Optimal wager for fixed Bankroll

[Rich Boy]

How can I calculate the optimal wager if I keep my bankroll the same, no matter what happens?

For example, if your using full kelly, the optimal wager for a play of 1.8 at 60.3%, with a bankroll of $1000 is about $107

What would the optimal wager be if my bankroll is always $1000

is it the same?

[brettd]

yes

[Wrecktangle]

I guess I'd have to ask, why would you want to keep your BR at the same number?

[trixtrix]

is you br going to magically replenish to 1k when you lose as well?

if so, you're concerned w/ maximizing wrt to ev and NOT eg, in which case you should just bet the entire 1k for every shot you consider yourself to have an edge

[u21c3f6]

is you br going to magically replenish to 1k when you lose as well?

if so, you're concerned w/ maximizing wrt to ev and NOT eg, in which case you should just bet the entire 1k for every shot you consider yourself to have an edge

I assume the intent comes from the investment world where your size of investment can be based on a "notional" bankroll. As pointed out by brettd, yes, your Kelly wager is the same if your bankroll is "always" the same (of course this also assumes that your edge is static).

Joe.

[Rich Boy]

Im comfortable with my bankroll being the same, and I understand that it is NOT the optimal strategy in terms of net profit over a period of time.