Mind bender

[Beyond the Bets]

Assume you withdrew $1,000 from your bank account. You must bet all of it on sports. You can place wagers of either $250, $500 or $750. Go broke, and you're gone.

All bets are even money.

How much do you wager on your first bet? If it wins, then how much would you wager on your second bet? If it loses, then how much?

[gynecologist]

There is two ways to go about this IMO.

A. Bet $250 always because a three game losing streak would bury you.

B. Bet $750 the first time and hope you hit and then bet $250 so that way you can lose 5 maybe 6 in a row and still have a bank.

[BetThemDogs]

I'd bet $250 until it was either gone, or I had run it up to $12,500--- at that point I'd start betting 2% on each game.

[ChiefZilla]

Hmm, I guess I'd treat it like blackjack. Bet the minimum until I can get up, and then start wagering more if/when that happens.

[zman1415]

Strongly depends on what the goal is and if you have an edge.

Let's start by assuming you are getting even money on the bet and the bet has no edge to it. If the goal is to reach 2K, the right play is to bet it all once. Assuming 50/50 play, your odds of reaching 2k are then 50/50. If you min-bet forever, your odds of reaching 2k never climb above 27.8% (42 bets in). Around there you end up regressing even further and by bet 100 your odds of being up 4 min bets or more are below 25%. Compare that with the odds of having lost all 4 of your min-bets: By bet #34, your odds of being broke also reach 50% (cumulative from bet 4 to 34). By bet #100, your odds of being broke are 69.1%. By bet 350, it rises all the way to 83.1%.

On the other hand, if you have a 55% chance of winning your bet and you have an unlimited number of bets available to you, it actually makes sense to min-bet. With a 55% win rate, by bet 86, you reach a 55% chance of having doubled up (including a 40% chance of being up over 10 min bets) while only having a 39.7% chance of being broke. That's clearly preferable to the 55/45 proposition of 1 bet for all the marbles.

I did a little bit of looking with various win-rates and it seems the right spot to move to min-betting is in the 54.5% range, as long as you have unlimited time to find bets have a constant win rate. The only other idea for a betting strategy is a 'half the bankroll" strategy, but I haven't closely looked at how that would work because I don't know how to automate that in excel....