I know you did lol. And I'm sorry if I'm beating a dead horse again. Or I'm forcing you to :whip: a stupid horse again, fun as that may be for me, lol. It's just that this is one of those subjects, amongst many I might add, that I have always had questions about.blackjack avenger said:
So, maybe put another way, when you said "I believe the 5% ror is your total ror from the beginning when you decide to play the cut stakes in half style. One's chances of doubling before losing half I believe is 66%. If you lose half your stake and then cut your bets in half from that point forward if you do not resize again the ror should be 13.53%?", how did you arrive at that 5%?
Did you use the .333 chance of halving roll before doubling it so maybe .1353*.3333 * .1353 after resizing? Where I would use .1353*.1353=.36 *.1353 after resizing. I do agree with the 66.6 chance of doubling roll before halving it and also that the risk going forward after resizing is the original risk since the number of units in roll is the same as it was originally.
But going back to that .78% chance for a quarter-Kelly bettor of ever losing half his roll wouldn't that be a 50% for a full-Kelly bettor? How do you get to 5% from there after resizing?
Ultimately I guess it goes back to I've never clearly understood the underlying assumptions in that paper you cited. Was "they were only playing with an advantage" one of them? Was each "continuous" bet with their 1 unit roll always made with the same .1353 ROR but always based on the original unit roll as opposed to proportional betting where each bet is made with a constantly changing bankroll? Isn't it true, either way, the ROR can never reach 0, just approach it?
Anyway, I guess whatever, from a practical point of view, since no one lives forever, maybe you're saying to use the chances of doubling roll before halving it as a practical lifetime ROR. Just like the old adage says, if they don't get you early, you'll win money forever. And, once you have doubled original roll, one is much less likely to ever lose all from that point forward. That original 1 in 10 risk is now 1 in 100, that original 1 in 100 now 1 in 10000, etc.
And I got no problem with that. It's the best thing one can do, before one bets at all, to figure out the chances of losing half before achieving whatever in how long, etc. Maybe one could never practically halve one's stakes after losing half a roll if the original min unit was table min in the first place. Nice to maybe know that and what to expect before starting lol.
Like .1353 might not sound so bad but it also means you have a 10% chance of losing 90% of original roll at some point, doesn't it? Which doesn't sound quite as good lol.
Most of all, ignoring all this minutiae and getting back to your original question, which to me is basically the whole ball of wax, I just want any aspiring AP to be able to come home, ideally maybe even before he left home lol, and be able to measure to some degree what happened that day. I don't care when you choose to upsize or downsize or by how much, play-all or back-count, play with a high risk or low risk, play 8D and then SD, play full tables or heads-up, use the same spread for a 4/6 game even if it suddenly changes to a 5.5/6 game, bet to a 1000 unit roll when you only have 500 units, play 50 hours a year or 2000, etc. If a guy knowingly chooses an EV of $4/hr or less at whatever risk for however long he chooses to play, in my book he's no less of an AP, and probably more than most, just because he knows it and what to expect from it.
I'm probably too crude and too simplistic, and certainly have no right to even comment about it but, if one can't measure one session, is one truly an AP player?
