Chances of a streak in BJ

I'm trying to explain why a reverse martingale doesn't work but could use some help with real numbers.
How often would a streak of seven, eight or nine decisions turn up in the players favor.
Betting and doubling each win would result in 5-10-20-40-80-160-320-640 would mean an eight hand win streak results in a win of $640. It means you can lose 127 times, but if you average one such streak every 128 times you end up breaking even. So my real question would be how often can you expect to win eight decisions in a row. A double would count for two wins, a split would be two if you win both, a push if you split and a loss if you lose. All loses immediately fall back to minimum bet.

Rough estimate, 1 in 850.

Quote: Ace2

Rough estimate, 1 in 850.

I appreciate it, but how did you come up with that?

Quote: billryan

I'm trying to explain why a reverse martingale doesn't work but could use some help with real numbers.
How often would a streak of seven, eight or nine decisions turn up in the players favor.
Betting and doubling each win would result in 5-10-20-40-80-160-320-640 would mean an eight hand win streak results in a win of $640. It means you can lose 127 times, but if you average one such streak every 128 times you end up breaking even. So my real question would be how often can you expect to win eight decisions in a row. A double would count for two wins, a split would be two if you win both, a push if you split and a loss if you lose. All loses immediately fall back to minimum bet.

Martingale is fun... You tend to be up, up, up until you are massively down.
Reverse martingale is not fun because you tend to be down, down, down until you are massively up... and then you are down again

Been there, got the t-shirt
:o)

Quote: billryan

I appreciate it, but how did you come up with that?

just looking for a streak of at least 8 in a row using a fair coin at 50% success (p=.5)

one should get 510 for the average number of flips.
=(1-(p^run))/(q*(p^run))

for blackjack where the probability of a win is way less than 50%
it must be higher

I get about 801 rounds of play (counting a push as a round)
a simple Markov chain solution (or recursion in Excel works too)
*****
I must point out that many times trying to double down on your hand
using BS
that can LOWER the chance of
winning the hand played.
sometimes by a lot.

it sure does increase the expected value of the hand but the
anit-Marty needs to be concerned about the highest possible winning probability in order to hit a win streak of greater than 7 and that should consider not attempting a double down and just to hit the hand (maybe more than 1 hit)

streaks in 21 are funny that way
Sally

added: I am going to change my answer a bit later

anti-Marty is only concerned about attempts
1/ .5^8 = 256 attempts
for a fair coin
so 255 times you lose 1 and 1 time you net 255 (256-1) for a 0 net

Quote: OnceDear

Reverse martingale is not fun because you tend to be down, down, down until you are massively up... and then you are down again

you mean until you have a massive win, not necessarily making you massively up
Sally

Quote: OnceDear

Martingale is fun... You tend to be up, up, up until you are massively down.
Reverse martingale is not fun because you tend to be down, down, down until you are massively up... and then you are down again

Been there, got the t-shirt
:o)

I think I have tried every variation of the mart since I "invented" it in the 1990s. It's a powerful seductress for the naive.

you have an approximately 54% chance of losing any given hand, so the probability of losing X hands in a row is .54 to the power of X