- #1

elegysix

- 406

- 15

This is about a 47% chance to win. Payout is 1 to 1.

Say minimum bet is 1$ and bets are allowed in multiples of 1$. up to some limit.

Suppose I want to win 1$ for every spin I play.

I bet 1$, and I lose. so my net gain= -1$

Now if I want to have won 1$ for each spin to this point, I need to bet 3$ and win. (1$ for the net, 1$ for the last spin, and 1$ for this spin)

I lose my 3$ bet. now my net gain = -4$

So then I bet (4 + 3)$ = 7$. winning this bet will cover my -4 net and give me 1$ for each spin I've done.

If I win at any time, I restart my betting at 1$.

table of bets on a losing streak:

N(streak) | B(bet)

...1|1

...2|3

...3|7

...4|15

...5|31

...6|63

...7|127

and so on.

recurrence relation:

[itex]B_{N}=2*B_{N-1}+1[/itex]

Usually there is a maximum bet limit, and if my losing streak is so great that I cannot bet the required amount, I will consider that money lost and restart my betting at 1$.

There is some probability that I will have a losing streak too long, and at that point lose a fixed amount of money. But will that loss be greater than what I have gained up to that point?

Suppose the maximum bet is a multiple of the minimum bet. At what point does this ratio cause my net gain to become probably negative or probably positive?

there must be some minimum multiple which gives me a higher probability of having a net gain than a net loss, and some maximum multiple for which the probability of a negative net exceeds the probability of a positive net. ( the higher the ratio of max/min bets, the less likely I'll have a streak too long, thus meaning I'll be less likely to lose that money and vice versa )

I don't know much about statistics, and I would love to have someone help me solve this before I decide to go to vegas and try this out :)