Guynoire said:
Why would you ever play with a risk of ruin higher than 50%? A 35% chance of doubling vs a 65% chance of going bust sounds horrible when you could just bet it all on black and achieve a better deal faster.
Well, when you introduce a goal of doubling before going bust, assuming no time limit on your play, a guy with a 65% "lifetime ROR" would have like a 60%chance of doubling roll before busting and only a 40% chance of busting. Even a guy with a 90% "lifetime ROR" might have greater than a 50% chance of doubling roll before busting if he played with no time limit and stopped when either busting or doubling occurred.
It's, I think, probably because a guy with a 90% ROR might only have, say, a 35 unit roll when he would have,say, a 700 unit roll if playing Kelly.
We all know how relatively easy it is to double a 35 unit roll. All you have to do is win 35 units. The trouble is, even when you have 70 units, if you choose to play beyond that point, you will pretty often, not hard to imagine, eventually often lose the 70 units from that point forward. So all those times you'd double, triple your original 35 unit roll account for the difference between a 90% "lifetime ROR" and a 50+% ROR of doubling before going bust.
Now a full-kelly guy with that 13.5% ROR would have to have those 700 units as a roll to have that risk. Obviously he won't win 700 units and double his roll that often so the chances of doubling before busting are more in line with the "lifetime" 13.5% risk. Yet, even then, sometimes he still would lose his doubled roll if he continued to play. So he might have, say, an 88% chance of doubling and a 12% chance of busting. The extra 1.5% of "lifetime" risk happens when he occasionally still loses his doubled roll of 700 units.
Kind of like you could play with a 1-unit roll and have a 99.99999% lifetime risk yet only have a 50%ish chance of doubling before busting if you see what I mean.
So, perverse as it may sound, the higher the lifetime risk the lower the risk of busting before doubling relative to original risk.
I think
Again, the above assuming no time limit on one's play.
Goals, time, roll, risk.