes an additional overall prize in the open section - satisfies the first two conditions
If the low turnout meant there were no other open players then the $100 becomes an additional prize somewhere (maybe even a general increase in all prizes if there were more prizes than players) - satisfies the first condition

Note that this reallocation applies only to the balance of prizes getting paid to limited players and is different from there being only two U2300s in the Open section (or two left after the top-scoring U2300s took higher value overall prizes). In that case the $300 would have nobody to try to claim it and would not need to be paid.

Also note that Tom Doan’s algorithm handles the cases where at least the first three conditions can be met. I’m not sure how he would do an algorithm for the times when the balance of an under prize needs to become an overall prize or when a prize needs to be transferred to another section. I’m also not sure if that would happen often enough that he’d need to programmatically handle it.

10

Currently when using WinTD to calculate limited prizes what I do is:

  1. Run the prize list to see if any limited players are getting too much

If any are then
2) Assign a prize group of Z to all non-limited players (and limited players that are not going to win too much)
3) Find the smallest prize (of the type the player would be winning) that is greater than or equal to the limited player
4) Make that prize equal to the limit (moving the remainder to the next prize in line)
5) Make all other prizes available only to prize group Z
6) Rerun the prize list

If there are multiple limited players winning too much then it will need to be done for multiple prizes.

PS I used to just manually override the prizes but some people prefer to see a printout generated by the computer.

11

That would be pretty much impossible for the program to recognize that some money was going unclaimed and figure out a way to redistribute it.

Kevin is correct that the description of what to do with the unclaimed money is somehow reversed or (as Jeff points out) the verb form was the reverse of what was intended. However, my main point was that, unlike the situation with unrestricted moneys, it’s far from clear what the correct way to handle this is when there isn’t a single set of prizes. When no one is restricted from taking the max of prizes from which she is eligible, you take the biggest ones and (in case of a tie) take the one for higher ratings. When there’s a restriction where a restricted player is eligible for more than one set of prizes, you have what is likely to be a forced “tie” but that might give a different result from the biggest prize (which the player can’t receive). So basically you have the two standard rules in a bit of a conflict in this case.

12

Here’s what I would do with the following: an Open prize fund of 2000-1000-500-300, U2200 800-400 and a 2187 in a tie for second and third place with a 250 limit.

  1. determine the applicable prizes (2nd overall and top U2200)
  2. apply the limit to the lowest prize of the type the limited player is bringing in and take it from that
  3. distribute the remainder as that type of prize.
    Here is would be to award 2nd to the non-limited player and 250 of the U2200 second place to the limited player with 150 left over for third place [added: if both are limited then two is taken from each type of prize leaving Open 1000-500-50 U2200 800-150]

If the only U2200 prize was 400 then the two prizes selected of 2nd and 3rd with the unlimited players getting 2nd and the limited player pulling from 4th (leaving 3rd untouched and created a 5th place prize of 50) [added: if both are limited than the three remaining open prizes go from 1000-500-300–>1000-500-50–>1000-300]

Using the initial prize fund and if the limited player was now over 2200 then the two prizes are again 2nd and 1st U2200 but this time 450 needs to be pulled from the overall fund’s prize of 500 (so the U2200 gets 1000 and the limited player gets 250), leaving the 400 second place U2200 and also leaving 1000 and 350 for the open prizes.

PS I wouldn’t be surprised if the need to reallocate to different prize groups or sections is so rare that it doesn’t need to be programmed in.
PPS I’m not sure how difficult it would be to program in the above (in one case taking from 2nd overall/2nd U2200, in another case from third overall/1st U2200 and in another form 2nd overall and 4th overall - more difficult than when dealing with a single group of prizes)

13

Yes, that’s why it seems backwards. Any remainder should fall to the next bigger group (bucket) right? Aren’t the 5/9 players the priority? But when worded as you show above, it looks like they are last in line.

If one starts by paying any remainder of the prize to players in the World Open, it seems likely that the 5/9 players might not see much of it.

14

Could always go with

  1. Within the event.
    and preferably
  2. Within the section in which the limit was awarded.
    and preferably
  3. Within the prize group (e.g. place, class or under) in which the limit was awarded.
    and preferably
  4. Within the point group in which the limit was awarded.
15

You have to go as far down the list as you can, not just start at the top. (Or, if you prefer, go to the bottom, and only move back up the the previous level when no one remains eligible at the current level.)

Perhaps you would prefer the following:

  1. Within the point group, prize group (e.g. place, class or under), section, and event in which the limit was awarded.
  2. If the above is impossible, then within the prize group (e.g. place, class or under), section, and event in which the limit was awarded.
  3. If the above is impossible, then within the section and event in which the limit was awarded.
  4. If the above is impossible, then within the event.

