[THESCOUT]

if really good and you can bump up your stake after acouple losses and come out ahead.

[Ganchrow]

In the real world, the chances of a casino surviving a need for, say, 18 consequetive wins are 0.000003%.

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.

I really don't know how much more I can explain the math.

In the real world, I cant martingale you because I dont have the bankroll to dwarf yours.

Even if you did you couldn't. Not on the average anyway.

Its not about statistics anymore when you get to these probabilities, its about common sense.

Sure it's about statistics. Whether Trump understand them or not.

[Mudcat]

From what I have read, Ganchrow is 100% correct on every single point here.

[Ganchrow]

From what I have read, Ganchrow is 100% correct on every single point here.

But natrass is better looking.

[natrass]

From what I have read, Ganchrow is 100% correct on every single point here.

That may well be ... but, then, why do casinos limit stakes if not to protect their bankroll?

[Ganchrow]

That may well be ... but, then, why do casinos limit stakes if not to protect their bankroll?

Two words: Risk Management.

Example: A casino has a bankroll of $20 billion. A player wants to bet $20 billion on black. If the casino allowed the player to make this bet the casino would have a 47.37% chance of being put out of business. From the perspective of the casino as a growing concern it's risk management team would be wise to limit the player to a much more reasonable limit even though the casino's expected profit on the bet would be positive (about $1.05 billion) .

[natrass]

Two words: Risk Management.

Example: A casino has a bankroll of $20 billion. A player wants to bet $20 billion on black. If the casino allowed the player to make this bet the casino would have a 47.37% chance of being put out of business. From the perspective of the casino as a growing concern it's risk management team would be wise to limit the player to a much more reasonable limit even though the casino's expected profit on the bet would be positive (about $1.05 billion) .

Bingo!!!

Remember how I said above that if a casino had a $100,000 bankroll and Donald Trump was to martingale them then hed inevitably put them out of business. If he went to the max, they would have a 0.00003% of surviving.

That is what weve been talking about isnt it? How the bank of Monte Carlo could be broke by a rich punter playing the martingale? The 52.6/47.4 house advantage is relatively meaningless in the face of 0.00003% odds.

[raiders72001]

It's statistically impossible to turn a house advantage into a player advantage.

It's also statistically impossible to turn a player advantage into a house advantage.

[natrass]

It's also statistically impossible to turn a player advantage into a house advantage.

I wish Id thought of that!!

[raiders72001]

Thanks natrass

[Ganchrow]

Remember how I said above that if a casino had a $100,000 bankroll and Donald Trump was to martingale them then hed inevitably put them out of business. If he went to the max, they would have a 0.00003% of surviving.

That is what weve been talking about isnt it? How the bank of Monte Carlo could be broke by a rich punter playing the martingale? The 52.6/47.4 house advantage is relatively meaningless in the face of 0.00003% odds.

And what I said was:

That is not at all [that a big player could readily bankrupt a casino using Martingale] 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 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.

Regardless, I hope you by now agree with the mathematical fact that even if the casino did allow to bet such large stakes, the casino would still have positive expectation of profit. $127,210.78 to be exact in the Trump example.

[Ganchrow]

Casinos have limits only because of MArtingale system

100% incorrect.

[tacomax]

Congratulations to ganchrow for keeping cool throughout the thread - it helps when yhou know you're right, though.

More information on the martingale system (complete with graphs, tables and stuff) and other betting "systems" can be found here:

http://wizardofodds.com/gambling/betting-systems.html

[raiders72001]

Infinite money with infinite limits with infinite trials is a guaranteed winner.

[David]

Number Tries It Takes To Win / Profit
-----------------------------------------
1 ........................................ .(1-0) = 1
2 ........................................ .(2-1) = 1
4 ........................................ .(4-3) = 1
8 ........................................ .(8-7) = 1
16 .......................................( 16-15) = 1
.
.
1048576................................( 1048576-1048575) = 1


If I keep doubling up and have an unlimited bankroll I will always win 1 unit.

[tacomax]

It's also statistically impossible to turn a player advantage into a house advantage.

No, it's perfectly possible to turn a player advantage into a house advantage.

[natrass]

Original discussion?

Could a Donald Trump bankrupt a $100.000 casino easily?

Facts established, all but a 0.00003% chance that he would.

Fact established = all casinos know the risk from this and will not take the bets.

Real world = big roller can bankrupt small casino playing the martingale very very easily. (That is what we were talking about wasnt it?)

But, yes, the house has a 52.6/47.4 advantage in the rolls. I never disputed that.

[natrass]

No, it's perfectly possible to turn a player advantage into a house advantage.

How?

[Ganchrow]

Infinite money with infinite limits with infinite trials is a guaranteed winner.

Assuming no limit on either bet size or number of trials, the mathematically correct way to put this is: As a gambler's bankroll approaches infinity, the probability of his making a profit approaches 100%. However, the amount risked by the gambler also approaches infinity. Therefore, even in the limiting case of an infinite bankroll, the gambler's expected profit is nevertheless still negative.

