Is there a mathematician in the house?
How do I analyse the odds of this strategy working?
http://i.imgur.com/HDPSMTA.pngHe bets at 66%, which pays out 1.5x. He starts at 0.06 BTC (this first bet is not shown in the screenshot), doubles on loss, halves on win, never halves below 0.06.
So it's a random walk, which makes a net profit of 0.03 BTC each time it gets back to betting 0.06. Steps down are about twice as likely as steps up, so it seems unlikely to reach max bet and bust very quickly.
But the question is how do I calculate the probability of such a progression busting, given that he can afford to go N steps up the random walk?
Is it a Markov Chain thing? Or how do I analyse it?
I can't analyze this but I can run a simulation.
My simulation:
edge = 0.01
probability of winning a bet = 0.66
First Bet = 1.0
startingBank = 100.0
Goal = desiredBank / startingBank.
Bet firstBet
do
If win bet max(previousBet/2, firstBet)
If lose bet min(bank, previousBet*2.0)
until Bank = goal * startingBank or bank = 0.0.
The simulation calculates the results over 100,000 tries. It shows the ratio of reaching the goal to losing the bank.
Goal Wins ratio Equivalent House Edge
1.01 0.988 0.0012
1.1 0.8904 0.0195
2.0 0.423 0.153
The house edge for a single bet is 0.01.
