Simple coinflipping problem.

[BruceZ]

I went ahead and ran those average durations.

55% game

$1 bets:
win 95.3%
Average duration = 135.9 flips

$0.50 bets
win 99.76%
Average duration = 298.5 flips


52.5% game

$1 bets
win 81.8%
Average duration = 190.7 flips

$0.50 bets
win 95.3%
Average duration = 543.2 flips

[jason_t]

Wow. This is really really beautiful. Thank you for taking the time to write this.

[BruceZ]

[ QUOTE ]

ror(0) = c1 + c2 = 1
ror(T) = c1 + (q/p)^T = 0

[/ QUOTE ]

This should be:

ror(0) = c1 + c2 = 1
c1 + c2*(q/p)^T = 0

[Mr_J]

"It really is amazing how such a small advantage per flip gives you such a large advantage in the overall game with only 15 bets."

Sure is (this was what I was thinking, but I'm surprised at how great the effect is). Thanks for the replies & formulae guys.