Quote from: freeyourmind on March 20, 2015, 10:43:32 PM

Quote from: dooglus on March 20, 2015, 03:55:00 PM

Quote from: freeyourmind on March 20, 2015, 05:05:27 AM

To your point, perhaps it has involved luck, but I don't think it's very odd for people to double their money before losing it all when following martingale.

No, it's not unusual. It just has to happen less than half the time on average, due to the house edge. Otherwise this simple strategy would be profitable:

* start with X; martingale until doubling; quit

If you successfully double Y% of the time, your expected profit would be:

(Y*X - (100-Y)*X) / 100
= X(2Y - 100) / 100

which is positive exactly when 2Y > 100, ie. when Y > 50%

]

Yeah, good point, so the question is what is Y?

If I look at a high/low game with 47.5% odds of doubling your bet, after the house takes its cut, then let's say I'm willing to go 11 consecutive bets before I lose it all.

Bet Total Loss
1 1
2 3
4 7
8 15
16 31
32 63
64 127
128 255
256 511
512 1023
1024 2047

So assuming an initial bet of 1 satoshi, using martingale, my 11th bet would be 1024 and at that point I lose 2047 satoshi. The odds of losing 11 bets in a row is (0.525^11) = 0.0835% or 1/1197 bets. So for every 1197 bets, there will be one losing streak, on average, which will lose 2047+ on making 1196...not the best strategy in the long run.

Hopefully the math makes sense - feel free to correct if I made a mistake.

I think Y will be close to 1-(1196/2047) = 41.573%