Why the martingale is always counted till maximum table bet?

Ok, so we all know that every spin is individual and not affected by previous one's and that playing martingale with 10 reds in a row or randomly putting on black/red or any other even bets will make no difference.
Therefore, the player could start on an automatic roulette machine, where the min bet is 0.5 and max is around 140, then when he exceeded the max. bet, he can just go to a table with a higher bet and then to even a higher bet and etc and always bet on even chances. In fact the player could double up his bets as far as the maximum bet in the whole world or as high as his bankroll.

Now I AM VERY AWARE, that the more times you double up, the more you will lose and that one loss will cover the rest of the winnings, so I know that in the long run result will be same. PLEASE NOTE that this is NOT what this thread is about =)

The question in this thread: Why when there's an article about martingale, the comparison is always done with the min. bet and the max. bet of THE SAME table? It makes the player think that he MUST continue the same serie at the same table to increase his chances, but he doesn't. He can just play even bets on any other tables and chance to win will be the same..

Because to do otherwise, acknowledges the possibility that something may be "different" about the next table? That and there are only so many tables, with progressively higher limits, available to you at any one time. Can you imagine someone starting out at AZ Charlie's, hitting the table limit there, so he runs over to Circus Circus, hits the limit there, chases the loss to Mirage, Bellagio, and then Aria?

Quote: GH

Because to do otherwise, acknowledges the possibility that something may be "different" about the next table? That and there are only so many tables, with progressively higher limits, available to you at any one time.

Sorry, I didn't get both of the points you said =))

1. What do you mean maybe "different"?
2. OK, i see that you edited the answer =) Yes, I don't see a problem in this. He can start wherever he wants and finish wherever he wants for the sake of a calculation..

Why? Becaue it is both irrelevant and ridiculous.

Jumping from casino to casino, searching for a higher limit table as GH suggests is no different than finding a mythical table where the spread is $1 min to $1,000,000 max. Or no max.

All it does is change the ratio of whether or not you'll run out of bankroll before you hit the table limit.

Table limits, particularly in the Martingale discussion, provide a good benchmark for asking the question, "Just how many units are you going to bet, while chasing down a win of 1 unit?" I.E. Are you really going to bet a million bucks, to win one lousy buck?

Quote: DJTeddyBear

Why? Becaue it is both irrelevant and ridiculous.

Jumping from casino to casino, searching for a higher limit table as GH suggests is no different than finding a mythical table where the spread is $1 min to $1,000,000 max. Or no max.

All it does is change the ratio of whether or not you'll run out of bankroll before you hit the table limit.

Table limits, particularly in the Martingale discussion, provide a good benchmark for asking the question, "Just how many units are you going to bet, while chasing down a win of 1 unit?"

+1 LOL, our hero finally ends up in Monaco, before getting his $1 back!

Quote: DJTeddyBear

Why? Becaue it is both irrelevant and ridiculous.

Jumping from casino to casino, searching for a higher limit table as GH suggests is no different than finding a mythical table where the spread is $1 min to $1,000,000 max. Or no max.

All it does is change the ratio of whether or not you'll run out of bankroll before you hit the table limit.

Table limits, particularly in the Martingale discussion, provide a good benchmark for asking the question, "Just how many units are you going to bet, while chasing down a win of 1 unit?"

Sure, as I said I understand that doesn't matter how many times you double the ratio stays more or less same and you will lose what you won, but that's not the question.
I was just checking articles about martingale and they always make the calculation based on min. bet 5 and max. 500 or 1000 or something like that and I was just wondering why they do that. Why they limit the calculation on the same table where you start the play.. just this is what makes me curious.

Quote: GH

+1 LOL, our hero finally ends up in Monaco, before getting his $1 back!

Haha, yes, that would be funny indeed.

But seriously though, when counting how many bets you can double up, I think that AT LEAST they should take the minimum bet of the lowest bet table and the maximum bet of the highest bet table, in the same casino. That's IMHO.

Figure on a limit of 50 losses. If memory serves, the number of Banker wins recorded some 70 years ago. Just have enough money to cover that and you are good to go!

Quote: DeMango

Figure on a limit of 50 losses. If memory serves, the number of Banker wins recorded some 70 years ago. Just have enough money to cover that and you are good to go!

Nah, if I could double up 50 times, I wouldn't play casino :D
I was just curious why the articles compare only min. bet and max. bet at one table, because it makes others confused and think that switching to another table actually makes a difference, while it's not.

Quote: whatever61

But seriously though, when counting how many bets you can double up, I think that AT LEAST they should take the minimum bet of the lowest bet table and the maximum bet of the highest bet table, in the same casino. That's IMHO.

