How much is correct to wager?

[Hawklet]

If you were offered a game where u had a 51% chance of winning and a win payed 1:1, how much of your bankroll would it be correct to wager.

I'm thinking it's X * (number of outcomes to be ahead 1 bet) = bankroll

Algebra: bankroll / (outcomes) = X

So in this example, in 100 trials, you would be 2 bets ahead (51 wins +51, 49 loses - 49, net +2). So in 50 trials you would be 1 bet ahead so I think it would be correct to bet 1/50th of your bankroll.

Is this correct?

[AllinLife]

not even close...

[vqc]

not even close doesnt answer the question. Whats the asnwer? Wouldnt it be some amount that minimizes ur risk of ruin as much as possible?

[euphoricism]

Think of it this way: Out of 100 trials, you'll win 51 of them. The other 49 you'll lose. With these odds, and an infinite number of trials, you'd put your entire bankroll on it!

[vqc]

using the word bankroll would most likely imply a limited amount of money to wager over an infinite amount of time, once u lose ur bankroll you are done and out.

[Muxy]

Pot odds tell you to call, otherwise fold preflop.

jk, i dont know what we are talking about.

[arkana]

The rake is going to kill you

[BreakfastMan]

Yes 1/50th is correct.

The Kelly Criterion (in simple terms) tells you to bet the pecentage of your bankroll equal to your percentage advantage. This makes the risk of ruin zero. You have a 2% edge in these bets so you would wager 2% of your bankroll each time.

[vqc]

could u explain the kelly criterion in more complicated terms?

[arkana]

I assume you adjust the value you use for your bankroll to reflect your current bankroll at each step. In that way you are risking a lesser amount at each step if you are on a losing streak.

[BreakfastMan]

Yes you use your current bankroll for each bet. The simple version of "bet the percentage of your bankroll equal to your percentage advantage." is only good for even money bets or a bet when you have already included the odds in your percentage advantage.

Adjusted for Poker the Kelly Criterion could read:
"Bet the fraction of your bankroll equal your percentage advantage divided by the 'to-1' odds."
For example, if you have a 10% advantage and you are getting 5-to-2 odds, then the fraction of your bankroll to bet is (0.10)/2.5 = 0.04 = 4%.
Posted by Tom Weideman on rec.gambling.poker

Rather than going in great detail, I will give you a few links.

Coin Tossing:
http://www.bjmath.com/bjmath/thorp/ch2.pdf By Ed Thorpe for fellow blackjack players

Tom Weideman post referenced above:
http://teamfu.freeshell.org/poker/kelly_criterion.html

[TylerK]

It depends what criteria you use to determine "correct."

In a risk-neutral universe, you would wager 100%.

[Zangief]

It depends what criteria you use to determine "correct."

In a risk-neutral universe, you would wager 100%.

You would want to wager 100% to maximize your EV ... but I think they are asking how to maximize your EV while also guaranteeing you don't lose your bankroll.

[BreakfastMan]

A 100% bet dosen't maximize you long term expected value.

Let's define bankroll as all the money you will ever have to play this game. If you bet 100% each time, you would maxmize you EV for this one trial. However if you lose, you will never gain 1 cent in EV from this game again. Even if you win the first bet, do you then bet 100% of your bankroll again. If you do, you will go broke at sometime.

This is a solved problem. You will maximize your long term EV by betting according to the Kelly Criterion. Remember that this is a game with a built in advantage. You want to keep playing the game the rest of your life. The sum of the EV's for each of these indivdual bets will be much greater than any other betting system.

This would be like putting everything you own on the line with AA in poker or in a high count situation in Blackjack. If you contiune to do this, you will go broke.