Can we stand another martingale question?

First, I know no system works. But everyone knows the theory of martingale would work *if* you had the bankroll and *if* the casino was dumb enough to have no upper table limit.

So, in the interest of science, how many units would you need to cover yourself to say a less than 1% probability of wipeout betting the following:

Any even-money single-zero roulette bet (red/black, even/odd, etc.)

The field bet in craps (even with a low payout there are extra payout on 2/12.)

Blackjack both with and without splits/double-down/surrender.

Interesting question.


Roulette:

This chart assumes that on a single zero wheel, even money bets lose. On a double zero wheel, even money bets lose half.

Therefore, the formula is 18/37 and 18.5/38 respectively, to the power of the number of spins in a row that you've lost.

For both wheels, you can sustain only 7 loses.


Craps Field Bet:

D/D is for Harrahs and other cheap properties that pay double on both 2 and 12. D/T is for normal casinos that pay triple on one of them.

I'm not sure if I have the formula right. I came up with ((16/36)*($win/20))^losses I.E. The chance of a win (16/36) times the payoff divided by the loss to the power of the consecutive losses.

If I have it right, then it's six losses.


The bet, obviously, is the Martingale bet. Therefore, if you believe that you'll at maximum sustain the 1% chance of 6 or 7 consecutive losses, then you're well within the table limits.

But that's still something of a leap of faith. How many times have you walked past a Roulette table and glanced at the display to see 7 or more in a row of red, or black, or odd, or....



For comparison, I included a simple 50/50 column.

Losses	Bet	0	00	D/D	D/T	50/50
1	1	0.4865	0.4868	0.4000	0.4222	0.5000
2	2	0.2367	0.2370	0.1600	0.1783	0.2500
3	4	0.1151	0.1154	0.0640	0.0753	0.1250
4	8	0.0560	0.0562	0.0256	0.0318	0.0625
5	16	0.0272	0.0273	0.0102	0.0134	0.0313
6	32	0.0133	0.0133	0.0041	0.0057	0.0156
7	64	0.0064	0.0065	0.0016	0.0024	0.0078
8	128	0.0031	0.0032	0.0007	0.0010	0.0039
9	256	0.0015	0.0015	0.0003	0.0004	0.0020
10	512	0.0007	0.0007	0.0001	0.0002	0.0010

The more I think about it, the more unsure I am about my formulas on everything I posted.

I enjoyed stretching my brain muscle, but I gotta wait for it to snap back to figure out if I got it right or where I went wrong....

Quote: DJTeddyBear

Interesting question.


Roulette:

This chart assumes that on a single zero wheel, even money bets lose. On a double zero wheel, even money bets lose half.

Therefore, the formula is 18/37 and 18.5/38 respectively, to the power of the number of spins in a row that you've lost.

For both wheels, you can sustain only 7 loses.


Craps Field Bet:

D/D is for Harrahs and other cheap properties that pay double on both 2 and 12. D/T is for normal casinos that pay triple on one of them.

I'm not sure if I have the formula right. I came up with ((16/36)*($win/20))^losses I.E. The chance of a win (16/36) times the payoff divided by the loss to the power of the consecutive losses.

If I have it right, then it's six losses.


The bet, obviously, is the Martingale bet. Therefore, if you believe that you'll at maximum sustain the 1% chance of 6 or 7 consecutive losses, then you're well within the table limits.

But that's still something of a leap of faith. How many times have you walked past a Roulette table and glanced at the display to see 7 or more in a row of red, or black, or odd, or....



For comparison, I included a simple 50/50 column.

Losses	Bet	0	00	D/D	D/T	50/50
1	1	0.4865	0.4868	0.4000	0.4222	0.5000
2	2	0.2367	0.2370	0.1600	0.1783	0.2500
3	4	0.1151	0.1154	0.0640	0.0753	0.1250
4	8	0.0560	0.0562	0.0256	0.0318	0.0625
5	16	0.0272	0.0273	0.0102	0.0134	0.0313
6	32	0.0133	0.0133	0.0041	0.0057	0.0156
7	64	0.0064	0.0065	0.0016	0.0024	0.0078
8	128	0.0031	0.0032	0.0007	0.0010	0.0039
9	256	0.0015	0.0015	0.0003	0.0004	0.0020
10	512	0.0007	0.0007	0.0001	0.0002	0.0010

So if I am reading this right, multiply the decimal number by 100 and that gives the % of chance of this kind of a streak happening?