That's probably not a bad idea, as long as it's a reasonable spread. Say the MGM Grand has some tables with $5 minimums and other tables with a $100,000 maximum - why is a guy who can sustain the $100,000 single-hand loss playing a martingale starting at $5? We're talking about risking a total of $300,000 to win $5 at that point...

edit: that's actually a really messy spread - if you lose at $81,920 you're capped out. So maybe it's more like risking $165,000 to win $5. Making the $100,000 bet doesn't get you back to even after the $81,920 loss.

Quote: rdw4potus

That's probably not a bad idea, as long as it's a reasonable spread. Say the MGM Grand has some tables with $5 minimums and other tables with a $100,000 maximum - why is a guy who can sustain the $100,000 single-hand loss playing a martingale starting at $5? We're talking about risking a total of $300,000 to win $5 at that point...

edit: that's actually a really messy spread - if you lose at $81,920 you're capped out. So maybe it's more like risking $165,000 to win $5. Making the $100,000 bet doesn't get you back to even after the $81,920 loss.

Wow, didn't know there are places with such high bets as 100K.
I think you see it a bit wrongly though, at the point when you bet let's say 50K, AT THAT POINT it's already not to win back the 5$, it's to win back 25K and all the losses that were before the 25K. In the end your balance will be 5$, but again, at the point of putting that huge bet, it's already not 5$. I hope you got my point.

Anyway, it's just for the sake of the calculation when talking about martingale it should be the way you said, with spread from 5$ till 100K$ in MGM Grand. So when writing about martingale the comparison should be per casino, not per one table.
Either someone will have the guts or the money to do that, it's another thing (and probably no), so that player should decide on a limit for himself, but for the most accurate calculation of the martingale betting strategy he should know how high he can go and how many times he can double up.

Otherwise it's subjective, I mean you can say that doubling 8 times bet of 1$, which will be a loss of 255$ if you loss on the eight time, is might be "too much" of a risk to win back that 1$. Maybe for someone yes and for someone no. When making a calculation you shouldn't take this into account. You should show just show figures.

Btw, what about roulette machines in that MGM Grand? They should have even lower bets..

2^29 = 536870912

After the 28th loss, I'm sure our hero can buy his own casino for $536,870,912 and wait for the next "guest."

Quote: whatever61

Wow, didn't know there are places with such high bets as 100K.
I think you see it a bit wrongly though, at the point when you bet let's say 50K, AT THAT POINT it's already not to win back the 5$, it's to win back 25K and all the losses that were before the 25K. In the end your balance will be 5$, but again, at the point of putting that huge bet, it's already not 5$. I hope you got my point.

Anyway, it's just for the sake of the calculation when talking about martingale it should be the way you said, with spread from 5$ till 100K$ in MGM Grand. So when writing about martingale the comparison should be per casino, not per one table.
Either someone will have the guts or the money to do that, it's another thing (and probably no), so that player should decide on a limit for himself, but for the most accurate calculation of the martingale betting strategy he should know how high he can go and how many times he can double up.

Btw, what about roulette machines in that MGM Grand? They should have even lower bets..

I don't know the situation with the roulette machines in the MGM Grand. But, I doubt the limit is lower than $5 on the outside bets.

I guess you're sort of right that the $50k bet is to recoup all of the previous losses. But I don't think that's the correct way to look at the martingale at all. The first bet was an attempt to net $5. After a loss, the sum of all future bets up to and including 1 win are also an attempt to net $5. The fact that it might take 16 bets totaling $330,000 to get that $5 win is exactly the reason that a martingale is a terrible betting scheme to employ.

Quote: rdw4potus

I don't know the situation with the roulette machines in the MGM Grand. But, I doubt the limit is lower than $5 on the outside bets.

I guess you're sort of right that the $50k bet is to recoup all of the previous losses. But I don't think that's the correct way to look at the martingale at all. The first bet was an attempt to net $5. After a loss, the sum of all future bets up to and including 1 win are also an attempt to net $5. The fact that it might take 16 bets totaling $330,000 to get that $5 win is exactly the reason that a martingale is a terrible betting scheme to employ.

Where I played (in Belgium), the machines had a min. bet of 0.5EUR, while the tables had a min. bet of 25EUR. So I assume, that usually machines are like muuuuch more cheaper than even the lowest table, so probably there's something there in MGM Grand also.

Well, first of all, I'm not talking about if mart. is good or bad strategy =) I suppose it's a really a matter of how you look at it. I was just saying that if you will look at it after the losses already occurred, then you win back not the initial 5 already.. I mean you look at the chances of winning every next spin separately, right? You see it again as another 50% - HE to win, so imho you should also look at each bet separately, but I think we got each other. It's just a matter of how to look at it, from different angles.

