Want a ‘plus-score system’ that will work with a 4 round G/30 event, one day event with the room rent being $30 for the tournament. The tournament will be a open, looking to have around 20 players each and every tournament. Make the case for this format under the ‘plus-score system’.
Doug,
LOL,
AJG
Increasing differences does not necessarily imply a geometric sequence, but a geometric sequence does imply increasing differences.
In any geometric sequence, such as 1,2,4,8,16,32 etc, each difference is greater than the last (unless the ratio is less than 1, in which case each difference is LESS than the last).
In any case, it’s certainly NOT an arithmetic sequence, like 2,4,6,8,10,12 etc.
The plus-score structures we have been discussing are pretty close to geometric. As I’ve said before, I’m less scientific about this than you are. Anything that looks about right, and works out right with Pascal’s triangle, suits me fine.
Bill Smythe
The format we’ve been discussing should work fine. With a $20 entry fee and payouts of $100-50-25-10, you’ll take in $320 and pay out at most $200, assuming a turnout of 16 players. If you have more or fewer players, both entry fee income and prize fund will increase or decrease proportionally. You’ll have a lot more than $30 left over to pay the room rent.
G/30 vs G/60 makes no difference – the math is the same.
Bill Smythe
No, you have plenty of company, but most people have given up on that particular soapbox by now.
I have moved this reply to the Plus Score thread because the plus-score prize format offers a possible answer. With prizes by score instead of place, and with a decreasing-differences prize structure, fighting chess is encouraged. An example of a plus-score payout with a relatively affordable entry fee would be as follows:
Number of rounds: 4
Entry fee: $20
Prize for 4-0: $100
Prize for 3.5-0.5: $50
Prize for 3-1: $25
Prize for 2.5-1.5: $10
See the earlier contributions to this thread for additional discussion.
Bill Smythe
Have run 3 plus-score events (Western Michigan Open, Western Michigan Open II, Western Michigan Open III), for the first two only had only one draw during the last round. With Western Michigan Open III, out of 33 ratable games, 8 were draws: making the draw percentage 24%.
I notice you had decent turnouts, too.
Did you go with the $100-$50-$25-$10 payout scheme, or did you chicken out and award only $40 for 4-0?
Bill Smythe
The $40 = 4.0, but nobody has a problem with the prize money. The masters are going to play with a $40 prize award or the $100 prize. The players in the middle like the $25 prize then the $10 prize.
Having a large prize award or a small prize award has not made a difference in the turnout. Western Michigan Open, had a player from Texas on vacation in Detroit. Western Michigan Open II, had two players not from Michigan (one from Chicago and the other from Ohio). Western Michigan Open III, had a player all the way up north. The last one did have 18 players, but it was during a lake effect snow storm.
I was thinking about holding a 5SS tournament with a plus scoring payoff. To better understand what the chances of making or losing money were for various numbers of entries in the tournament, drawing percentages, and payout schemes, I wrote a simulation program. The results are interesting. The payout I assume was 8-4-2-1-0.5. Where number is the factor multiplied by the entrance fee. So 5-0 gets 8 times the entrance fee, 4.5-0.5 get 4 times the entrance fee etc.
The only real risk of paying out more than you take in is at the low number of players. Here is a sample where I’ve used the above payout and assumed 10% of the games are drawn. For each number of entries I simulated 10,000 tournaments and determined the total payouts [in units of entrance fees]. The column headings are Number of entries, Minimum payout, 10th percentile payout, 20th percentile payout, 80th percentile payout, 90th percentile payout, max payout, average payout, and median payout.
Num Min 0.1 0.2 0.8 0.9 Max avg median
Ent
8 2.0 3.4 4 6.5 9 11 5.2 4.5
10 2.5 4.5 5 9.5 10 11.5 6.4 5.5
12 2.5 5.5 6 10.5 11.5 12.5 7.7 7
14 3 6.5 7 11.5 12 14 8.9 8
16 3 8 8.5 13 13 15 10.3 9.5
18 6.5 9 9.5 14 14.5 16.5 11.5 11
20 7.5 10 10.5 15 15.5 17.5 12.8 12.5
26 10.5 13.5 14.5 18.5 19 21.5 16.5 17
32 13.5 17.5 18.5 21.5 22.5 25 20.2 20.5
The big uncertainty at the low number of entries is whether someone will go 5-0 or not. At the large number of entries things average out and there is no way to lose money. Even at a large number of entries the distribution of payouts shows two peaks. This is due to the variation in total payout if the final games between undefeated players are drawn or not.
