The reader?s main goal seems to be, to achieve and/or to consolidate a 50K bankroll.
If I had a known BR, to be collected at the rate of $2,000 every two weeks for the next twelve and a half months -my 'lifetime bank' is also $50K.
After doing this he will be able to:
If I had a BR in hand of $50K, I could set up a game plan for that and it might crank out a max bet of say $300 and a respective ROR of say 1% (I'm guessing about the 1%.)
So let us do not lose perspective on this, his main goal being to arrive at the desired level.
So far we have considered the following:
1) Staying quietly at home without playing a single hand. There is a 100% probability of having 50K after one year and a half-month.
2) Starting to spread $25 to $300 like as if he had the promised money in his pocket, actually. An announced failure, surely.
3) Flirting with full-Kelly and/or 1.5 or double-Kelly. Who knows?
While building his bankroll, let?s assume the following:
1) The player will play 20 hours every two weeks with a fixed RoR = 13.55%. He will never adjust or reduce his bets during any given session. Here a session is, obviously, playing 20 hours straight.
2) Money won plus the added one is always risked as stated, until reaching the 50K level.
3) What if we consider the 25 sessions (more or less, as a function of the gain/losses) as independent trials? (While building the bankroll). With a fixed p = .8645 (success) and a q = .1355 (failure), we can a apply a binomial test, in order to evaluate our chances.
Here we go.
Succ.Failures Probability Cum.Probability
0 25 0.000% 0.000%
1 24 0.000% 0.000%
2 23 0.000% 0.000%
3 22 0.000% 0.000%
4 21 0.000% 0.000%
5 20 0.000% 0.000%
6 19 0.000% 0.000%
7 18 0.000% 0.000%
8 17 0.000% 0.000%
9 16 0.000% 0.000%
10 15 0.000% 0.000%
11 14 0.000% 0.000%
12 13 0.000% 0.001%
13 12 0.003% 0.004%
14 11 0.016% 0.020%
15 10 0.077% 0.097%
16 9 0.306% 0.403%
17 8 1.034% 1.437%
18 7 2.932% 4.369%
19 6 6.893% 11.262%
20 5 13.193% 24.455%
21 4 20.041% 44.496%
22 3 23.247% 67.743%
23 2 19.346% 87.089%
24 1 10.286% 97.375%
25 0 2.625% 100.000%
A random walk through 25 full-Kelly sessions (no bankroll adjustments, remember) without a single failure is not an easy thing to achieve!
To be continued, I guess.
Zenfighter
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