[raiders72001]

Ganchgrow- I sent you a PM

[natrass]

Can I just say, guys, dont gamble on this .... for all I have said, i am 100% sure i am right, and I know ganchrow believes he is also, thats a legitimate difference of opinion, but we are not here to make money off each other.

[jjgold]

I cannot beleive some guys here saying the martingale system is not a 100% winning system with no house limits.

All you do is keep betting red in roulette and then when it hits you go back to 1 unit bets.

It is automatic

[Ganchrow]

I cannot beleive some guys here saying the martingale system is not a 100% winning system with no house limits.

All you do is keep betting red in roulette and then when it hits you go back to 1 unit bets.

It is automatic

This statement belies a complete lack of understanding of rather elementary concepts of probability.

[Ganchrow]

Can I just say, guys, dont gamble on this .... for all I have said, i am 100% sure i am right, and I know ganchrow believes he is also, thats a legitimate difference of opinion, but we are not here to make money off each other.

You're a smart guy, natrass, you just fail to grasp these basic conecepts of probability. This isn't a matter of opinion. It's a matter of mathematical fact. And the mathematical fact this time My Friend, just happens to be on the side of the mathematician. Go figure.

Just check out those two links posted by myself and taco. Read an intoductory book on probability. Talk to another mathematican. The more you research this more you'll understand.

[Ganchrow]

In your example ($100K vs. $4.2 bn) it was only 16 times. The probability of the casino's winning
16 times in a row are 0.0034669%.

When the casino wins 16 times in a row it wins $6.5536bn (2^16 * 100,000) . Otherwise it loses $100,000. Hence it's expected profit is:
0.0034669% * 6.5536bn - (1-0.0034669%) * 100,000 = $127,210.78 profit expectancy for the casino.

Anyone see a problem with the above? Fairly starightforward, no?

[Ganchrow]

OK. I just ran the simulator for 10,004,491 trials.

The average number of spins per trials was 2.11.

The expected profit for the casino was $132,202.79.

The expected loss for Trump was -$132,202.79.

Of the 10,004,491 trials Trump was rendered bankrupt 566 times.

Of the 10,004,491 trials the casino was rendered bankrupt 10,003,925 times.

The casino was rendered bankrupt 17,675 times more frequently than Trump (way less than 42,000 times required to make the game "fair".)

Anyone see a problem with the results of this Monte Carlo simulation?

[natrass]

Many pages ago, I believe you disagreed with me when I said that a big roller could bankrupt a small casino by playing the martingale system.

Since then, you have kept referring to the house advantage on black/red and that, statistically speaking, the house would have a fractional advantage. No one has disagreed.

However, surely we can both agree that "a big roller coukld easily bankrupt a small casino by playing the martingale"?

I cannot understand how you can disagree with that statement some three pages later.

[Ganchrow]

Many pages ago, I believe you disagreed with me when I said that a big roller could bankrupt a small casino by playing the martingale system.

However, surely we can both agree that "a big roller coukld easily bankrupt a small casino by playing the martingale"?

I cannot understand how you can disagree with that statement some three pages later.

I've been diagreeing with you all along. What you hadn't noticed?

As I said earlier (and quoted after that):

I don't know how casinos were run a hundred years ago, but it would be positively astonishing to me if a casino, even back then, would have allowed wagers so enormous relative to its own bankroll, that a Martingale could realistically bankrupt it. Remember that to run a sucessful Martingale over a decent stretch of time you'd likely need to place wagers thousands and thousands of times larger than your base wager.

....

No. That [a big roller could easily bankrupt a small casino by playing the martingale] is not at all true for a casino with anything even approaching reasonably set limits. Even for a casino with infinite limits and a de minimis bank roll, the expectation would would still be for the "Big Player" to lose (although the most common occurance would be for the casino to lose, the times that it did win would its winnings would dwarf its losses.)

What you're describing is but a common (and highly dangerous) fallacy regarding the Martingale system.

Remember: there exist no betting strategies which can ever ever ever turn a negative EV game into a positive.

Just for the record, you do finally at least agree that the big player's expected profit is in fact negative here, right? If so, then you're getting somewhere!

[natrass]

We have never been arguing this ... I believe you couldn't understand how a big roller could bankrupt a casino playing the martunbgale.

I say they could, you cant see how.

But if you still say that a big roller with unlimited stakes cant bankrupt a casino playing the martingale ... well just agree to disagee.

I think you have got stuck on the probability thing.