Quote: whatever61

I was just curious why the articles compare only min. bet and max. bet at one table

Maybe because you read poor quality articles. I doubt there is something new about the martingale system on roulette which as never been investigated before.

The ratio of max to min bet is simply the maximum number of levels you can play without changing the strategy to something else.
Of course there are many martingale-equivalent bets available (i.e. bet the appropriate number of inside bets).

Anyway I don`t understand the max bet on roulette (unless some significant amount to the owner) anyway. Actually the house should love to take a $1M bet with 5% edge from anyone.

Quote: MangoJ

Maybe because you read poor quality articles. I doubt there is something new about the martingale system on roulette which as never been investigated before.

The ratio of max to min bet is simply the maximum number of levels you can play without changing the strategy to something else.
Of course there are many martingale-equivalent bets available (i.e. bet the appropriate number of inside bets).

Anyway I don`t understand the max bet on roulette (unless some significant amount to the owner) anyway. Actually the house should love to take a $1M bet with 5% edge from anyone.

Well, I'm talking about the typical martingale review, which is not usually written on some professional gambling site, so yeah, it's like for amateurs more like. It's just that they always present the problem of martingale as the table limit and not the fact that you will lose it all back at one shot, no matter how many time you double up.

Interesting point about the max bet. Well, maybe also from administrative reasons.
I mean you would need to keep a huge amount of chips with different ranges and it would be weird if someone would play 1$ and next to him someone with 100,000$. Maybe they wanna group the high rollers with low rollers separately.. I don't know actually, just giving assumptions.

Quote: MangoJ

Anyway I don`t understand the max bet on roulette (unless some significant amount to the owner) anyway. Actually the house should love to take a $1M bet with 5% edge from anyone.

that's because the punter can get lucky a few times and wipe out profits for the entire month. casinos have corp parents and they would rather grind out steady guaranteed profits.

Martingale works for the banks. hehehehe

Quote: whatever61

The question in this thread: Why when there's an article about martingale, the comparison is always done with the min. bet and the max. bet of THE SAME table? It makes the player think that he MUST continue the same serie at the same table to increase his chances, but he doesn't. He can just play even bets on any other tables and chance to win will be the same..

Because as you walk from a $1000 max table to place a $2000 bet on another, common sense starts to kick in. Whereupon you realize that all you're about to do is to plonk down 2 grand on a less than 50/50 chance. Nothing like the "sure thing" you were going for.

More seriously, I think most martingalers believe that a very long streak is impossible on a single table, but the same doesn't apply to streaks for an individual.

Quote: DeMango

Figure on a limit of 50 losses. If memory serves, the number of Banker wins recorded some 70 years ago. Just have enough money to cover that and you are good to go!

There is a widespread mythology that the number losses permitted before hitting the maximum bet, the more effective martingale is. It is a complete myth. If you evaluate the game by the probability that you will double your bankroll before going broke, then the number of times you can double is immaterial.

For most tables the number of times you can lose in a row is 6, but on rare occasions I have seen as high as 10. However, as pointed out, you can bounce around from table to table. A limit of 20 goes from $1 to $1 million. A limit of 50 implies 2^50 which is implies a quadrillion dollar bet.



If the table will let you lose 6 times in a row before you reach maximum, then your bankroll must be $63* Unit Bet. In a game with no house edge you are expected to play 126 times before you lose 6 in a row. In a line bet in craps you are expected to play 117.3 times before you lose 6 in a row. In roulette you are expected to play 97.2 times before you lose 6 in a row.

If the table will let you lose 7 times in a row before you reach maximum, then your bankroll must be $127* Unit Bet. In a game with no house edge you are expected to play 254 times before you lose 7 in a row. In a line bet in craps you are expected to play 233.3 times before you lose 7 in a row. In roulette you are expected to play 186.6 times before you lose 7 in a row.

So you play roughly twice as long, but your required bankroll is roughly twice as big, so it is harder to double your bankroll.

Quote: pacomartin

There is a widespread mythology that the number losses permitted before hitting the maximum bet, the more effective martingale is. It is a complete myth.
If you evaluate the game by the probability that you will double your bankroll before going broke
, then the number of times you can double is immaterial.

If the table will let you lose 6 times in a row before you reach maximum, then your bankroll must be $63* Unit Bet.

If the table will let you lose 7 times in a row before you reach maximum, then your bankroll must be $127* Unit Bet.
So you play roughly twice as long, but your required bankroll is roughly twice as big,
so it is harder to double your bankroll.

