This

I meant Bill Gates has to start by betting a billion.

I used to think exactly that way.
the Bold a's above should read "at least one" . Yes it can get worse. Using BruceZ Excel VBA code for multiple streak probabilities I get the following table.
One can see that there is a 93.6480% probability of at least 4 runs of length 9 or more in 5k trials. Talk about many chances for a beating.


His code can be found at the link below in some Excel spreadsheets. I do not know if he has another link to them.
Multiple Losing Streak Probability Calculator

Yes, I see a flaw in your example.

your 4 step Marty risking $75 to double up is not a 50/50 prop.

18/37 = 33.92% chance of success to double your $75 stake.
You would have to win 15 times in a row
with a win probability of 93.05% [1-(1-18/37)^4]
avg number of spins = 29

18/38 = 30.19% to double the $75 stake.
avg number of spins = 30

You got the number of trials right.
Of course you can have some winnings IF and when the 4 losses in row happen.

A much larger bankroll will increase your winning probability of doubling a stake, but you can do the math on that.

At times a Martingale can give the highest probability of hitting a win goal. This is the concept, a real good math exercise also, known as Bold Play.

Maybe BruceZ has done the math for the Red and Black game in another thread.

Sally

i think maybe the best way to martingale is with blackjack.

That way when you do get those huge bets out you can get a BJ/ split/ double down.

Instead of winning $5.

You could find a craps table with 32768x odds

+1

If you were going to martigale it, blackjack would be the game for exactly this reason IMO.

what about when you lose 8 in a row and you get dealt 8 8,split then 8, 3 then double and you lose all three bets. You just loss $5120, then what is your next bet? 10k? however if you get a BJ on that you are baller and should go party it up for the night.

If you are really going to martingale then I would do it this way

5, 11, 23, 47, 95
instead of
5, 10, 20, 40, 80

At least on the top one you will win $9 instead of $5 at the end of the run.

Yes, that's right but it still says the same thing. Your word would clarify for someone who that wasn't obvious to.

no money in roulette, everyones solid

Its simple you just kill yourself.

.

@op

This will only work if you switch colours every spin. It might hit black 20 times in a row (as mentioned above) but keep switching and it can't dodge you forever

The Epaminondas System

Always place the next wager on the winner of the previous trial. The system is designed to profit from imagined or undetermined bias, anticipating a non-alternating outcome.