Should be logically equivalent to Jeff’s way, but wordier.

If you use this

then you are missing all the extra qualifiers, and a 5/9 player from the U1700 section might try to claim a higher right to a prize from the U2300 section than a 4.5/9 in the U2300 section.

16

“You have to go as far down the list as you can, not just start at the top.” I get that it’s worded that way. That’s my complaint. People READ top to bottom. The rule buries the leed, and doesn’t provide for easy explanation. I’m not disagreeing with the rule, I’m disagreeing with the wording.

If I list the group by priority (which seems like the best way to do it) rather than “reverse priority”, then we can describe the prize payments as a series of buckets of prizes due.

When the top, 5/9 bucket, is filled, and overflows, it first falls to the prize group. When the prize group bucket is full and overflows, it does so to the section bucket and then from section to event. This is a very natural wording - by priority, and by a reasonable analogy. Reverse priority requires anti-gravity to explain, and AFAIK, upsidasium exists only in Rocky and Bullwinkle.

Here is the full wording of the rule:

32C6. Limited Prizes: In general, when a player is allowed to enter a given event or section, that player is eligible for the prizes in that section. However, when a player (e.g. an unrated in a lower section) receives a limited prize, the distribution of the remaining prize is to follow the following
priority list. The total dollar amount of all cash prizes announced or computed by “based on” shall be paid:

  1. Within the event.
  2. Within the section in which the limit was awarded.
  3. Within the prize group (e.g. place, class or under) in which the limit was awarded.
  4. Within the point group in which the limit was awarded.

So, if an unrated wins a limited prize, anyone who normally reads US English will quickly conclude that the rest of the prize should be paid within the event. But in reality, the prize should first be paid “4. Within the point group in which the limit was awarded.” - which means that “4” should be “1.”

Additionally, I don’t see the need for other restrictions to be added here. It seems clear as worded, so long as items 1-4 are listed in priority order, rather than reverse priority.

Finally, I do have to question whether all or a portion of this rule shouldn’t fall earlier, where the principles of paying prizes are defined. Maybe this is the only case where this priority is needed, but the idea of a prioritization makes sense.

17

If the rule is considered to be ambiguous as it currently stands I would rather not change it to something that can also be seen as ambiguous. Listing the point group first would introduce what is either a potentially erroneous ambiguity or a definitely erroneous clarity.

Use this instead.
Pay the remainder of the prize using the following guidelines.

  1. In the Event
    and, if possible
  2. In the Section of the event
    and, if possible
  3. In the Prize group of the section (overall section prizes have everybody in the section as part of the overall group)
    and, if possible
  4. In the Point group of the prize group

This is one case where the following lines do not replace the earlier lines, but rather enhance them. You don’t even look at the point group unless the other three are already applicable and the non-existence of anybody else satisfying #3 would mean that #4 would be ignored. If the point group was considered primary then that would not be true.

Take the following prize fund
Open section: 5000, 4000, 3000, 2500, 2000, 1500 U2200 1000, 500
Reserve section (U2000) - something
Booster section (U1600) - something

Open results
7/7 - 2480 ($5000)
6/7 - 2520, 2360, 2340, 2270, 2180 ($2600 each)
5.5/7 - 2430, 2380, 2275 ($0 each)
5/7 - 2350, 2240, 2170 (provisional - limited to $600)
4.5/7 - 2310 ($0), 2270 ($0), 2150 (should get $900 for the $500 2nd U2200 + the balance of the 1st U2200 which is still sums to no more than 1st U2200 - note that if the 2170s limit was $400 then the 2150 would get $1000 and there would be a 3rd U2200 of $100 for the lower scoring U2200 players)

If points are the highest priority then the 2350 and 2240 at 5/7 can claim that they get the remaining $400 before it gets added to prize won by the 2150 at 4.5/7 and before it goes to the 2430, 2380, 2275 at 5.5/7.

If the 2180 (overall prize winner) and the 2170 (limited prize) are the only U2200 players in the section (no 2150 or any others) then the 2350 and 2240 can again claim that since they had the same score at the 2170 that means they split the $400 before the higher scoring 2430, 2380 and 2275. (note the the second place U2200 would not be awarded in that case since there are no remaining players eligible to win it and this prize reallocation only applies to the balance of limited prizes)

Also, if there are only 6 players in the open section and the lowest scoring player is a U2200 that is limited then the balance of the first place U2200 would go into the other sections (and the second place U2200 would not get paid out).

18

Now THAT has to be the classically definitive statement of all time. I think I’ll make it into a bumper sticker.

:smiling_imp: It is potentially erroneous to describe an ambiguity as a definitely erroneous clarity. :smiling_imp:

Bill Smythe