MJ: Kelly Betting

[MJ]

What does betting "one quarter kelly" mean? How about "one half kelly"? Thanks for any help.

-MJ

[Don Schlesinger]

> What does betting "one quarter
> kelly" mean? How about "one half
> kelly"? Thanks for any help.

Do you know what betting Kelly means? If so, then betting one-half or one-quarter means betting those fractions of what a full Kelly bet would be, in order to reduce (considerably) risk of ruin.

Don

[MJ]

Thanks Don. If I understand correctly then a full Kelly bet maximizes the geometric growth rate of the bankroll while limiting ROR to about 13.5%.

Does one-half or one-quarter Kelly pertain to a specific ROR? For example, if ROR is proportional to Kelly then one-half kelly would constitute a 6.75% ROR and one-quarter Kelly would constitute a 3.375% ROR.

-MJ

[Don Schlesinger]

> Thanks Don. If I understand correctly then a
> full Kelly bet maximizes the geometric
> growth rate of the bankroll while limiting
> ROR to about 13.5%.

Well, yes and no. Pure Kelly betting has you resizing your unit after every bet, which, of course, is impossible. Until or unless you bump into the table minimum, or reach a unit size that can't be bet, ROR for the pure Kelly bettor is theoretically zero.

The 13.5% ROR pertains to someone who begins betting Kelly and never resizes his bet, no matter what the bankroll.

> Does one-half or one-quarter Kelly pertain
> to a specific ROR? For example, if ROR is
> proportional to Kelly then one-half kelly
> would constitute a 6.75% ROR and one-quarter
> Kelly would constitute a 3.375% ROR.

It relates, but not your way (linearly). Rather it relates exponentially. That is, one-half Kelly reduces ROR to 0.135^2, or 0.018225 (1.8%), while, for one-fourth Kelly, ROR of 0.135^4 isn't really worth talking about (0.033%)! :-)

Don

[MJ]