As you increase the drawing percentage the average payout decreases and the variation in payout decreases.
From this I feel pretty good about using this payout as long as I can get at least 15 entries.
Mike Regan
I’m a little surprised you’d be willing to go with 8 times the EF for a perfect score. If you extended this philosophy to six rounds, I don’t think you could afford to pay out 16 times the EF for a perfect score.
You might want to make it 5 times the EF, regardless of the number of rounds, but just taper it a little more slowly for each added round. For example, with a $20 EF:
4 rounds: $100-$50-$25-$10
5 rounds: $100-$60-$35-$20-$8
6 rounds: $100-$65-$40-$25-$16-$6
The other problem with 8-4-2-1-0.5 is that, at the last step, you are no longer discouraging draws. At every other point, draws help the organizer, because for example 8+2 is greater than 4+4 (each difference is less than the preceding difference). But at the bottom end, 1+0 is not greater than 0.5+0.5.
So maybe something like 8-4-2-1-0.4 would be more in keeping with the philosophy of encouraging fighting chess. (Yes, I know that spoils the mathematical symmetry, but … )
Bill Smythe
I’m a little surprised you’d be willing to go with 8 times the EF for a perfect score. If you extended this philosophy to six rounds, I don’t think you could afford to pay out 16 times the EF for a perfect score.
You might want to make it 5 times the EF, regardless of the number of rounds, but just taper it a little more slowly for each added round. For example, with a $20 EF:
4 rounds: $100-$50-$25-$10
5 rounds: $100-$60-$35-$20-$8
6 rounds: $100-$65-$40-$25-$16-$6
The other problem with 8-4-2-1-0.5 is that, at the last step, you are no longer discouraging draws. At every other point, draws help the organizer, because for example 8+2 is greater than 4+4 (each difference is less than the preceding difference). But at the bottom end, 1+0 is not greater than 0.5+0.5.
So maybe something like 8-4-2-1-0.4 would be more in keeping with the philosophy of encouraging fighting chess. (Yes, I know that spoils the mathematical symmetry, but … )
Bill Smythe
Bill,
You’re right about the last payout. I missed that. I agree that maybe 0.4 * entrance fee is best.
Your proposed payout levels are really quite conservative. From a quick run of the simulator I see that on average they payout 50% of the entrance fees for the 5 round payouts. 8-4-2-1-0.5 pays out around 62% of the entrance fees for a large number of entries. So if you were confident that you were going to get a large number of entries you could even have a higher payout. The only risk is at the low number of entries where they average is still 62% but you can get unlucky and lose money. I feel you want to have a large prize for 5-0 to attract more players.
I’ll try some six round versions and see what happens.
Mike
Bill,
I ran some simulations for a $20 entrance fee. Assuming a conservative draw rate of 10%.
Your: 4 rounds: $100-$50-$25-$10
This averages paying out 57% of the total entrance fees.
Your:5 rounds:$100-$60-$35-$20-$8
This averages payout out 50% of the total entrance fees.
Yours: 6 rounds: $100-$65-$40-$25-$16-$6
This payout averages paying back only 40% of the total entrance fees. This seems a little low to me. It is harder to go 6-0 than to go 4-0 but in your proposed payouts they both earn $100.
Mine: 6 rounds: $320-$160-$80-$40-$20-$8
This payout averages paying back 76% of the total entrance fees. This is probably too aggressive and will lead to losing money sometimes when the number of entries is low. But if the drawing percentage is 20% then this payout averages paying back 66% of the total entrance fees.
So I think the right answer is somewhere between the two possible payouts. I think averaging 65-70% payouts is a good goal. What I like about this format is that the ratio of income to prizes is constant no matter how many entries. So instead of the organizer either making or losing money, the total prize fund scales with the number of entries but the players always get the same amount for a given score. You don’t end up where six people who are 4-1 tieing for second and third and going home with just their entrance fees. Fixed place prize tournaments are like the lottery. The big prizes attract a lot of players making it more likely that you will have to split the prize money.
