Interesting to note that this month’s Chess Life has a report on the Chesapeake Open using a point based award structure. Does anyone know how the directors/organizers figured out an award structure that they could predict wouldn’t be a big loss for the tournament? Because if it weren’t for that uncertainty, I like that award structure a lot more than the “winner take all” structure that most tournaments seem to have.
Trick number one is to use Pascal’s Triangle:
rounds players distribution
0 1 1
1 2 1 1
2 4 1 2 1
3 8 1 3 3 1
4 16 1 4 6 4 1
5 32 1 5 10 10 5 1
6 64 1 6 15 20 15 6 1
For each extra round, double the number of players. To construct Pascal’s triangle, start with 1’s down the left and right sides. Each internal entry is the sum of the two entries immediately above it, to the left and right.
Pascal’s Triangle gives the expected number of players with each score, assuming no draws, no upsets, no byes, etc. For example, with 4 rounds and 16 players, you would expect
1 player at 4-0
4 players at 3-1
6 players at 2-2
4 players at 1-3
1 player at 0-4
Trick number 2 is to have a decreasing-difference prize scale, such as
4.0 wins $100
3.5 wins $50
3.0 wins $25
2.5 wins $10
Each difference is less than the difference above it:
($50 minus $25) is less than ($100 minus $50)
($25 minus $10) is less than ($50 minus $25)
($10 minus $0) is less than ($25 minus $10)
The decreasing differences justify the no-draws no-upsets assumption as the worst-case (for the organizer) scenario. Draws reduce the total payout and thus help the organizer. For example, two players at 3-0 paired against each other in round 4 will win a total of $125 ($100+$25) if their result is decisive, $100 ($50+$50) if they draw.
Now just put two and two together – Pascal’s Triangle (worst case) plus payout scale:
$100 (1 player at 4-0 wins $100)
$100 (4 players at 3-1 win $25 each)
$200 total prizes
So a $20 entry fee should cover it (16 players paying $320 total in entry fees).
If you want to try a different scale, make sure you are still obeying Tricks 1 and 2, then do the math as above. If the ratio of total prizes to total entry fees turns out unfavorable, make some adjustments.
Note 1. If the total turnout is higher or lower than the “theoretical” number (e.g. 16 players for 4 rounds), it doesn’t matter. Both total entry fee income and total prize payout will increase or decrease automatically, in proportion to the number of players. Each individual prize is guaranteed, yet the total prize fund expands or contracts with the turnout.
Note 2. If you want to have higher or lower prizes, just increase or decrease everything in proportion. For example, if you double each prize and double the entry fee, the ratio of total prizes to total entry fees stays the same.
Note 3. There should be prizes only for plus scores, and the prize for having barely a plus score (e.g. 2.5-1.5) should be lower than the entry fee. Otherwise the math just doesn’t work out.
For 5 or 6 rounds, the decreasing-differences scale needs to be a little less drastic than for 4 rounds. For 5 rounds it could be something like:
5.0 wins $100
4.5 wins $60
4.0 wins $35
3.5 wins $20
3.0 wins $8
while for 6 rounds the following should work:
6.0 wins $100
5.5 wins $65
5.0 wins $45
4.5 wins $30
4.0 wins $17
3.5 wins $7
Again, do the math to make sure you don’t lose your shirt, and make sure you are still obeying Trick number 2.
Bill Smythe
Thanks, Bill. I was struck by how harsh the typical prize structure was after this weekend’s Marshall U1800, where places were only paid for 1st, 2nd, and U1500 for a field of 42. Going into the last round, my opponent was a 1610 rated kid and the only perfect score (to my 2.5), but a last round loss left him completely out of the awards despite his excellent tournament.
I also remember regular Friday night tournaments in Cleveland in my scholastic days–always with a standard prize schedule, always dominated by a local 2500 rated player who just needed the money. Decent just to get games in, but even local masters didn’t have much hope at a prize.
Really, what this prize structure does is take the typical 1st place award and limit it to perfect scores, while dividing lower places more evenly among other plus scores. I don’t know that I’d want to bother with sub-entry prizes for scores a half point above even, but a prize structure that guarantees something for 3.0s in a 4 round, 3.5s in a 5 round, or 4.0s in a 6 round would be a lot better at encouraging amateur players.
Bill’s summary is basically correct but very conservative. If you based your payouts under the assumption of no draws, you would not be able to have much of a prize for 5-0. Bill’s sample payout of 5x the entry fee for going 5-0 is low. At the Chesapeake Open the payout is as high as 15x the entry fee in the open section.
The problem is that once you include draws, the number of players at each score group is no longer deterministic. Instead there’s a random factor. You also have to assume what the draw fraction will be. To deal with this I wrote a simulation program where I could try out different payout structures and draw fractions. I then would run the simulation for a large number of times to figure out the average payout.
The only way to really have things turn out bad is when you have a very small section and someone goes 5-0. At my first Chesapeake Open I had a 3 player U2100 section and one player went 5-0 ($1200). That was painful.
