# Prize Distribution -- Shoulda Hadda V-8 **URL:** \ **Category:** Running Chess Tournaments\ **Created:** [August 8, 2008, 1:59am UTC](https://forum.uschess.org/t/prize-distribution-shoulda-hadda-v-8/7310 "2008-08-08T01:59:13Z")\ **Posts on this page:** 9\ **Page:** 2
**Author:** ![bbentrup](https://avatars.discourse-cdn.com/v4/letter/b/e47774/32.png) [@bbentrup](https://forum.uschess.org/u/bbentrup)\ **Post date:** [August 11, 2008, 9:45pm UTC](https://forum.uschess.org/t/prize-distribution-shoulda-hadda-v-8/7310/21 "2008-08-11T21:45:44Z")
More examples from Bill using the proportionate pot system. > [@BillSmythe](#): > > Here is one of the examples from the Distribute Prizes thread: > > 1st $150, 2nd $101, 1st U1800 $99 > > p1 2100 5.0, p2 1700 4.5, p3 1900 4.0, p4 1650 3.5 > > A. Award the place prizes to p1 ($150) and p2 ($101). > > B. Award the under-1800 prize. p2 has already won more than $99, so this amount goes to the next under-1800, p4. p1, a 2100, clearly receives 1st place. p2 is eligible for both pots and his prize should come from both, to have the most equitible distribution. The 2 pots combine to equal $200 - with a slight mathematical weight to the 2nd place prize over the U1800 prize. I showed how the percentages worked in the post above, so I will merely estimate here. Of the $101 2nd place prize approximately 50.5% moves up which is, say, around $50.55, leaving the rest for others. Of the $99 U1800 prize, 49.5% or so moves up, which is around $49.45. So, in all, ($50.55 + $49.45) $100 moves up which is what p2 receives. p3, next in line, is only eligible for the remaining 2nd place prize and receives that which is ($101 - 50.55) $50.45. p4 is next in line and is eligible for what’s left of the last remaining prize of U1800, which is ($99 - $49.45) $49.55. * * * > [@BillSmythe](#): > > Here is a slightly different example from the same thread, an example originally designed as a companion case to expose the flaws in the standard prize distribution methods: > > 1st $150 > 2nd $99 > 1st U1800 $101 > > p1 2100 5.0 > p2 1700 4.5 > p3 1900 4.0 > p4 1650 3.5 > > A. Award the place prizes to p1 ($150) and p2 ($99). > > B. Award the under-1800 prize. p2 has already won $99, so he is entitled to an additional $2. (More would violate one-prize-per-player.) This $2 comes from the U1800 prize. p2 wins $101 total, with the remaining $99 (of the U1800 prize) going to the next under-1800, p4. Here is where my system looks like a genious - switching around $2 in the prize fund makes practically 0 difference in the prize fund distribution, as it should be, whereas in the other systems violent changes results based on which order you award the prizes often leaving some people out in the cold entirely. P2 would get his highest eligble prize, the $101, but this is taken proportionately from the 2nd place and U1800 prizes. ---
**Author:** ![bbentrup](https://avatars.discourse-cdn.com/v4/letter/b/e47774/32.png) [@bbentrup](https://forum.uschess.org/u/bbentrup)\ **Post date:** [August 11, 2008, 11:53pm UTC](https://forum.uschess.org/t/prize-distribution-shoulda-hadda-v-8/7310/22 "2008-08-11T23:53:13Z")
From Josh’s example: 1st: 200, 2nd: 100, U2000 1st:80, U2000 2nd:60 2210: 5.0, 2190: 5.0, 2150: 5.0, 2100: 5.0, 2050: 5.0, 1980: 5.0, 1950: 4.5, 1920: 4.0 The proportionate system says that the players over 2000 get some split of 1st and 2nd and that the player under 2000 who also tied with them gets the highest prize he is due but at a proportion of each pot. This player must earn $80 total which is the highest pot for which he is solely eligible. His share of the overall pot is $300/6 or $50. His share of the U2000 pot is an undivided $80. His shares combine to $130. The $80 prize is 61.53% of his pot and the $50 prize is the remaining 38.47%. These percentages tell us how much need to come out of each prize to best make up the $80 he is due. 61.53% was the percentage of the $80 prize that he is due that needs to come out of the U2000 prize. This total is $49.22. The remaining part of the $80 he is due, which is 30.78, comes out of the 1st-2nd prize. So 1st-2nd prize is now ($300 - $30.78) $269.22, which should be divided equally between the five highest rated players who would each receive $53.844. There is still ($80-$49.22) $30.78 remaining in the U2000 1st prize and an unawarded U2000 2nd prize left of $60. The 1950 is next in line to receive prizes, and he is eligible for both, but since they are the same category of prizes, there is no need to split them proportionately. He would receive the higher prize of $60 and the 1920 player would receive the $30.78 as the next highest eligible scorer with just that one prize remaining. That was a lot weirder than the first two. Anyways, checking progress here: does anyone think I am remotely on the right track? ---