An interesting side question is how many Grand Prix Points would a plus score format tournament qualify for? The money is guaranteed but the total amount depends on the number of players. The amount the winner gets depends on their score.
Mike
Granted, my payout scheme is conservative.
If your club has few or no other expenses associated with the tournament, you can afford something a little higher.
A conservative scheme does, however, provide a better cushion in the event of an extremely small turnout.
Bill Smythe
Several years ago Bill Goichberg tried a plus-score format in a few of his tournaments (in all but the Open sections). To satisfy the grand prix requirement, he also guaranteed “minimum total payout $$XXXX, all prizes raised proportionally if necessary”. I don’t think most organizers could afford to do that, but the scope of his events was such that an actual payout of only $$XXXX was extremely unlikely.
Bill Smythe
While I’m posting on this topic, I might as well point out yet another advantage of the plus-score system, one which is often overlooked until the day of the tournament.
When you finish your last game, there is no need to wait for other games to finish to find out whether, and how much, you have won. The TD can fork over your moolah as soon as your own game is done.
How often, in a standard prizes-by-place event, have players finished early, only to have to wait a couple of hours to see whether they are in a 6- or 7-way tie for third?
Bill Smythe
With my plus score tournament, the prize money (if at the board) has been given to the player before packing up the set and board.
All of this talk about the Plus Score format has given me the drive to go ahead and organize my own tournament, but over 6 rounds.
Since it would be an Open Tournament with a large variety of ratings I’m wondering whether using accelerated pairings would have an effect on the prize allocation, e.g. would it give me more profit if I used them, or does it all work out to about the same in the long run?
Prize fund is going to be:
6 pts, $200
5.5 pts, $80
5 pts, $40
4.5 pts, $20
4 pts, $10
We’re also discussing whether to give a $5 prize to those who score 3.5 pts, or to give the winner of all last round games the $5 prize instead (unless they win a higher prize).
Chris
Hello Fantasychess,
Since draws help reduce the total payout, your worst case scenario is going to be with all decisive games.
Running the numbers on a 128-player 6-round tournament gives the following (every 6, 5 and 4 gets offset by a 0, 1 and 2 respectively with the remainder having 3):
Standard pairings - 2@6, 12@5, 30@4 for a maximum of $1180 in prizes;
Accelerated best case where round 2 has every top half loser defeating the bottom half winner - 1@6, 10@5, 31@4 for a maximum of $910 in prizes;
Accelerated worst case where round 2 has every top half loser losing to the bottom half winner - 3@6, 14@5, 29@4 for a maximum of $1450 in prizes.
The big changes are the number of 6s, with the number of 5s having noticeable but smaller effect.
Acceleration in a tournament with a wide variety of established ratings usually helps squeeze the score distribution towards 50%, which is what you want. It sounds like accelerating your expected player turnout would be more likely than not to squeeze the score distribution, but remember that there is always some risk of it not working as anticipated.
If you expect significantly less than 128 players, and especially if you are under 65 players, you are likely to be questioned as to why you would bother with accelerated pairings. Also, if you get 64, then the difference in payout could easily be saving just a single 5-point score (standard would be 1@6, 6@5, 15@4 while good accelerated would be 0.5@6, 5@5, 15.5@4 which can end up as 1@6, 5@5, 15@4). If you get noticeably less than 64 then the results may have the same distribution as standard pairings, resulting in the same payout while having to deal with the questions as to why you accelerated.
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If the payout matrix is properly designed, you WANT more players than the theoretical perfect number, because that improves the odds of last round draws, all of which make you money.
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Accelerated pairings seem somewhat contrary to the plus score spirit, which is to encourage players to think they can ‘beat the matrix’ and win your perfect score top prize. In the several times I ran 4 round plus-score events, I NEVER had anyone go 4-0, despite having more than 16 players.
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As a 1400 player who is seldom above the break in the 1st round, accelerated pairings deny me the chance to play against and knock off a high rated player.
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If you’re running a 7 round event and are worried about a turnout larger than 128, I think you’re worring about the wrong things!