Even in the best case with reasonable size sections, there’s a random factor in what your payout will be. That’s why it is good to have multiple sections. This averages out the payouts.
Mike Regan
Could you do a reasonable compromise saying that prizes will be score-based for sections with a minimum of 2^n players, where n is the number of rounds, with an more standard prize structure if the section doesn’t reach the minimum?
That gets uncomfortably close to the concept of based-on prizes. The whole idea of score-based prizes is to avoid based-on prizes, which tend to keep players away, while still allowing the total prize fund to expand or contract automatically with the turnout.
If there are fewer than 2^n players, the section probably still won’t lose money, because there will be fewer players with each score. The ratio of prizes to entry fees should remain almost constant regardless of turnout.
The only exception is an extremely low turnout. In my $20 example:
4.0 $100
3.5 $50
3.0 $25
2.5 $10
– if there are 6 players, worst case is one 4.0 and one 3.0, for a total prize payout of $125. The tournament loses $5.
Score-based prizes are not zero-risk – nothing worthwhile is zero-risk – but it’s extremely low-risk, if you do the math correctly. And the tournament remains attractive to the players.
Bill Smythe
I don’t think it’s “based-on” prizes that scare people away, but “winner-take-all” prizes. Say you have a 4 round tournament with a prize structure:
EF towards prize fund: $20
Prizes if fewer than 16 players:
1st: 40% of prize fund
2nd: 25% of prize fund
3rd: 15% of prize fund
4th: 10% of prize fund
Class prize: 10% of prize fund.
Prizes if 16 or more players: score based.
With 15 or fewer players, at least 5 are getting something, so there’s enough there for people to play for, with less chance of causing the TD to take a big hit if only 5 people show up. This is more of a concern at a 5-round or 6-round tournament where you have a bigger perfect score prize, so you don’t have a disaster like Mike’s 3 player U2100 section with a perfect score.
I know you were concerned about “rulebook legal” - but I looked at - LAW legal.
Ran such an event in 1978 at the Waukegan, IL recreation center, called the Play at Your Own Risk Open. Certainly legal.
Probably not legal in most states. Typical chess prizes don’t fall under gambling rules, this probably does. Also typically, if there is an exception to being counted under gambling rules, there needs to be no purchase necessary. (It’s not gambling if you put nothing up.)
Wouldn’t impact me in the least.
What do you mean by “winner-take-all” prizes?
Alex Relyea
Where only the top few players get anything of value, or where being a half point off of first knocks you out of the prize fund. Tournaments that pay only 2 places to a field of 40+. Tournaments where you can be the only perfect score going into the final round, but a loss leaves you with no prize at all. That sort of thing.
That sounds almost guaranteed to drive players away. All those percent signs – ugh! (Maybe that’s not logical, but it’s the way most players react. Prizes with percents in them are just as unattractive as based-on prizes. In fact, they actually are based-on prizes.)
With the payout structure I mentioned before – $100, $50, $25, $10 for a $20 entry fee – the odds of the entry fees not covering the prizes are near zero, down to about 6 players. And below that, the probable loss is minuscule.
Just take a deep breath, and use the score-based prizes no matter what. It will attract more players. If you can’t afford even the almost non-existent risk of a tiny loss, you probably shouldn’t be organizing chess.
He was taking a bigger risk, with multiple sections, and with a top prize about 15X the entry fee. Still, even in that year, I’d bet his entry fees covered the prizes overall, with the other sections making up for the U2100.
Bill Smythe
First, are chess players so radically different from poker players to be driven away by prizes stated as percentages? Because pretty much every poker tournament sets is prizes in terms of percentages, usually much more confusing ones than the ones I listed (e.g., 10th place gets 2.45%).
Second, the risk of loss is insignificant for your prize list for a 4 round tournament, but that’s because your prizes are fairly low. For a 16 player section and no draws, you expect $320 in entry fees and $200 in prizes, creating a prize fund of at most 60% of entries. Of course draws decrease that further. Give more prizes and make it a five round tournament and the risk goes up.
And third, if the attitude towards prospective TDs is “You should be willing to take a personal loss to run tournaments in which you have no chance at financial gain and are essentially acting as a volunteer,” well, you get what you pay for. Is it any wonder there are more scholastic organizers than adult organizers when only the scholastic organizers can stay financially safe (thanks to cheap trophies and free school playing sites)?
There was an interesting article in the last CL about prizes based solely on scores, not final place. In other words the TD announces beforehand that a score of 3/5 wins $75, 3.5 wins $125, etc.
Would this require banning players from playing up? Otherwise there would be more positive scores would normally be expected due to all those players scoring 0, .5, and 1. Or does the pairing system work that out?
The only negative effect of people playing up is that there are potentially less draws. Even if someone goes 0-5 that doesn’t directly lead to more money being paid out. The main variable in the total payout is the draw fraction of people with perfect scores. People playing up only have perfect scores in the first round.
Mike Regan