This whole bankroll topic is so interesting! I can't comment on the
bankroll for short sessions, but I do have some input on very large
sessions, such as 50,000 games or more.
I mentioned a discussion on the WinPoker board (last year) as to
whether the Normal Distribution applied to VP. To test this idea,
Dean did a WinPoker simulation based on 50,000 games. He ran 100,000
simulations of 50,000 games and plotted the results, based on 9/6
JorB. It turned out the normal approximation for 50,000 hands was
fairly good, but definitely not exact. If the Normal does apply, it
takes more than 50,000 games, although I doubt the 4,000,000 estimate
offered by Jazbo, especially for a low variance game like 9/6 JorB!
The results of his simulation are shown below, along with the
expectation if the Normal Distribution actually applied.
Pct Sim Normal
···
------------------------------
1% -9970 -12630 3.69%
5% -8140 -9264 7.82%
10% -7025 -7470 11.67%
25% -4800 -4472 22.93%
50% -1695 -1140 45.53%
75% 1860 2191 72.82%
90% 5535 5189 91.17%
95% 7820 6984 96.52%
99% 12520 10349 99.72%
At the "losing" tail, 1% of the 100,000 tests had losses of -9970
coins or more. The Normal expectation would be -12630 coins (or
3.69%) of the tests.
Unfortunately these results can't be directly compared to Jazbo's
charts, because his were based on only 5,000 or 10,000 games.
However, its interesting because the above tests, and in Jazbo's
charts too, the "worst case" results turn out better than the Normal
Distribution would suggest. That's important because it
suggests the Normal Distribution is a "conservative" estimator of the
bankroll required for a very large session. Its possible a player
might get further behind than these counts before the 50,000 games
have all been played, but I doubt it because these "worst case"
results occur when no RF occurs during the 50,000 games.
If this simulation is correct, it means there is only a 1% chance of
needing a bankroll of more than 9970 coins ($2492.50 for a quarter
game), with the qualification just mentioned above. Similar bankroll
estimates can be made at the 5%, 10%, and 25% level.