Not as hard as one thinks.
Here is a table for the probability of doubling a starting bankroll using an N-Step Martingale Betting Strat with different type of bets.
I even verified the calculations by simulation. Some results seemed too high but are not.
When the player lost a betting sequence, most times started over with what bankroll was left and made an all in bet at some point.
added: Rules: Player plays to double starting bankroll or complete ruin

Marty Step	Max Bet	Required Bank Units	Double to	pass Line success Prob %	Field 2X	Field 3X	Bac Player	Bac Banker	0 Roulette	00 Roulette
3	4	7	14	47.71	41.28	43.97	47.78	49.54	45.64	41.56
4	8	15	30	46.87	38.98	43.17	46.98	49.58	44.04	38.57
5	16	31	62	46.01	36.75	42.27	46.14	49.2	42.43	35.6
6	32	63	126	45.13	34.66	41.37	45.3	48.58	40.8	32.71
7	64	127	254	44.26	32.75	40.51	44.45	47.86	39.2	29.95
8	128	255	510	43.27	31.03	39.71	43.5	46.8	37.55	27.3

Triple Bankroll table

Marty Step	Max Bet	Required Bank Units	Triple to	pass Line success Prob %	Field 2X	Field 3X	Bac Player	Bac Banker	0 Roulette	00 Roulette
3	4	7	21	30.39	23.64	27.96	30.49	32.78	27.81	23.01
4	8	15	45	29.36	.	26.78	29.5	.	25.94	19.81
5	16	31	93	28.33	.	25.65	28.5	.	24.11	16.87
6	32	63	189	27.3	.	24.6	27.51	.	22.34	14.22
7	64	127	381	26.2	.	23.65	26.43	.	20.58	11.86
8	128	255	765	22.74	.	22.7	22.97	.	17.33	9.26

Roulette bets are even money bets
Baccarat Banker pays 5% commission on a win

The time it takes to double or ruin can also be calculated or simulated.
The line bets in Craps takes many dice rolls to double a bankroll and would discourage many in the process.
The Player bet in Baccarat has the same curve as the Pass Line bet in Craps but a way shorter average number of games played.

For a 6 Step Marty, a player has about a 25-35% chance of winning 63 bets in a row to double the bankroll
(depending on the type of bet made).
That leaves a very large window open to have a large loss before the bankroll double.
Not all hope is lost, but the Marty player can still play with what is left, most times going all in to keep the double or bust method going.

A flat bettor, to have a same or better chance of doubling a bankroll vs the Marty,
must make higher bets than the average Marty bettor.
That may take the fun out of playing making too many large bets.

Example: Craps Pass Line to double a 63 stake with a prob of 45% requires a $9 bet (gamblers risk of ruin formula)
where the 6 step Marty bettor has at most a $6.22 average bet

Of course, for many, flat betting is no fun, so they make bets that add to their fun.

Quote: 7craps

Here is a table for the probability of doubling a starting bankroll using an N-Step Martingale Betting Strat with different type of bets.
I even verified the calculations by simulation. Some results seemed too high but are not.
When the player lost a betting sequence, most times started over with what bankroll was left and made an all in bet at some point.

I am not sure of your rules. Say a player is playing a 6 step Martingale. The number 126 is the "expected value" of number of plays before the player will lose 6 times in a row. What are your stopping conditions? Are they only double or bankruptcy? Does the player stop if he reaches 126 plays?

Quote: pacomartin

What are your stopping conditions? Are they only double or bankruptcy?

Yep.
Double or Ruin always using a Marty bet except if it is not a true double last bet where the player is all in.

Example. Player loses 6 in a row and only has $23 left from the starting bankroll.
The next bet starts over at $1 and tries to complete a double-up bet on a loss or bust out totally.

I had also run sims where the player would go all in (say with $23) to get back to the beginning starting bankroll level,
but the probabilities were just not that much different.

Quote: pacomartin

Does the player stop if he reaches 126 plays?

No.

