Can't wrap my mind around this...

[moot]

Alright, so my friend and I were talking about a hypothetical situation:

Let's say you make a casino bet that pays 1:1 where the house has only a minor edge. For instance, betting on black in roulette.

So you bet $1. If you lose, you bet another $1. If you lose that you bet $2. If you lose that you bet $4, etc etc. So you always bet enough so that you'd get back to even if you won.

Then, when you're back to even, you start over and if you win the $1 bet, you pocket that money and start the process over.

Assuming you had a big enough bank roll, enough time, and there was no cap on the roulette bet, could this be profitable?

There's gotta be something I'm missing. Usually my theory is pretty solid but it feels like there's a hole in it. Is it simply the reward isn't worth the risk of busting, even though it might only be a .001% chance (because if you did finally run out, you would lose a ton)? For instance, if you had a bad run of 10 misses, you'd stand to lose $512, while only having a chance for a small reward. But what if you have an almost indefinite bankroll?

Am I missing something?

[Siegmund]

"Almost indefinite" is the key word there. ANY finite bankroll has some small chance of being busted, and that chance is enough to keep the expectation against you.

Suppose you played this strategy on a fair 50-50 bet.
Consider the following betting propositions:
Win $1 50% of the time; lose $1 50% of the time;
Win $1 75% of the time; lose $3 25% of the time;
Win $1 87.5% of the time; lose $7 12.5% of the time;
...
Win $1 1-(1/2)^N of the time; lose 2^N-1 (1/2)^N of the time

all of these are the same break-even bet in the long run. A bigger bankroll leads to both an increased chance of winning $1 and a more catastrophic bankruptcy and the two exactly cancel out.

In the case of an roulette bet, you are worse off. Quite a lot worse off. You are now only winning 9/19 of the time and losing 10/19 of the time; every dollar you put on the table increases the size of your expected loss.

If you have a $1 bankroll, you win 9/19, lose 10/19, EV = -$0.0526.
With a $3 bankroll, you win 261/361, lose 100/361, EV =-$.108.
With a $7 bankroll, win 5859/6859, lose 1000/6859, EV = -$.166.
With a $15 bankroll, win 120321/130321, lose 10000/130321 = EV = -$.228.
worse and worse the deeper you dig into your pocket.

[bos]

Check out the thread "Help me convince friend that Martingale Betting Strategy Doesn't work" for more details.

[meow_meow]

Ahhhh Martingale, how I've missed thee....

[Paul2432]

[ QUOTE ]
Assuming you had a big enough bank roll, enough time, and there was no cap on the roulette bet, could this be profitable?

[/ QUOTE ]

In the short run, yes. In the long run, no. Of course in the short run any gambling situation can potentially be profitable.

Consider your chance of doubling your bankroll. Suppose you start with $1024 with a house edge of 0.52. If you bet everything you have a 48% chance of doubling. On the other hand suppose we use your system. For each trial win $1 unless you lose ten times in a row. The chance of losing ten in a row is 0.52^10. You need to not lose ten in a row 1024 times. The odds of that are (1-0.52^10)^1024 = 22%. So, you are less than half as likely to double your money using your system compared to just betting everything at once.

Paul

[Beerfund]

[ QUOTE ]
Alright, so my friend and I were talking about a hypothetical situation:

Let's say you make a casino bet that pays 1:1 where the house has only a minor edge. For instance, betting on black in roulette.

So you bet $1. If you lose, you bet another $1. If you lose that you bet $2. If you lose that you bet $4, etc etc. So you always bet enough so that you'd get back to even if you won.

Then, when you're back to even, you start over and if you win the $1 bet, you pocket that money and start the process over.

Assuming you had a big enough bank roll, enough time, and there was no cap on the roulette bet, could this be profitable?

There's gotta be something I'm missing. Usually my theory is pretty solid but it feels like there's a hole in it. Is it simply the reward isn't worth the risk of busting, even though it might only be a .001% chance (because if you did finally run out, you would lose a ton)? For instance, if you had a bad run of 10 misses, you'd stand to lose $512, while only having a chance for a small reward. But what if you have an almost indefinite bankroll?

Am I missing something?

[/ QUOTE ]

Nope, you got it. Someone finally fiqured out how to beat the dumb casino. Enjoy your new life as a millionaire.