responding to your points
"While it may be very liberal, say he is playing via half the Kelly criterion without resizing. Then the probability of doubling a bank before going bust (RoR) is about 1.8%."
If a player is using 0.5 kelly, then wouldn't the probability of doubling the bank before going broke be 98.2%?
Your numbers look reasonable. I probably screwed up here and wrote 1.8% instead of 1-1.8%.
Here, CRoR stands for cumulative risk of ruin. Unfortunately, this means that that the probability of not surviving 5 years in the above scenario is (1-13%)^10=17%. The probability of not surviving 10 years is (1-13%)^20=31.1%".
First, where does MB come up with 13% for ROR? Second, (1-13%)^10=25% , not 17% as MB wrote. Same goes for (1-13%)^20, it equals 6%, not 31%. Somebody please clarify, this is an interesting article.
The 13% is an estimate of what your RoR is if you start out betting kelly on your bankroll and never resize. On the numbers, you are right. I probably edited the example and did not change everything. As some other posted has noted, sometimes I wrote the (1-r)^n number instead of the correct 1-(1-r)^n number.
MB stipulated 0.5 kelly and also made it clear that the counter could double a 20k bank twice in a year. Unfortunately, the 40k winnings are used to pay expenses. If expenses = earnings, then ROR becomes 100% in the long run.
The only way it could be full kelly is if expenses were 1/2 earnings and the counter did NOT stop prematurely when he doubled the bank. In other words, he would play until he either went broke or won all the money in the world. But these are not the parameters we are given!
Your writings above seem to be correct. I probably screwed up somewhere in the editing. I do remember that I was assuming expenses and profit taking were done continuously as hours were put in. People usually take them in chunks, but that is harder to model.