As a JD Investor, lowering the max profit decreases variance. For instance betting your life savings with 51% is stupid. Betting your life savings in 100,000,000 bets, with a 1% edge, will put you ahead by a large amount, with little variance, in total gain.
You keep returning to this variance thing. What you call variance other people call luck. There is no such thing as variance, just the house edge and a nice bell shape called normal distribution.
Betting your life savings over 100,000,000 bets and betting it all on a single bet carries the exact same risk and reward. You risk less by wagering less on each bet, but if you sum up all those little "risks" across all those millions of bets you end up with the same as just making one single, large bet.
In your terms, placing many small bets means you have to be lucky and win 50,000,000 times. Placing a single bet means you only have to be lucky once.
-Michael
This is not true. The probability of being up 100% on a single bet is 0.49.5. The probability of being up 100% across 100,000,000 smaller bets is basically zero. That is called variance, and more smaller bets have less of it. I believe variance goes down linearly proportional to n, with sigma going down linearly proportional to sqrt(n).
You're clearly confusing mean or expected value with variance. EV is the same no matter what the size of n is, variance is much lower with more rolls.