I think we have shown that for the example given ... in all but 0.0003% of the time the casino would be bankrupted. How much proof do you need that a big roller can bankrupt a smalle casino?

[Ganchrow]

We have never been arguing [that the big player's expected profit is negative]

You did say:

The only way the house can not be bankrupted is if its gets probably endless consecutive blacks or something. It cannot suffer one loss.

Do you still believe the expectation is for the house to win?

I think we have shown that for the example given ... in all but 0.0003% of the time the casino would be bankrupted. How much proof do you need that a big roller can bankrupt a smalle casino?

You utterly miss the point. This 0.0003% figure only holds if the casino's maximum bet is
65,000 times greater than the entirety of its net assets. 65,000 times. You couldn't even find a casino who would except a maximum bet that was .1% of its assets and yet the max bet needs to be 65,000,000 times greater than that for the 0.0003% to hold.

And guess what? the lower the maximum stake, the lower the chances of bankruptcy.

What I did say, however, and again what I do wish to make certain, is that by now you see that even if there were no maximum bet imposed by the casino, the casino would still have a positive expectancy versus the Big Martingale Player (regardless of how Big he was). This even holds if the Big Martingale Player had an unlimited stake. Yep. Even for an infinite player bankroll the casino still expects to profit from a player using the Martingale.

[natrass]

You utterly miss the point. This 0.0003% figure only holds if the casino's maximum bet is
65,000 times greater than the entirety of its net assets. 65,000 times. You couldn't even find a casino who would except a maximum bet that was .1% of its assets and yet the max bet needs to be 65,000,000 times greater than that for the 0.0003% to hold.

.

Didn;t you say .. unlimited bets ... so, now, its "well, maybe if its x bigger" ... as I said, the whole premise relies on unlimited bets.

We were talking $4.2 bn against $100,000 ... so you have just agreed in a typically round about way.

Its very simple ... a big roller can easily bankrupt a small casino using the martingale

You are just falling back on "oh yes, but over the long turn the casino would have the edge". Once again, that has not been disputed.

I still say that a $4.2bn big player could bankrupt a $100,00 casino. Could do that easily (I think we agreed that the chances of it not happening was 0.0003%). Right at the start and throughout the term unlimited was stressed, now you are saying "ah, well no casino would take the bet" ... you are now backtracking (I always pointed out that no casino would take him on for this very reason).

But, OK, you think the casino cant be bankrupted ... there is nothing more for me to add.

You are still arguing about probabilities and house advantage ... but you are arguing with yourself here because its not the basis of my statement.

[Ganchrow]

Check post 14, where we first start talking about this. I say (emphasis added):

That is not at all true for a casino with anything even approaching reasonably set limits. Even for a casino with infinite limits and a de minimis bank roll, the expectation would would still be for the "Big Player" to lose (although the most common occurance would be for the casino to lose, the times that it did win would its winnings would dwarf its losses.)

I think my point has been quite clear from the start.

A casino with reasonable limits: De minimis chance of bankruptcy. Postive expectancy for casino.

A casino with no limit: Most likely occurance is bankruptcy. Postive expectancy for casino.

[THESCOUT]

martingale systems is a proven loser system it is just a matter of time, not worth the trouble

[jjgold]

Scouter you are correct but it is a proven winner if the gambler has unlimited money but then again that is not realistic.

Good Luck

[Ganchrow]

Scouter you are correct but it is a proven winner if the gambler has unlimited money

And JJ, you are incorrect. Even if the gambler has an infinite bankroll, the expectation is still for the gambler to lose.

[jjgold]

Ganch (man I love that name) I still cannot see how you can lose. I have been reading your excellent posts too but it is impossible to lose.

Maybe you can explain in a very broad way how the gambler can lose if he has say 30 Billion Dollars.

[natrass]

A casino with no limit: Most likely occurance is bankruptcy. .

Hurrah!!!

We started with how you disagreed that with unlimited bets a big player could easily bankrupt a small casino.

We finish with you saying just that.

You then start to go on about long term probabilities ... I dont think anyone argued about that. It was and is irrelevant to the fact that a big player could easily (NOT always, NOT profitably over 10 million trials, etc) but easily, in the real world, bankrupt a small casino if there were unlimited bets..

So, you have agreed that with unlimited stakes a big player can easily bankrupt a small casino.

All you are doing now is arguing with yourself and trying to re-introduce limited bets, limited bankroll, etc.

