If he is the only one of the group to win, that something will be three times smaller.

This is essentially a fair bet.

Solved

Posted on 2012-09-05

My son is going to a poker tournament which pays out equal amounts to the top 10%.

Asssuming that all the players have equal ability, then the odds of my son winning is 1 in 10. My son is trying to help decide whether he and two friends should share evenly their prizes. If they do so, how do the odds improve that they will all take home a prize?

Tournament begins in 3 hours so please answer quickly; explaining your results will help me understand the results better.

Do the number of entries in the tournament affect the results, whether it be 100 or 1000 players?

Thanks,

Paul

Asssuming that all the players have equal ability, then the odds of my son winning is 1 in 10. My son is trying to help decide whether he and two friends should share evenly their prizes. If they do so, how do the odds improve that they will all take home a prize?

Tournament begins in 3 hours so please answer quickly; explaining your results will help me understand the results better.

Do the number of entries in the tournament affect the results, whether it be 100 or 1000 players?

Thanks,

Paul

21 Comments

If he is the only one of the group to win, that something will be three times smaller.

This is essentially a fair bet.

Assume 100 players.

If the player who is first loses enough in the last hand to move his teammate from 12th to 9th, he doubles his winnings.

Be aware of it and beware of it: This is cheating. Ask the poor fellow who would have been 10th.

Team play of the sort you are describing may in fact be prohibited. I would check.

>> The odds are three times higher to win something

Originally, the odds of my son winning is 10%. Now, I think you are saying that by sharing the prize pool with his two friends, the odds is now triple or 30%. That would be nice, but if I extrapolate and if he had 9 friends, then it couldn't be that the odds of winning would be 10 times higher (or 100%), which would be very nice; but not realizable. Maybe I am misunderstanding what you mean.

By team play, I understand that you are talking about collaboration which is not allowed. They have never collaborated in any way. But thanks for the cautionary advice!

They are not team playing. They are just considering sharing any prizes amongst themselves to try to at least take home something. It is a form of chopping, which is legit.

p = 0.729 LLL

P = 0.081 LLW LWL WLL

p = 0.009 LWW WLW WWL

P = 0.001 WWW

Probability of winning something would be 3*(0.081 + 0.009) + 0.001 ==> 0.271

EV = 0.081 + 2*0.009 + 3*0.001 = 0.1

This is the same as for a single player, which is why I said this is a fair bet.

It there are fewer than 30 players, there may only be two winners.

the EV for an individual is 0.10 with a 10% chance of winning

the EV for an individual is 0.0333 with a 27.1% chance of winning

Thanks.
Is the following individual take-home correct?

No Sharing:

10*$1000 = $10000

Sharing:

27.1*$1000/3 = $9033

Even bet?

I do not understand why there is false hope.

And I am not sure if I am doing something wrong with the 100 tournament scenario. I thought "even bet" meant that the outcome would be the same over a large number of tournaments; yet, the "not sharing" scenario appears to pay out better.

(btw, to correct typos, you can now hit the Edit Comment button.)

I think d-glitch showed how the expected values for each possibility worked out, and that the total prize taken from the prize fund did not vary whether it was shared or not. This was to show that sharing gave no disadvantage to the other players.

The odds listed for each of the possible outcomes show that for instance there is a .009 chance of just two of the three winning, and so the prize would be 2/3 each (Two wins divided between three people).

To extrapolate this into a total chance of winning a certain amount loses a lot of its meaning, a bit like saying I have a chance of winning $1000 on a lottery ticket, when I really only have a slight chance of winning millions. The maths aren't incorrect, but they are describing a near impossible event. There is only that single multi-million prize and a very slim chance of winning it. Offering to share (syndicate) with others does increase my chances of winning, and assuming the shares are even and there are enough people, then my chances are increased, but certainly not so much that I can be assured of a profit on my gamble.

(Thanks for the typo tip, but it doesn't work on my phone.)

27.1*$1000/3 = $9033

That is not correct. You are missing the probability of multiple wins in a particular round.

```
A single player will win 100 times for a total of $10,000
A team of three can expect the following:
729 No winners
243 One winner 24,300
27 Two winners 5,400
1 Three winners 300
------------------------------------------
$30,000 which must be shared three ways.
```

The Expected Value for each player is identical in both scenarios.
That is not correct either. You were missing the

The 27.1 is the chances of winning a part of any prize. The actual value of the prize is not included in that figure, in fact it is a mix of three values in varying quantities.

The chances of winning an exact value were shown above and separately shiwn was the 27.1 chance of receiving any of those values. You can't just divide the odds of winning any prize into the total prize pool and expect to calculate your win.

the chance of all 3 players getting no prize is 0.9^3 = .729

the chance of at least 1 player getting a prize is 1 - chance of no prizes = 1-.9^3 = .271

**************************

the chances of getting a prize is higher, but expected winnings will be unaltered

expected winnings is always 10% of the prize

@deighton: It seems that your post summarizes nicely what was said before, or am I missing something?

>> $30,000 which must be shared three ways

Ok, thanks. I believe I may have mixed up probability of winning with expectation. I will straighten this out and try to post a correction.

>> ... false hope ... lottery ... The maths aren't incorrect, but they are describing a near impossible event.

Not sure I agree (or maybe just not following you - I follow better with concrete math examples). If there is a slim chance of winning, but the game or lottery has a positive expectation, then you can be confident of winning if participating in a large number of events. Most state lotteries have a negative expectation; and therefore, it is a losing proposition. But not always! Although each ticket had a slim chance of winning, the group purchase large buckets of tickets and won millions, as they predicted for their school project. I think they got an 'A' for the project. I also read once (maybe this was the case) that there was a lottery promotion - buy one get one free - and a group computed a positive expectation and also won millions.

Title | # Comments | Views | Activity |
---|---|---|---|

Turning on aircon while car is stationary is hazardous (CO & harmful gases?) | 16 | 838 | |

Probability Calculation | 2 | 33 | |

Discrete Probability | 2 | 40 | |

Revenue table | 8 | 53 |

Join the community of 500,000 technology professionals and ask your questions.

Connect with top rated Experts

**16** Experts available now in Live!