Time it takes for progression to bite

[hawkeye]

I know the math on why a progression is bad, why a martingale is bad. I would never play it with serious money in a casino.

But I was thinking about how a martingale or other progression is beaten because of a possibility of a nasty losing streak, of which I have experienced myself. But does anyone have any data on the odds of hitting that losing streak before hitting the winning hand you need?

Take a the $5 table at my local casino, it's $5-$500. Doing a martingale from $5 means that you need to lose 7 straight hands to bust out. I know that happens a lot, but does anyone know the rough data on how often you will hit that bad losing streak before winning a hand?


Please don't lecture me on why this is a bad idea in the casino, I know it is. I'm just talking about the theoretical here, just a discussion.

 

[Sonny]

The probability of losing a single hand is about 49% so the probability of losing 7 hands in a row is 0.49^7 = 1-in-147 hands. At 75 hands per hour you will expect to go broke about once every two hours. In reality it will be worse than that. You can easily lose more than one bet per hand because of splits, doubles and insurance bets so it could take less than 7 hands to go broke.

-Sonny-

 

[k_c]

Anatomy of a progression

I know the math on why a progression is bad, why a martingale is bad. I would never play it with serious money in a casino.

But I was thinking about how a martingale or other progression is beaten because of a possibility of a nasty losing streak, of which I have experienced myself. But does anyone have any data on the odds of hitting that losing streak before hitting the winning hand you need?

Take a the $5 table at my local casino, it's $5-$500. Doing a martingale from $5 means that you need to lose 7 straight hands to bust out. I know that happens a lot, but does anyone know the rough data on how often you will hit that bad losing streak before winning a hand?


Please don't lecture me on why this is a bad idea in the casino, I know it is. I'm just talking about the theoretical here, just a discussion.

Gambler has 31 units to invest in a martingale progression betting on a fair coin toss. This is an even game (gambler's expected value = 0 as gambler expects to win 1/2 of the time and lose 1/2 of the time.)
His starting bet is 1 unit. Upon successive losses he will bet 2, 4, 8, and 16 units. If at any point he wins, he will be up 1 unit. His possible outcomes are:
W (probability = 1/2) [result +1 unit]
LW ((probability = 1/2*1/2) [result +1 unit]
LLW ((probability = 1/2*1/2*12) [result +1 unit]
LLLW ((probability = 1/2*1/2*1/2*1/2) [result +1 unit]
LLLLW ((probability = 1/2*1/2*1/2*1/2*1/2) [result +1 unit]
LLLLL ((probability = 1/2*1/2*1/2*1/2) [result -(1+2+4+8+16) units]

Summary:
He will win 1 unit 1/2+1/4+1/8+1/16+1/32 = 31/32 of the time
He will lose 31 units (1/2)^5 = 1/32 of the time
His expected value = +1*(31/32)-31(1/32) = 0

Gambler will succeed 31/32 = 96.875% of the time (+1 unit)
Gambler will run out of money 1/32 = 3.125% of the time (-31 units)

Betting a progression didn't change gambler's expected value at all. All he did was increase his chances of winning a small amount (1 unit) most of the time at the expense of losing a large amount (31 units) a small portion of the time.

So if gambler's goal is to win 1 unit and then quit gambling forever if he wins, he will succeed 96.875% of the time if he is willing to risk 31 units in the event he doesn't succeed. This is for a fair coin toss, but the priciple is the same for any gambling game. A gambler's expected value isn't changed in any way by a betting progression. Even if the gambler has an infinite bankroll and is prepared to stick to the progression come hell or high water, expected value doesn't change.

If I had an infinite bankroll, I wouldn't gamble at all though, but maybe that's just me. :grin:

 

[hawkeye]

Thanks, interesting.

I've tried this at home a few times, and I can see why non-math people could buy into the voodoo. It works pretty well when you look at it only in the short-term. I would like to rename the Martingale and sell a book, I think I'll use the info you guys just put down.

"Who loses 147 hands in a row? Nobody, buy my system today!"

 

[bjcount]

Serious Money

Just a quick story:

I just recently saw it with my own eyes and was absolutely floored.

I was talking to a guy I see often playing at the crap table and this couple walk up next to us and start playing with a rainbow of chips in their hands. The best I could tell a couple black, purple, yellow (1,000), and two of them are grey (5,000 each).

Plays the field bet:

1st bet $100 in the field - lost
2nd bet $250 in the field - won - let's it ride
3rd $500 in the field - lost
4th $1000 in the field - lost
5th $1500 in the field - lost
6th $3000 in the field - lost
7th him and his girlfriend $3000 ea ($6000 total - 3000 was table max) LOST!

They looked at each other in horror and walked away. :cry:

$12,350 in 7 rolls of the dice, which were (1) 10, (4) 6's, (2) 8's,


I have also recently seen a progression BJ player loose $7,500 in about 10 hands.

During my first LV visit some 14 years ago I also witnessed a similar event at Harrahs where a guy throws paper on the table, 100bucks. Lost about 10 hands in a row and a very, very large stack of paper to boot. Talk about one very angry person.. he was storming out the door.

BJC

 

[hawkeye]

"7 rolls of the dice, which were (1) 10, (4) 6's, (2) 8's, "

I wish I would've been at that craps table, 4 sixes and 2 eights, I would've cashed in 6 times in a row and not been upset about losing my pass line bet.

I know this site is all about math and blackjack, but damn, craps is fun!

 

[bjcount]

"7 rolls of the dice, which were (1) 10, (4) 6's, (2) 8's, "

I wish I would've been at that craps table, 4 sixes and 2 eights, I would've cashed in 6 times in a row and not been upset about losing my pass line bet.

I know this site is all about math and blackjack, but damn, craps is fun!

The guy I was talking to was a come bettor. Had $200 flat with $1000 odds each on 6, 8, & 9. Was doing very nicely with this shooter.

BJC

 

[hawkeye]

I would think so, most people at tables I have seen load up 6 and 8 pretty heavily.

Last time I played craps I rolled 5 sevens in a row immediately after getting the dice handed to me. A couple of younger college age guys were betting like $25 or so, and kept adding on after each 7. They easily had $200 a piece out when I finally got my number, and they bought me drinks for the rest of the night. That's why craps is so much fun.