[tacomax]

jjgold, try reading the previous pages - everything is explained very clearly and unfortunately ganchrow has had to repeat himself a number of times.

If after reading that you still think that the Martingale is a winning system then I've got some magic beans that you might be interested in. I'll sell them to you for a very good price.

[natrass]

Ganch (man I love that name) I still cannot see how you can lose. I have been reading your excellent posts too but it is impossible to lose.

Maybe you can explain in a very broad way how the gambler can lose if he has say 30 Billion Dollars.

I think ganchcrow will answer that with "out of 10 million tries, the casino would end up in profit". It will be long term probabilities.

The chances of ganchrow being right are 0.00003% in a real world test.

[jjgold]

Wait a minute the question really is can you win using the martingale system not bankrupt a casino .

Yes the gambler will win with unlimited money and he is not going to be at the casino 24 hrs a day to achieve therefore the probablities of a huge amount of reds coming up in a row is even further diminshed.

It is mathmatically impossible to lose using the martingale system given the player has unlmited bankroll and casino has no limits.

Again we are not talking about bankrupting a casino but a player turning a profit for his lifetime using this system.

[raiders72001]

Sharp post JJ

[Ganchrow]

Ganch (man I love that name) I still cannot see how you can lose. I have been reading your excellent posts too but it is impossible to lose.

Maybe you can explain in a very broad way how the gambler can lose if he has say 30 Billion Dollars.

OK, let's assume that the base value of the bets is $1. This means that a player bets $1. If he loses, he then doubles his bet. He continues doubling his bet until he wins. We'll say the player is betting red/black in American roulette and as such his probability of losing any given roll is 20/38 or 52.63%.

The question is this what is the player's expected profit or loss as a function of his bankroll for one cycle (in other playing the game until either he is bankrupt or until he finally wins).

To make things easier we'll assume that the player's bankroll must be of the form 2^n - 1 where n is a positive integer (in other words, the bankroll has to be a number like $1, $3, $7, $15, $31, $63, $127, $255, $511, $1,023, etc.)

So if the player's bankroll is 2^n-1m that means he can withstand n losses before going bankrupt. The probability of losing n rolls is a row is 52.63%^n. The probability of this not happening is obviously 1 - 52.63%^n. If the player wins, his net gain $1. If he loses,he loses his entire bankroll. Hence:

Expected Value = - 52.63%^n * (2^n-1) + 1 - 52.63%^n

Simplifying yields:

EV = 1 - 1.0526^n

Because 1.0526^n > 1 for all values of n >= 1, the expected value of the bet cycle is always negative.

QED

We should also note that as n approches infinity (representing bankroll approaching infinity) the expected value approaches negative infinity. This means that not only would an infinite bankroll Martingale NOT yield an expected profit, it would in fact yield an INFINITE EXPECTED LOSS.

Now let's just plug in a few numbers and see what we get:

Bankroll of $1: EV: -$0.05
Bankroll of $1,023: EV: -$0.67
Bankroll of $1,048,575: EV: -$1.79
Bankroll of $1bn: EV:-$3.66
Bankroll of $34.4bn: EV: -$5.02
Bankroll of $342 trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion:
EV:
-$24,421,744,576,581,700,000,000

[Ganchrow]

A casino with no limit: Most likely occurance is bankruptcy.

Hurrah!!!

You just aren't reading what I'm writing. I first said this in post #14. I'll quote it again for the fourth time now:

for a casino with infinite limits ... the most common occurance would be for the casino to lose

In the context of our discussion, a casino's losing results in bankruptcy.Again, I first said this over 90 posts ago!

We started with how you disagreed that with unlimited bets a big player could easily bankrupt a small casino.

I only disagreed in the case of (and again I quote for the fourth time) "a casino with anything even approaching reasonably set limits".

natrass, you need to read what I write. I've been quite consistent throughout.

[natrass]

jjgold, try reading the previous pages - everything is explained very clearly and unfortunately ganchrow has had to repeat himself a number of times.

If after reading that you still think that the Martingale is a winning system then I've got some magic beans that you might be interested in. I'll sell them to you for a very good price.

Who said it was a winning system? Show me where I have said the system is a winner always.

But a big player using it against a small casino "can easily bankrupt a casino".

There is a difference there.

[tacomax]

Well done, ganchrow.

When it comes to maths, you're sharper than a sharp thing that's just been sharpened by a sharpening machine.

[tacomax]

Who said it was a winning system? Show me where I have said the system is a winner always.

