Need help on math question.

Say I play a backgammon tournament with a buy in of $7 and a guaranteed prize pool of $49. Assume there will always be only 6 players in it, and all players are of equal skills, so each player have about 50% chances to win a game against any of the opponents.

Always out of these six players, two random players will get their first game directly in the semi finals, while the others will get in the quarter finals. The prize distribution is as follow: 1st place $37, and 2nd place $12. OK, this is a +EV event, and since the total buy ins are 6*$7=$42 but a guaranteed amount $49, this would result in ($49-$42)/6=+$1.66 per person for each event, in the long run.

My question is: - what bankroll you need in order to have a Risk of Ruin lower than 0.1% ? (and same question, but for a scenario where there would be a "winner takes all" format where the 1st place take the pot ?) (*each player have 16.66% to win the tourney)

You do have a 16.67% advantage on this. The question you should be asking is how much should I wager on every match, to grow my bankroll as quickly as possible. The answer to that question is 3.26% of your bankroll on every tournament. To answer the question you asked would require computer simulations, which I don't think anybody is going to do for free.

Quote: Wizard

The question you should be asking is how much should I wager on every match, to grow my bankroll as quickly as possible. The answer to that question is 3.26% of your bankroll on every tournament.

Thank you Mr. Wizard, this info might help me too. - But I can not change the amount I wager on a game, because the ticket for participating into the tournament is always $7, and the games have no additional stake, except the winner advance to the next level.

Quote: Wizard

To answer the question you asked would require computer simulations, which I don't think anybody is going to do for free.

This is also very true, but .. if someone is in a great mode, can and want to help me .. I would deeply appreciate his or her effort !

Quote: PlayHunter

This is also very true, but .. if someone is in a great mode, can and want to help me .. I would deeply appreciate his or her effort !

Just bet the $7 every time. It is a great bet.

Quote: Wizard

You do have a 16.67% advantage on this. The question you should be asking is how much should I wager on every match, to grow my bankroll as quickly as possible. The answer to that question is 3.26% of your bankroll on every tournament. To answer the question you asked would require computer simulations, which I don't think anybody is going to do for free.

I disagree, in premise, b/c optimal wagers can only really apply to games in which you can control the amount wagered. In this case, You can use Kelly to define what would be an overbet... esssentially in these cases I think Kelly is only really useful to show you when it's TOO risky, not the optimal bet, since you can't make that optimal bet even if you wanted.

But since this is such a great bet and at such low stakes, I also don't think Kelly is very useful, b/c the required bankroll is only something around 210ish dollars. And if I didn't have that, and was going to gamble anyway this would likely be the best bet.


IMO, just take the bet, don't worry about RoR. If you're worried about RoR with a 7 dollar bet with a 16.66% advantage and a relatively small variance, you don't have what it takes bankroll-wise to even think about long term AP, so you might as well not worry about the risk of ruin.



So I guess I agree with your last post, which is to say, JUST TAKE THE BET. Worrying about RoR with such small stakes is basically pointless, because if that's a concern for you at these stakes then it's not likely that you will ever find a more profitable way to play your money, and you also are very unlikely to find a less risky way to play your money.

Thank you Boney526 well, it is not exactly that I am worried about the RoR on this $7 wager. - But if I would be able to get this information, then I would be able to make a correlation for any other stakes. (say "x" times higher - but yes, this is theoretically)

About this $7 tourney, overall I have made a good profit, but recently I have lost $300+ playing it, and made me ask about RoR.

How long does the average game take ? It should be faster than 5 minutes. On a single entry you would be playing almost 2 games on average. Earning $1.66 in EV per entry would equal to $10 per hour (if you could play continuously).

A game takes about ~6 minutes to end, and a tournament takes about ~18 minutes to end. This would be ~$5.5/hour, with wait time.