BTW: why "D/D" amd "D/T?"

I still disagree that even in theory Martingale works. In another thread I argued why in theory you could have a infinite losing streak, and thus require infinite bankroll to ever turn a profit. Math & philosophy get weird once you approach infinity.

That being said, you can't guarantee a 1% risk of ruin unless you have a stopping point! If you play -EV bets forever, it doesn't matter what your bankroll is, you lose it all...

Quote: AZDuffman

BTW: why "D/D" amd "D/T?"

I guess I was a little too vague on that point.

D/D is Double on 2, Double on 12 - I believe Harrahs properties is the only ones that do that.
D/T is Double on 2, Triple on 3 (or vice versa), which is the norm.

Quote: DJTeddyBear

The more I think about it, the more unsure I am about my formulas on everything I posted.

I figured out where I was going wrong.

I was including the payoff in the calculations. That had nothing to do with the question.

The question is, how many losses in a row can be sustain until you pass the < 1% chance of another loss.

For that, it's a simple matter of 19/37 for zero, 20/38 for double zero, and 20/36 for field, to the power of the loss in a row.

Mind you, these are all FUTURE odds. Once you hit 'x' losses in a row, the chance of another loss remains at the top row figure.

Use these numbers instead.

Also, these numbers represent the chance of LOOSING. So it takes just a little longer to hit that 1%.

Losses	Bet	0	00	Field	50/50
1	1	0.5135	0.5263	0.5556	0.5000
2	2	0.2637	0.2770	0.3086	0.2500
3	4	0.1354	0.1458	0.1715	0.1250
4	8	0.0695	0.0767	0.0953	0.0625
5	16	0.0357	0.0404	0.0529	0.0313
6	32	0.0183	0.0213	0.0294	0.0156
7	64	0.0094	0.0112	0.0163	0.0078
8	128	0.0048	0.0059	0.0091	0.0039
9	256	0.0025	0.0031	0.0050	0.0020
10	512	0.0013	0.0016	0.0028	0.0010

Quote: dwheatley

I still disagree that even in theory Martingale works...

I agrre completely. Of course, in the original post, AZ was looking for the 1% chance calculation. Yeah, 1% is a decent "feel good" number.... until you realize that it's only 7 losses to hit that number, and suddenlt, you realize that the 1% 7 losses in a row event occurs far too frequently.

DJTeddyBear, should the first step after one loss not be a doubled bet?

Seems to me one problem with infinity and Martingale is that you can't reasonably postulate that some high figure, let's say a million dollars, approximates an infinite amount for the computations; not infinity but a figure that would never be reached for all practical purposes. To be clear, $1,000,000 is not enough!

Certainly not with a $5 bet as sooner or later you would require that million dollars [18 losses in a row would happen probably sooner than later]!

Quote: AZDuffman

So if I am reading this right, multiply the decimal number by 100 and that gives the % of chance of this kind of a streak happening?

Yeah.


BTW: I left out BlackJack simply because I have no idea what the formulas are. Complex, to say the least.

I would guess that since BJ includes so many ways of getting more than an even money payoff, the simple chance of losing is even greater than the even mony Roulette or Field bets. Therefore, you'll hit that 1% a little slower.

Quote: dwheatley

I still disagree that even in theory Martingale works. In another thread I argued why in theory you could have a infinite losing streak, and thus require infinite bankroll to ever turn a profit. Math & philosophy get weird once you approach infinity.

That being said, you can't guarantee a 1% risk of ruin unless you have a stopping point! If you play -EV bets forever, it doesn't matter what your bankroll is, you lose it all...

Well, anything could go to infinity, but some part of the "fun" of betting systems is figuring out when and why they don't work. I just consider it mind exercise. I also asked this martingale system question for another reason. Say you were a whale with a big bankroll. You play craps and tell the host you want a table with no limit. You just bet the field and hope to take advantatge of the D/T on 2/12. Theoretically you could eventually walk in with "$x" and if you play long enough walk out with the deed.

It's fun to just think about as long as you don't try it. Most fun with martingale except for calling the bar at O'Shea's and saying, "Yes, I'm babysitting Mr Gale's kids and there is a problem, can you page him? Yes, last name 'Gale' first name 'Martin."

"Hey, everybody, I'm looking for a Martin Gale! Is there a Martin Gale in the house?"