Craps Pass Line bet as an example for a 6step Marty
63 begin stake and stop when double or complete ruin
Sim data:
45.53% of sessions did double the bankroll with
avg # bets: 165.41
avg # rolls: 555.53
When busted
avg # bets: 113.75
avg # rolls: 386.77
combined:
avg # bets: 137.27
avg # rolls: 463.61
median # rolls: 399

Quote: 7craps

Marty Step	Max Bet	Required Bank Units	Double to	pass Line success Prob %	Field 2X	Field 3X	Bac Player	Bac Banker	0 Roulette	00 Roulette
5	16	31	62	46.01	36.75	42.27	46.14	49.2	42.43	35.6
6	32	63	126	45.13	34.66	41.37	45.3	48.58	40.8	32.71

I wanted to work with the craps pass line bet and the 5 and 6 step Marty
I set up - the 1st i know of - an absorbing transition matrix in Excel
because for me it is fun to see
(the 5 step is 218x218 matrix but 30 rows/cols are just a placeholder and sum to 0 so i could have made the matrix even smaller)
see


example:
a 5 step Marty requires a 31 unit bankroll
and trying to double that before complete ruin to 62 units

i get 0.466360854 for success
(avg # of rounds - bets - 52.88)

compare this to betting 1 unit and always 345x odds
that i simulated at
Bankroll was busted . . = 52.762% of the time ( 5276206)
Win goal was met . . . = 47.238% of the time ( 4723794)
(avg # of rounds - bets - 45.71)
of course this success probability can be improved by hitting the target exactly instead of going over as it normally will with full odds bet

a matrix answer may follow for 345x odds if it looks interesting

(when 30 units or below, the object i placed was to get back to 31 units asap so a 5 step can be continued
this MAY require an all in bet or two)

Oh yes,
46.636% Marty
vs
47.238% pass with odds
close i says

of course the Marty has a larger avg unit bet at abouts 5.15
where the 345x player is abouts 3 7/9

still another close race
when just attempting to double a starting bankroll

and Marty still gets the bad rap (yes, i too have said that)
that must come from the fact the 5 Step Marty has only a 34.748615%
chance of winning 31 times in a row B4 that 1st loss
at least all is not lost but an uphill climb does remain

=============================
Oh, the 6 step Marty
63 units to 126 units
46.018% i get calculated (6.22 avg unit bet)
simulated pass 345x
47.224%

Bankroll was busted . . = 52.776% of the time ( 5277625)
Win goal was met . . . = 47.224% of the time ( 4722375)

looks to me Marty works just fine (and could be super fun for some time for some) at the craps table
compared of course

nice to compare
Sally

Quote: whatever61

Nah, if I could double up 50 times, I wouldn't play casino :D

I'll tell ya one reason a person might want to do it if they had that kind of cash (I would for one....)

Because people make websites where they say things like "all betting systems are worthelss...."

And other people say things like Martingale systems doesn't work....etc.

When Mr Wynn says no person has come out ahead over a lifetime of gambling...

Things like this would make me want to show that I could beat the damn casino - even if it was only by $1.

So here is my hypothertical -Mostly for MathExtremist...

If I had some sort of vision of the future from here on out but could only see one thing...and that was the max number of reds that would ever happen in a row on roullette. I don't know when...or I don't know where....all I know is the number.

If I knew that number, do you concede that I could then beat the house using martingale? (Question is for anyone really...just would really like to hear from mathextremist on this).

Quote: slackyhacky

I'll tell ya one reason a person might want to do it if they had that kind of cash (I would for one....)

Because people make websites where they say things like "all betting systems are worthelss...."

And other people say things like Martingale systems doesn't work....etc.

When Mr Wynn says no person has come out ahead over a lifetime of gambling...

Things like this would make me want to show that I could beat the damn casino - even if it was only by $1.

So here is my hypothertical -Mostly for MathExtremist...

If I had some sort of vision of the future from here on out but could only see one thing...and that was the max number of reds that would ever happen in a row on roullette. I don't know when...or I don't know where....all I know is the number.

If I knew that number, do you concede that I could then beat the house using martingale? (Question is for anyone really...just would really like to hear from mathextremist on this).

Sure with this type of foreknowledge you could beat the casino if you had a large enough bankroll by just having an n+1 step marty where n is the max number of reds that can appear in a streak. The problem is that number doesn't exist. There is no reason for a max number of reds in a row to exist. Two you almost definitely wouldn't have enough money even if such a thing exist since we know it would have to be over 50 and with that you are talking quadrillion times your initial bet. Three this doesn't really prove the martingale works at all since it requires foreknowledge of something that is unknowable. I mean its like asking whether someone could win money on the lottery if they had knowledge of exactly 1 number that would be on the next lottery drawing and sure the answer is yes, but so what.

If I knew there was never going to be more than X reds in a row... I'd wait till I saw 30 reds in a row and bet the Max on black. I'd not need no Martingale.

The Martingale is horribly inefficient when you have an advantage, and a great way to have ruinious time when you don't.

Not mentioned in all this logic is the time element. You can lose you "daily" or "session" limit then move on starting at higher stakes(double your last losing bet) the next hour or day or month or year.