Risk of halving instead of RoR

Has anyone done the math on the risk of losing half of one's bankroll before doubling it when playing with a 1% advantage? What is the risk of halving before doubling with full Kelly bets? Is there a way to calculate this (publicly known formula)? I think it's more relevant since a 10% risk of halving would be acceptable. If 9 times the bankroll is doubled for every 1 time it's halved, as long as you continuously contribute back to the BR; you can rapidly grow. 10% risk of ruin is a little more scary. Is a 10% ror equal to a 20% roh?

Quote: billionaireben

Has anyone done the math on the risk of losing half of one's bankroll before doubling it when playing with a 1% advantage? What is the risk of halving before doubling with full Kelly bets? Is there a way to calculate this (publicly known formula)? I think it's more relevant since a 10% risk of halving would be acceptable. If 9 times the bankroll is doubled for every 1 time it's halved, as long as you continuously contribute back to the BR; you can rapidly grow. 10% risk of ruin is a little more scary. Is a 10% ror equal to a 20% roh?

Good question. I searched and found a discussion of this on another forum. Will PM you the link. Research continues. . .

Quote: billionaireben

Has anyone done the math on the risk of losing half of one's bankroll before doubling it when playing with a 1% advantage? What is the risk of halving before doubling with full Kelly bets? Is there a way to calculate this (publicly known formula)? I think it's more relevant since a 10% risk of halving would be acceptable. If 9 times the bankroll is doubled for every 1 time it's halved, as long as you continuously contribute back to the BR; you can rapidly grow. 10% risk of ruin is a little more scary. Is a 10% ror equal to a 20% roh?

If you have a $10k bankroll and have a 10% risk of halving....is that any different than a $5k BR with a 10% risk of ruin?

I'm almost certain 10% ROR !== 20% ROH.

Based on the link I got, it's actually 31.6% ROH for a 10% ROR. I wish they had included a formula for calculating this, but it's generally 3.16xROR (that's what it generally appears to be.) Also, you need to be sure your ROR calculation is correct. Some charts out there are ROR for flat betting with normal house edge for the purposes of sign on bonuses. If card counting with a 1% player advantage, the numbers change. If shuffle tracking with a 3% edge it's different. If hole carding with a 13% edge, it's different. Also different based on where the edge comes from, if it's an over payment on a rare event (like a royal flush), loss rebate or good blackjack rules and counting.

The risk of losing half of a given bankroll is the exact same as the risk of ruin (total loss) for a bankroll of half that size. So for example, the risk of losing half of a bankroll of $10,000 is the same as the RoR for a bankroll of $5,000. The two calculations are exactly equivalent.

There's really no point in figuring out the chances of losing half your bankroll unless you intend to make some alteration in your play strategy should that point be reached. In reality, RoR is fluid, and will increase as your bankroll decreases as long as all other things remain equal--bet sizes, chosen games, etc. So if your bankroll shrinks to 50%, it's possible that your RoR is no longer within your parameters. You might want to lower your bet sizes.

If you calculate RoR for a bankroll of $X, that takes into account all possible outcomes, including those where you lose 50%, 90%, or 100% of your bankroll. Therefore, if you intend to alter something if your bankroll is halved, then your original RoR calculation wasn't relevant anyway.