Well there are a couple of people here who think it's a 100% winning system. Casinos always love a sucker.

Theoretically the martingale system is a 100% winning system..

I cannot beleive some guys here saying the martingale system is not a 100% winning system with no house limits.

All you do is keep betting red in roulette and then when it hits you go back to 1 unit bets.

It is automatic

Ganch (man I love that name) I still cannot see how you can lose. I have been reading your excellent posts too but it is impossible to lose.

[Ganchrow]

Who said it was a winning system? Show me where I have said the system is a winner always.

Wel, you did question at least twice whether the house has an edge. To wit:

In post 15 you write: "Are you still saying that the "expectation will be for the big player to lose?"

In post 20 you write: "Do you still believe the expectation is for the house to win?"

My answers are of course "yes" and "yes".

But a big player using it against a small casino "can easily bankrupt a casino".

Except not in the real world.

[Ganchrow]

[The gambler] is not going to be at the casino 24 hrs a day to achieve therefore the probablities of a huge amount of reds coming up in a row is even further diminshed.

This is a prototypical example of the so-called gambler's fallacy.

[natrass]

You just aren't reading what I'm writing. I first said this in post #14. I'll quote it again for the fourth time now: In the context of our discussion, a casino's losing results in bankruptcy.Again, I first said this over 90 posts ago!


I only disagreed in the case of (and again I quote for the fourth time) "a casino with anything even approaching reasonably set limits".

natrass, you need to read what I write. I've been quite consistent throughout.

To summarise :

1. The house has a fractional advantage ... no has argued that.

2. The house will almost certainly go bankrupt with unlimited bets and an overwhelming bankroll.

At no point have I said anything other than that.

But you keep coming back with "no, over a long running trial the house would show a profit". My point is that it is irrelevant to the premise that the martingale system "could easily" (again NOT always, NOT profitably, NOT over 10 million trials, etc) but "could easily" bankrupt a casino.

Again, you could not believe a martingale system could have been used to bankrupt a casino. I think you said they would need to be "lucky" in fact. Isnt that incorrect belief of yours what we have been arguing about?

We have shown that the odds of this not happening, in a real world example, were around 0.00003% .. not much luck needed there dont you think.

I have no doubt that you believe that the house adbantage over-rules this statement. The fact is it does not.

[Ganchrow]

So if your point has now morphed into simply:

Given a casino which places no limits on a player's bets, if a player's bankroll is at least 116% that of the casino, then by playing an American red/black-style Martingale with a unit bet equal to the casino's initial bankroll, it's more likely than not that the player will bankrupt the casino.

Then I do agree. You'll note that I have been saying just this (although without giving specific figures) since way back in post #14. Still, I hope that we can also agree that:

1. The player's expectation is to lose and the house's expectation is to win. The greater the player's initial bankroll, the more likely he is to win but the more he expects to lose.
2. In the real world, the chances of any player (regardless of the size of his bankroll and whether he is using Martingale or not) bankrupting a casino with reasonably established limits is de minimis.
3. Casinos would still impose betting limits even if not for the Martingale.
4. If the house limit is less than or equal to the casino's initial stake, then when playing American red/black roulette there are other systems which are more likely ways to bankrupt the Casino than the Martingale.

If so, then we are in agreement.

[natrass]

Sorry ... double post

[natrass]

So if your point has now morphed into simply:

Given a casino which places no limits on a player's bets, if a player's bankroll is at least 116% that of the casino, then by playing an American red/black-style Martingale with a unit bet equal to the casino's initial bankroll, it's more likely than not that the player will bankrupt the casino.


No morphing at all ... $4.2 bn against $100,000 with no limits. Same as three pages back.

Then I do agree. You'll note that I have been saying just this (although without giving specific figures) since way back in post #14.


No, I think you have been arguing that the house advantage makes this somehow illogical or at least a flawed argument..


Still, I hope that we can also agree that:

1. The player's expectation is to lose and the house's expectation is to win. The greater the player's initial bankroll, the more likely he is to win but the more he expects to lose.
   
   Agreed . Long term profitablity has never been argued. I think one of my first posts on this referred to the the "martingale system" being flawed,
   
   
2. In the real world, the chances of any player (regardless of the size of his bankroll and whether he is using Martingale or not) bankrupting a casino with reasonably established limits is de minimis.
   
   
   Yes, but how often have I emphasised unlimited limits. That, again I repeat, forms the whole basis of my argument. I even pointed out that bankroll is the very reason casinos place limites.
   