**Author:** ![sloan](https://sea1.discourse-cdn.com/flex019/user_avatar/forum.uschess.org/sloan/32/83_2.png) [@sloan](https://forum.uschess.org/u/sloan)\ **Post date:** [August 12, 2008, 12:57am UTC](https://forum.uschess.org/t/prize-distribution-shoulda-hadda-v-8/7310/23 "2008-08-12T00:57:36Z")
> [@jwiewel](#): > > > [@sloan](#): > > > > I have a counter-proposal: design prize funds so that correct prize distribution is obviously correct in all situations. > > > > Most prize distribution questions can be answered by: > > > > … E. Shoot the Organizer > > Unfortunately, the term “obviously correct in all situations” is not something that everybody agrees on (at least as long as there are class or under prizes in addition to place prizes). I apologize - I meant “obviously correct in all situations to anyone who has read and understood the rulebook - but may perhaps need to double check the details”. A properly designed prize structure eliminates the need to check the details. As soon as you introduce the idea of proportional prize distribution, all bets are off. This is not about details - this is about changing _fundamental_ concepts of prize distribution. Once you open the door to _that_ idea, the sky’s the limit. Fun to discuss - but probably a serious non-starter of an idea. I’d put it in the same class as “why isn’t USCF run more like MENSA?” ---
**Author:** ![Crume](https://avatars.discourse-cdn.com/v4/letter/c/4af34b/32.png) [@Crume](https://forum.uschess.org/u/Crume)\ **Post date:** [August 12, 2008, 5:52am UTC](https://forum.uschess.org/t/prize-distribution-shoulda-hadda-v-8/7310/24 "2008-08-12T05:52:41Z")
Homework for someone way more motivated than I am. What does the payout of the 2008 US Open look like if the proposed system was used? Prize Fund @ [http://main.uschess.org/tournaments/2008/usopen/?page=ABOUT](http://main.uschess.org/tournaments/2008/usopen/?page=ABOUT) Results @ [http://main.uschess.org/tournaments/2008/usopen/?page=RESULTS](http://main.uschess.org/tournaments/2008/usopen/?page=RESULTS) Actual Payouts for comparison @ [http://www.alchess.com/chess/08/usopen/?page=WINNERS&xsection=MERGED](http://www.alchess.com/chess/08/usopen/?page=WINNERS&xsection=MERGED) (or click “Winners” from the above Results page) +++ On a historical note, am I correct in my assumption that the current system of splitting prize funds was started so no one needed to calculate tiebreaks? Spread the prize money love? This would make sense prior to laptops running pairings and calculating distributions, but I don’t have any rulebooks prior to 5th edition so not sure how far back the distribution system goes. ---
**Author:** ![rfeditor](https://avatars.discourse-cdn.com/v4/letter/r/aca169/32.png) [@rfeditor](https://forum.uschess.org/u/rfeditor)\ **Post date:** [August 12, 2008, 6:12am UTC](https://forum.uschess.org/t/prize-distribution-shoulda-hadda-v-8/7310/25 "2008-08-12T06:12:47Z")
> [@Crume](#): > > Homework for someone way more motivated than I am. What does the payout of the 2008 US Open look like if the proposed system was used? > > Prize Fund @ [http://main.uschess.org/tournaments/2008/usopen/?page=ABOUT](http://main.uschess.org/tournaments/2008/usopen/?page=ABOUT) > > Results @ [http://main.uschess.org/tournaments/2008/usopen/?page=RESULTS](http://main.uschess.org/tournaments/2008/usopen/?page=RESULTS) > > Actual Payouts for comparison @ [http://www.alchess.com/chess/08/usopen/?page=WINNERS&xsection=MERGED](http://www.alchess.com/chess/08/usopen/?page=WINNERS&xsection=MERGED) (or click “Winners” from the above Results page) > > +++ > > On a historical note, am I correct in my assumption that the current system of splitting prize funds was started so no one needed to calculate tiebreaks? Spread the prize money love? This would make sense prior to laptops running pairings and calculating distributions, but I don’t have any rulebooks prior to 5th edition so not sure how far back the distribution system goes. Not really. A consensus was formed at least 30 years ago that using tiebreaks for cash prizes was unacceptable. The standardization of prize fund distribution methods came later. ---
