Quote from: Coef on October 18, 2015, 07:28:30 PM

Chance of winning = 1 - ((1 - 0.02%) ^ 3430 * (1 - 0.01%)) = 49.649851332%.

Chance of winning = 1 - ((1 - 0.03%) ^ 2287) = 49.651579392%

I notice the word "them" in the quote. Do I get 0.1 btc for beating dooglus' solution? Tongue

My recent post shows strategies that give a 49.6522222% percent chance of winning, so your post (which came after) doesn't beat mine.

Are you able to beat 49.6522222%, or do you think that is a hard limit?

Here's a chart showing your two strategies, and where they fit on the curve of possible martingale strategies. The higher the payout multiplier you play with, the closer you get to the 49.652222% chance:

I wonder if flat-betting would be better?

Like we could divide the 1 BTC into N=10 0.1 bets.
Bet the first 0.1 at 11x. If we win, we're 1 BTC up, so we stop.
Bet the 2nd 0.1 12x. If we win, we're 1 BTC up, so we stop.
Etc.
Bet the Nth at (10+N)x. We're always 1 BTC up if we win.

Turns out it isn't better. What's funny is it is exactly the same.

Here's a Python script that calculates the chance of doubling up using this flat-betting strategy for various N:

Quote

for m in range(0, 6):
for N in range(10**m, 10**(m+1), 10**m):
p = 1.0
for i in range (1, N+1):
p *= (1 - 0.99 / (N+i))

print "%6d %.8f" % (N, 1 - p)

And here's its output:

Quote

1 0.49500000
2 0.49582500
3 0.49607333
4 0.49619171
5 0.49626081
6 0.49630606
7 0.49633797
8 0.49636168
9 0.49637999
10 0.49639455
20 0.49645915
30 0.49648035
40 0.49649088
50 0.49649718
60 0.49650137
70 0.49650436
80 0.49650660
90 0.49650834
100 0.49650973
200 0.49651599
300 0.49651807
400 0.49651911
500 0.49651973
600 0.49652015
700 0.49652044
800 0.49652067
900 0.49652084
1000 0.49652098
2000 0.49652160
3000 0.49652181
4000 0.49652191
5000 0.49652198
6000 0.49652202
7000 0.49652205
8000 0.49652207
9000 0.49652209
10000 0.49652210
20000 0.49652216
30000 0.49652218
40000 0.49652219
50000 0.49652220
60000 0.49652220
70000 0.49652221
80000 0.49652221
90000 0.49652221
100000 0.49652221
200000 0.49652222
300000 0.49652222
400000 0.49652222
500000 0.49652222
600000 0.49652222
700000 0.49652222
800000 0.49652222
900000 0.49652222

It converges on 49.6522222% chance of doubling up again!