I think the person who asked this question really wanted to know " How much should I have to play a given game for a set number of hours". In American Casino Guide, there was a chart that showed how much per hour you can expect to lose if you don't hit the big hands. You could use this reasoning as an approximate short term 'bankroll'.
Let's say I want to play 9/9 double double bonus. The game return just under 99% with perfect play. I want to play quarters for 4 hours at 600 hands per hour. I will play 2400 hands and run $3000 through the machine. My expected loss is about $30.
Now, let's look at the big hand contribution.
RF every 40,800 hands, 1.96% of return
SF every 9123 hands, 0.55% of return
Aces w/kicker every 16236 hands, 2.46% of return
Aces, no kicker every 5761 hands, 2.78%
2-4 w/kicker, every 6983 hands, 2.29%
All of the above occur less often than once per the 4 hour session you are playing. If we don't hit one of those hands, our EV is about 89% and we will lose $330 during our session. This is the expected value. Your low point for the session could be worse than this. For the above case, I'd say $330 is a reasonable , short term, session bankroll. If you hit a big hand , you will obviously need a lot more money.
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