Are you that good or feel lucky?

[S. Yama]

I just checked TXtour's poll "What would you do" in Announcements & Suggestion and I was a bit surprised seeing how (little) people wanted to restructure prizes of the $1Million Bj Tournament. The official prizes are: $1Mill, $40K, $25K, $15K, $10K, $5K, and $3K.

It is good to be confident but the matter of fact is that only a very few, very best, players will approach level where they are about 50% better than average to win a round – in our case the final round. And the earth shattering truth is that on average a player represents…an average skill level. Because of elimination process in rounds leading to final, remaining players usually represent better than average (slightly, though) level of skills, which in turns slightly “flattens†their chances of winning.

Let’s try to have a different view (okay, you can call it a spin) on participation in prize-pool sharing.
In the Hilton’s case there were $1,098,000 to be shared by seven finalists. If all players shared the money each player would get $156,857. At that point the money belonged to all finalists, and it was theirs, they have earned it.
Since even the last place finisher is paid $3K, we can say that players enter a lottery, or a drawing, where they have to pay almost $154K to draw one of the seven tickets where the “winnings†are: $0 (zero), $2K, $7K, $12K, $22K, $37K and $997K.
Would you do it? Imagine that you just inherited, or won, or that I personally handed you $157K cash and offered you this raffle. Would you do it, or would you happily keep the money?
This raffle is what finalists agree to do by playing for the official prizes and not sharing the money.

Of course it is a bit more complicated, but not that much. Let’s assume you are a very good player and you have 20% better chances of winning the final. Now, you could finish first about 17% of the time, second 17%, third to fifth 12% each, sixth or seventh about 15% each.
This means that by accepting the official prize structure you agree to pay (out of $157K that you just won and could take home) $154K for a ticket, just like in the above-mentioned case, except that now you draw from a box containing one hundred tickets, where there are 17 tickets worth $997K, 17 tickets worth $37K, 12 tickets worth $22K, 12 tickets worth $12K, and so on.
You are offered a game with almost $30K positive expectations, but are you willing to risk $154K of your own money to participate?

I think it is a fascinating subject – form of Certainty Equivalence - a place where psychology mingles with math.

Happy prize-pool sharing,
S. Yama

 

[TXtourplayer]

Good point

S. Yama makes a very good point (as he always does). My thought about making a deal in the Hilton was to cover 2nd - 7th place by getting $50,000 each and the winner $798,000. Anything other then first place and I could still walk away $10,000 more then the normal 2nd place payout of $40,000.

Now the first place prize of $1,000,000 would be very nice, but why get greedy (S. Yama's point). However look at it this way, what if you win and end up giving most of the money away in a seven way split? I would be sick the rest of my life...LOL. Now if I won and only give away $202,000 I may still get sick, but I could still walk away with $798,000 I could live with that. If I lost and walked with $50,000 I'd cry all the way to the bank. $50,000 is bigger then most of the major payouts around the country.

Unless I am in that situation I don't know what I would do. It would be very hard to turn down $157,000 (GARRENTEED)! Once again I would think more about how I would feel if I won then about losing. Walking away with $50,000 is not what I call losing.

 

[KenSmith]

My own preference for a heavily top-weighted prize structure cannot be justified by looking at the numbers. Your accurate representation of it as a drawing is sobering, yet I still have trouble agreeing to a more equitable split. Interestingly, if the first place prize money were half a million at the Hilton, I'd have no problem spreading the wealth around the final table. (Except for the paperwork and trust issues.)

There's an interesting psychological process at work with me, where I want to win near enough to a million dollars to be able to think of it as having won a million dollars. It's not a rationally justifiable position, as there's a large emotional element. I like the idea of having last place pay enough to be an appreciable amount, but I'm unwilling to dilute the large first place very much. I would find it disappointing to always be known as "the guy that won a million", when in truth I knew it was much lower than that due to a split.

Seeing the numbers behind my decision is a disturbing realization, because I surely can't afford the kind of variance we're talking about. It sounds like a decision made by a reckless gambler! Nice post Yama.

 

[tirle_bj]

Distribution

Of course it is a bit more complicated, but not that much. Let’s assume you are a very good player and you have 20% better chances of winning the final. Now, you could finish first about 17% of the time, second 17%, third to fifth 12% each, sixth or seventh about 15% each.

Well, Yama, I agree with conseption but desagree with distribution provided.
First of all the distribution should go from high to low upon getting worse place.

Here's the method of calculation:
1st 100/7 x 1.2 = 17.1 ~17%
2nd 82.9/6 x 1.2 = 16.6 ~17%
3rd 66.3/5 x 1.2 = 15.9 ~ 16%
4th 50.4/4 x 1.2 = 15.1 ~ 15%
5th 35.3/3 x 1.2 = 14.1 ~ 14%
6th 21.2/2 x 1.2 = 12.7 ~ 13%
7th 8.5/1 x 1.2 = 8.5 ~ 8%
Total 100%

Now it looks better to enter the drawing you've mentioned.
Psychology & Math... What should be a psychological criterion?
Let's say this way, if you play this game every day then you go by math and no questions asked. But unfortunately we don't have that kind of opportunity every day, so it comes to our financial situation. For some players $154,000 is not critical and they can afford to gamble for a Million (pride & money), for others it is a down payment for new house etc.
In other words, the more income we have the less interest we have to enter into the smaller tournaments.

So, I wish you all to lose the interest to enter in a smaller tournaments.

 

[S. Yama]

Tirle wrote: First of all the distribution should go from high to low upon getting worse place.
You assumed that if a player is 20% more likely to win he is also 20% more likely to get other places starting at the top. It ain’t so.
In top heavy tournaments (which Hilton’s is, to say it mildly) or in usual elimination rounds where only one person advances, good players win more than average share of them by trying (toward the end of a round) to become BR1 or second most money. Benefits of having good bankrolls come at the cost, almost equally often, of busting out or at least being severely disadvantaged with smaller bankrolls. Good players knowing what is needed to win will make an aggressive bet and play that often is successful but also will drop them toward bottom if it is unsuccessful. Thus, polarizing frequency of placements at the top and bottom.
Second place finishes in WTA tournaments also happen more often due to someone lucky(ier) beating our player by nose. I don’t have the exact data but my numbers seemed plausible. I would guess that with seven players and one person advancing, good player would finish fourth least often.

Tirle wrote: 7th =~8% (…) Now it looks better to enter the drawing you've mentioned.
In my analogy to drawing seven types of tickets only one is a carrot. It would be sweet to pick the $997K ticket. The rest of drawing tickets are sticks, some just hit you harder than the others– you “lose†$117K even with the second best ticket in the bunch.

You are absolutely right, if I could play Hilton’s type tournament hundred times I wouldn’t like to share a single cent of it. Let’s hope they continue offering it, and we live to be two hundred years old.
My psychological criteria would be: no sharing- lifestyle changing amount.
Yep, smaller tournaments don’t have this luster and radiance anymore but I think of $10 daily Maxim’s (included free buffet) tournaments with nostalgia.

S. Yama

 

[Walt]

No ego here

I'm with you Yama. If I had the situation every day, I'd make no deals. The same goes for the proposed 5k super-mini. I loved the concept, but for a one time event, it was very risky. And you're absolutely right about results. After reviewing my personal results, I found I had made 91 final tables with only a small percentage of 3rd through 5th outcomes. I tend to win or come in last and that's just final tables, obviously qualifying rounds would be even more extreme.

Barring trust problems, I would be willing to share the big prize. Unless of course, you and I were there together, then I would want to do a 50/50 deal with you.