Using your 2500 bets example at 2% edgehttp://wizardofvegas.com/forum/gambling/sports/10840-another-math-question/#post169697
This is using the normal distribution.
(When I have more time I can put more math and the formulas)
EV = 0.02*2500*110 = $5500
SD = $5237.6426 ( formula can be found here. I am lazy tody http://wizardofvegas.com/forum/gambling/tables/1213-variance-in-craps/)
EV and SD about the same
You have the same chance of being UP 15975.29 as you do being DOWN -4975.29
Now 12,500 bets
You have the same chance of being UP 50923 as you do being UP 4076.
The 3SD value can still kill.
Cant make 12,500 bets with a 2% edge???
So cappers bet more when their edge is higher.
Just as Kelly says to do, IF you believe in Kelly betting in Sports.
More bets with a hgher average bet.
Solves the problem to a certain degree but the variance does go up when the bet increases.
The win rate must also.
But I already spelled that out.
Hey look, No negative values for the -3SD.
SD: $16562.88018 way LESS than the EV.
Casinos can easily book 25,000 bets in one day.
Can one player?
So one player needs many days and many bets to over come the variance.
(and the proper bankroll to ride out the downswings)
winsome johnny (not Win some johnny)