**Author:** ![EricHammond](https://avatars.discourse-cdn.com/v4/letter/e/3da27b/32.png) [@EricHammond](https://forum.uschess.org/u/EricHammond)\ **Post date:** [August 12, 2008, 7:01am UTC](https://forum.uschess.org/t/prize-distribution-shoulda-hadda-v-8/7310/26 "2008-08-12T07:01:38Z")
> [@rfeditor](#): > > I just can’t accept that a system which filters more money down to lower-rated and lower-scoring players is an improvement. This can be addressed by adjusting the prize structure to award more dollars for place prizes and less for class prizes. Doing this in combination with the distribution method proposed by Smythe still accomplishes the stated intent: > [@Bill Smythe](#): > > As far as I can tell, this algorithm solves the discontinuity and anti-monotonicity problems of other methods, while still respecting the limit-one-prize-per-player rule…and is in harmony with the basic philosophy of class prizes… The Smythe method is simple relative to alternative proposals to reduce discontinuity and other perceived inequities. More class players will be able to understand why they did or did not share in their class prize, which is a win for both players and directors. I agree with Bill that this approach is an improvement. ---
**Author:** ![wintdoan](https://avatars.discourse-cdn.com/v4/letter/w/eada6e/32.png) [@wintdoan](https://forum.uschess.org/u/wintdoan)\ **Post date:** [August 13, 2008, 2:59pm UTC](https://forum.uschess.org/t/prize-distribution-shoulda-hadda-v-8/7310/27 "2008-08-13T14:59:11Z")
> [@Smythe Dakota](#): > > Suddenly, just the other day, I slapped my forehead. “I could have had a V-8.” An idea struck me which was so simple, and yet so logical, that I wondered why nobody had thought of it before. Stay tuned, and find out if you, too, should have had a V-8. > > Ideally, a prize distribution method should: > > 1. be continuous. A small change in the prize structure should result in only a small change in the actual prize won by any player. > > 2. be monotone. An increase in one of the prizes should never result in a decrease in the actual prize won by any player. > > 3. award class prizes to the players in that class. > > 4. be in agreement with the philosophy behind class prizes. > > 5. be simple to apply in the heat of tournament aftermath. There’s probably an Arrow impossibility theorem floating around here. I think you’re always going to have potential problems with discontinuities in the money flowing down to lower score groups. If you have $x for U2200 and $x for U2000 and a player is eligible for both, epsilon changes to either prize will shift the proportions from all coming out of one to all coming out of the other. So both continuity and monotonicity are out the window. Technically, the current USCF distribution system solves a sequence of optimization problems. Starting with the highest score group, maximize the amount awarded to that group (though not necessarily in equal amounts) subject to (1) the total shares across players of any prize is no more than 1.0, (2) the total shares across prizes for each players is no more than 1.0 and (3) in case of multiple ways to solve the maximization given (1) and (2), take place prizes first and class prizes from highest to lowest. Take whatever’s left and repeat for the next score group; continue until the money is gone. It sounds as if almost everyone agrees on constraints (1) and (2). I think most people would agree in principle with the notion that the payout to the highest score group should be maximized. The “problems” all arise in what flows down to the lower score groups. But as long as you stick with constraints (1) and (2), you can always construct problematic situations. And a proposal that discards the maximization at the highest score group (see John Hillery’s example where there are three prizes and three players in the top score group) and still doesn’t really fix the problems with the lower score groups doesn’t seem to be a step forward. ---
**Author:** ![bbentrup](https://avatars.discourse-cdn.com/v4/letter/b/e47774/32.png) [@bbentrup](https://forum.uschess.org/u/bbentrup)\ **Post date:** [August 13, 2008, 6:07pm UTC](https://forum.uschess.org/t/prize-distribution-shoulda-hadda-v-8/7310/28 "2008-08-13T18:07:19Z")
Mr. Doan, just the person I was hoping was watching this thread. I would claim that the proportional prize system I have been espousing has been by far the fairest with the most continuity. The problem is that the time-consuming math involved is a real turn-off, almost to the point of impracticality. Is there any way from a programmer’s perspective to fix this? I suspect there are just too many variables to just plug in all the prizes and amounts and have the program spit out the correct prize distributions, using any algorithm, much less the proportional system. Still, it doesn’t hurt to check. Peace. ---
**Author:** ![system](https://sea1.discourse-cdn.com/flex019/user_avatar/forum.uschess.org/system/32/2_2.png) [@system](https://forum.uschess.org/u/system)\ **Post date:** [April 22, 2024, 8:39am UTC](https://forum.uschess.org/t/prize-distribution-shoulda-hadda-v-8/7310/29 "2024-04-22T08:39:51Z")
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