   Limits are only placed to protect bankroll ... the house advantage is of absolutely no significance here in a casinos decision making.
   
   
3. Casinos would still impose betting limits even if not for the Martingale.
   
   
   Yes. Only to protect bankroll ... nothing to do with house advantage or not.
   
   But, I think you said for the the martingale system to beat the casino it would need to be "lucky". I have tried to show that given unlimted bets, an overwhelming bankroll needs practically no luck (in our example, enough luck to beat oversome a 0.00003% chance of it not happening).
   
   Without the martingale system, then there is no strategy to examine .. it would be a series of independent bets. The argument would then be "could a man with $4.2bn lose it all at a casino wihich has a bankroll of $100,00?" The answer to that would clearly be yes he could .. and then luck, etc would come into it.
   

If so, then we are in agreement.

Good. Like I said before, its been a good debate and has made me think ... you have not been wrong BTW, only your basis for saying I am wrong (does that make sense?).

GL

[slacker00]

You guys are killing me! lol

I am certain that ganchrow is correct in what he is trying to explain. I'm certain that JJGOLD is incorrect that the martingdale system is a reasonable choice under any reasonable circumstances. As for natrass, I think he is simply misunderstanding ganchrow or trying to make an different argument which I'm not quite sure I understand. But, I am certain that everyone is misunderstanding everyone else.

I'll try to explain a few things in a very simple way, that maybe everyone will at least understand what I'm trying to say.

If the casino was limited to $100,000 and offered unlimited-size bets to Donald Trump who wanted to gamble his entire liquidated fortune of say, $4.2 billion, Trump could "easily" bankrupt this poor casino playing RED on roulette for $100,000 a crack. First bet, Trump puts $100,000 on RED, where he has a 49% chance to break the bank. It lands on BLACK. Trump says "big deal" and plays again. Trump puts up $200,000 on RED because the casino now has $200,000 with the original $100,000 plus the $100,000 profit from the last roll. Trump has a 49% chance to break the bank AGAIN. BLACK comes up again. No big deal, trump digs deeper into his wallet, etc, etc. Now, I think the point that natrass is trying to make, is that under this situation, Trump can "easily" break the bank. Yes, this is a fact. 49% is a decent chance, plus another 49% after that, etc. Trump does run out of chances eventually, due to his limited bankroll, but I'm sure he gets close to a 90% chance or more of breaking the casino, which we can all agree is a decent chance. If this is natrass' point, then it is a valid point.

Now, ganchow, is trying to say that Trump is taking a -EV proposition. ganchow is correct. Every time Trump is placing a bet, the casino is making a 1% profit. Albeit, the casino is taking a HUGE risk under these conditions. Plus, the casino has a chance of busting Trump, albeit a small chance.

Now, the assumptions of an infinte bankroll by the casino patron, and the assumption that a casino will assume "infinite risk" are very unrealistic assumptions. We are making a circular mathematical argument. I'm not sure what the purpose is to suggest. Maybe it's an explanation why casinos cannot allow "infinite-sized bets", because of the high risk, which I think natrass is trying to make. Maybe it's an explanation of why the martingdale system is a loser, which I am certain ganchow is trying to make. But, it is getting pretty academic at this point, because of the unrealistc assumptions in the Trump scenario. I can make my own scenario, which is even simpler: I claim that I can break a $100,000 casino making $5 bets on a roulette wheel with an unlimited bankroll and unlimited time. It's basically the same argument, but unrealistic. Again, it would be a mathematical lesson in variance. There is a 1 in a gazillion chance that I would hit RED 20,000 times in a row, but there's a chance. If I just play long enough, I would break the casino. Unfortunately, I will probably only live into my 80's, and even more sadly, I don't have unlimited money with which I would like to occupy all of my time breaking a $100,000 casino.

Did I make any progress in this seemingly hopeless circular thread?

[natrass]

Slacker ... what I said was "a big roller can easily break a small casino using the martingale sysytem".

The Trump example showed the chances of it not happening were 0.0003%.

This could all be settled within 16 rolls of the roullette table. One or the other would be bankrupt .. but the casino would have a 0.0003% chance to cling to.

And thats it.

I think ganchrow has been saying (correctly) that the house has the advantage that given a high enough attempts would pay.

My disagreement is that this is irrelevant. The fact remains that the casino would have a 0.0003% chance of survival. The casino cannot come back from a single loss if the bets are high enough. This is why casinos set limits even if they have the probabilities on their side.