MBT Payouts

[jchiu]

I am thrilled to see that Money Bridge Tournaments have caught on like a wildfire!

 

Summary: However, I am not so excited about the current payout structure becuase it rewards a session with extreme good luck much more than it would for a small tournament. I am proposing a change in the payout structure. Rather than paying the top player about $10 and the fifth place player about $1, with an exponential dropoff in between, I suggest paying the top player about $6 and the tenth place player about $1 with a harmonic dropoff in between. This way, more players will feel like they have won something even with a decent game and return in hopes of winning the big prize. This would also give mediocre players with a lucky collection of cards a chance to scratch more often, thereby increasing the expected returns.

 

Details: Long and hypothetical, with the use of some basic mathematics.

 

Status Quo: In a thirty-player tournament, the prizes are $12.50, $6.00, $3.00, $1.50, and $1.00. No player finishing below fifth received anything back.

 

Possible Proposal: Give prizes according to the structure by which the ACBL awards masterpoints. In the most recent North American Swiss (For those who are not familiar, this is a six-session swiss team event, in which each session consists of four matches of seven boards. The IMP scores are converted to the 20-point VP scale. After every two sessions, half of the field is cut. This is a strong North American Bridge Championship event, but runs along the more famous Reisinger BAM teams.), the ACBL paid 160 masterpoints for first, 120 for second, 90 for third, and 160*(6/(rank+9)) for fourth through twenty-eighth. I suggest money bridge tournaments pay a depth of one-third, and proportional to some masterpoint structure like this one. In a thirty-player tournament, first place would get $4.82, and tenth would get $1.52.

 

Impact: Suppose we have two players, a flight A player (called A) who plays steady and averages 900 points per session with a standard deviation of 1500 (I just used my numbers here); a flight B player (called B ) who plays almost as steady and averages 150 points per session with a standard deviation of 1650; and a mediocre player (called C) who plays somewhat haphazardly by accident and averages -600 points per session with a standard deviation of 1800. We shall assume that the distribution is Gaussian (simplified!).

 

In the most recent tournaments this afternoon, it has taken anywhere from 3000 to 4000 total points to win, about 1800 points to finish fifth, and about 1100 points to finish tenth.

 

Under the current scheme, A would win approximately one time in fifteen, finish second or third once, barely scratch twice, and out of the money eleven times for an expectation of about $19.00 for fifteen games. How can such a player lose? Because other higher-variance players are stealing the pots and keeping A barely out of the money. In the new scheme, A would also finish sixth to tenth thrice (in fifteen games) for an expectation of about $18.50. Note that this is slightly less than the current payout structure for A. But it would be a much more satisfying way to play for me, and would be less susceptible to droughts. Personally, I would still play the $1 tournaments at the current payouts but less often; and would not play $20 tournaments if they came to be, for this reason alone.

 

B would win approximately one time in thirty, finish second or third twice, and fourth or fifth twice, for an expectation of about $22.50 for thirty games. Under the new scheme, B would finish sixth through tenth another three times in thirty for an expectation of about $23.50. Note how close this brings the expectation up to being almost par with the $24.00 expectation for the average player.

 

C would win approximately one time in ninty, finish second once, third twice, and fourth or fifth four times, for an expectation of about $29.50 for ninty games. Under the new scheme, C would finish sixth through tenth another ten times of ninty, for an expectation of about $38.00. Note that the payout structure more than doubles the number of times a mediocre player finishes in the money, and increases the expectation noticably.

[uday]

We could clone the acbl payout scheme - roughly 40% of the field gets something back.

Fred has been suggesting for a while that we flatten out the award structure.

 

We're not limited to a single structure and I dont mind experimenting. Won't the winners mind that their "prize" has been diluted? Won't longer tourneys ( I will probably try some 45 min tourneys sometime this week, once some new machines come online) be better for the stronger player? Or a duplicate-style scoring , either using old boards from the MBC or wherever, or russian scoring all increase the impact of skill ?

 

I'm not sure what we're looking for, exactly.

[jchiu]

Some very interesting points, Uday.

 

1. Won't the winners mind that their "prize" has been diluted?

 

I have played in about a dozen MBTs seriously (i.e. not for the sake of experimenting on the limits of GiB through psyching), and have used my numbers for player A above. I think that even if the prize is diluted, it will be more satisfying to win little chunks more often, rather than finish "out of the money" about 70% of the time.

 

2. Won't longer tourneys ( I will probably try some 45 min tourneys sometime this week, once some new machines come online) be better for the stronger player? Or a duplicate-style scoring , either using old boards from the MBC or wherever, or russian scoring all increase the impact of skill ?

 

I think so. In the model above I am figuring a positive bias of about 50 points per hand, which would increase skill almost to the point that a top player could usually scratch over a course of 32 hands (if it pays 33% to 40%). This is assuming that playing one board every ninety seconds does not wear the player's efficiency down.

 

I would like to see duplicate scoring, but from (very) old hands. I still have a hand memory that spans about six months. If I see an especially notable hand, then I may remember it in the tournament. That would be an unfair advantage. OTOH, you could probably filter the hands so no entrant has either played or kibitzed them ever.

 

3. I'm not sure what we're looking for, exactly.

 

Neither do I, or for that matter any of the forum posters. We are just happy it exists :P

 

Remark: The sample is still too small to conclusively conclude that the distribution is anything close to Gaussian. In reality, I think it is a convolution of a flat distribution between -1000 and +1000 and a slightly positive-skewed Gaussian depending on my actual play with standard deviation about 300, shifted over by the 900 point bias. Too hard to model on the back of an envelope here.