If that happened I wonder how many people would get it?

Some Martingale ideas that I have had to discard:

* it only matters in your own bets. Thus to go double or nothing you can get yourself together, let the dice roll a few more hands while you get your next bet lined up. And it doesnt matter if you change games. Up against a table limit, you could collect yourself, leave, and go to a higher limit table. And it doesnt matter what game it is, finally if at *your* limit you could go to a high house limit baccarat table and make that final martingale bet there. Discarded because no bankroll practical for me is big enough with a $5 starting bet to make the possibility of ruin remote, plus I know I would chicken out !

* taking out an unlikely string of maybe 15 losses in a row, not starting the martingale till getting 8 in a row, but stopping at that 15. Thus I would be betting that a particular session did not have a particularly long string of bets and take my lumps when it did. Discarded because it is possible to lose anyway and the influence on probabilities is math that eludes me.

Quote: odiousgambit

DJTeddyBear, should the first step after one loss not be a doubled bet?

With Martingale, you double after EVERY loss. Once you finally win, assuming it's an even money payoff, you're ahead one unit. If you don't double that first time, then when you win, you're back to zero, and you therefore never win unless you have consecutive wins.

With Martingale, assuming you don't exhaust your bankroll or hit the table limit, every win is a net win of one unit.

And, as we all know, those are bad / dangerous assumptions.

Quote: AZDuffman

Say you were a whale with a big bankroll. You play craps and tell the host you want a table with no limit. You just bet the field and hope to take advantatge of the D/T on 2/12. Theoretically you could eventually walk in with "$x" and if you play long enough walk out with the deed.

Interesting theory. Of course, he could also walk out with the deed even if he didn't use the Martingale. For example, if he just doubled his bets after a win and hit an enormous winning streak.

As an aside, does anybody actually find the Martingale fun? I've seen it in use. A young player at Bally's in Atlantic City was using it after quite obviously "discovering" it at that very moment. He was doing very well, was betting greens and had won a couple thousand already. I left before the inevitable bloodbath occurred.

The only other times I've seen it were people on the losing end of things getting progressively more angry and stressed out as they re-redoubled their bets. There's usually a lot of colorful language flying about as well.

Has anybody actually seen someone (e.g., a whale) using this method quasi-'successfully?'

Quote: teddys

Quote: AZDuffman

Say you were a whale with a big bankroll. You play craps and tell the host you want a table with no limit. You just bet the field and hope to take advantatge of the D/T on 2/12. Theoretically you could eventually walk in with "$x" and if you play long enough walk out with the deed.

Interesting theory. Of course, he could also walk out with the deed even if he didn't use the Martingale. For example, if he just doubled his bets after a win and hit an enormous winning streak.

As an aside, does anybody actually find the Martingale fun? I've seen it in use. A young player at Bally's in Atlantic City was using it after quite obviously "discovering" it at that very moment. He was doing very well, was betting greens and had won a couple thousand already. I left before the inevitable bloodbath occurred.

The only other times I've seen it were people on the losing end of things getting progressively more angry and stressed out as they re-redoubled their bets. There's usually a lot of colorful language flying about as well.

Has anybody actually seen someone (e.g., a whale) using this method quasi-'successfully?'

I used it on the practice mode here. Played the field bet. Trippled my money in 20 mins, but was one bet from wipeout. Got a "12" when betting $800 or something. Only way I could see using it would be if I didn't care about losing and just wanted some weird brand of fun. Then again, having a pit boss think you a loser and hitting for $2400 is fun.....

Quote: DJTeddyBear

With Martingale, you double after EVERY loss.

I'm suggesting your chart is wrong, the first item should show a doubled bet. Perhaps I don't know how to read it.

My boss uses the Martingale and to make things worse he tried to explain to me that the dealer's up card has nothing to do with how you play your hand. I tried to explain to him about probabilities but it didn't seem to sink in. He also said doubling on 11 is a chicken move because you can never bust. Drove me nuts.

Quote: derik999

My boss uses the Martingale and to make things worse he tried to explain to me that the dealer's up card has nothing to do with how you play your hand. I tried to explain to him about probabilities but it didn't seem to sink in. He also said doubling on 11 is a chicken move because you can never bust. Drove me nuts.

You wonder how people get to be the boss sometimes. My friend draws to inside straights because she considers it a challenge. We had an Admiral who used to say that nothing good ever came out of probability theory.