[natrass]

Assuming no limit on either bet size or number of trials, the mathematically correct way to put this is: As a gambler's bankroll approaches infinity, the probability of his making a profit approaches 100%. However, the amount risked by the gambler also approaches infinity. Therefore, even in the limiting case of an infinite bankroll, the gambler's expected profit is nevertheless still negative.

Yes, but its not an infinite universe.

That fact alone is crucial.

So, to the question could a big roller bankrupt the bank of monte carlo playing the martingale ...

... we have agreed the answer is very much a yes havent we?

[Ganchrow]

Facts established, all but a 0.00003% chance that he would.

This is only a "fact" if the casino (whose entire stake is only $100,000) would tale a single bet as large as $4.2 billion. This is highly implausible.

Fact established = all casinos know the risk from this and will not take the bets.

But only because of their risk aversion. It would still be a profitable strategy for the casino on the average. A hypothetical risk neutral casino would always take the bets.

Real world = big roller can bankrupt small casino playing the martingale very very easily. (That is what we were talking about wasnt it?)

We were talking about two things:
1) Does the high roller have a postive expectancy?
Answer: No. The casino dikes, however.

2) Is it realistic to expect in the real world that a big roller could very easily bankrupt a small casino playing the Martingale?
Answer: No, not in the real world. Only in the fake world of risk neutral (or very nearly risk neutral) casinos. In the real world no casino would accept a single bet that many times larger than the value of its current assets. (Or indeed even a single bet even half the value of its current assets.)

[Ganchrow]

Congratulations to ganchrow for keeping cool throughout the thread - it helps when yhou know you're right, though.

More information on the martingale system (complete with graphs, tables and stuff) and other betting "systems" can be found here:

http://wizardofodds.com/gambling/betting-systems.html

Thanks, Taco. Great link, by the way.

[raiders72001]

Wizard of odds is the best numbers guy that I have ever seen. Two other posters that aren't here yet are Fezzik and WillRaceForFood.They are both actuaries and are also great numbers guys.

[tacomax]

How?

By playing a game with player input and playing badly. You might have favourable blackjack rules and have a player advantage of 0.5%. However, if you don't play the cards the right way then you can turn a player advantage into a house advantage.

[Ganchrow]

Yes, but its not an infinite universe.

That fact alone is crucial.

Huh?

So, to the question could a big roller bankrupt the bank of monte carlo playing the martingale ...

... we have agreed the answer is very much a yes havent we?

natrass, this is all very simple probability. I urge you to check out the the link provide by taco. If you still don't get ir all I can do is suggest you get an introductory text book on the subject. What you're arguing is nothing more than an extremely common fallacy addressed in countless many statistical and probabilitic texts. It's wrong, patently wrong, utterly wrong. Read up on it. That's about all I can say.

[natrass]

1. The basis of your argument was "even with unlimited stakes". Go check ...

2. I never argued that the player had an advantage at the table. there is a zero as we know.

3. As I have shown, you have a 0.00003% chance of being correct.

4. A big roller can easily bankrupt a casino playing the martingale.

Only in a fake world do you need a speadsheet to prove in an infinite universe the casino would win every 10 million times or whatever it was.

Original question ... do you still dispute that a big roller could bankrupt a casino playing the martingale when (as you stated) there was no limits? Yes or no.

I think you will run yourself into the ground here and still be looking at a 0.00003% chance.

[Ganchrow]

Another Martingale link: http://www.okthen.com/martingale/

[raiders72001]

However, if you don't play the cards the right way then you can turn a player advantage into a house advantage.

If you don't play the cards correctly then you aren't playing player advantage.


In reality I would never suggest playing a martingale system. Theoretically the martingale system is a 100% winning system.

If you don't believe me I will make at least 100 picks using the martingale system and will put up money as a bet.

[Ganchrow]

1. The basis of your argument was "even with unlimited stakes". Go check ...

2. I never argued that the player had an advantage at the table. there is a zero as we know.

3. As I have shown, you have a 0.00003% chance of being correct.

4. A big roller can easily bankrupt a casino playing the martingale.

Only in a fake world do you need a speadsheet to prove in an infinite universe the casino would win every 10 million times or whatever it was.

Original question ... do you still dispute that a big roller could bankrupt a casino playing the martingale when (as you stated) there was no limits? Yes or no.

I think you will run yourself into the ground here and still be looking at a 0.00003% chance.

With all due respect, my Friend, I've already answered each one of these claims at least a couple of times. Just read up on the Martingale in particular and probability in general.

[Ganchrow]

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

Nope. Just ask one of your buddies Fezzik, WillRaceForFood, or WizardofOdds.

If you don't believe me I will make at least 100 picks using the martingale system and will put up money as a bet.

In a heartbeat, but only if we can repeat this a large number times. While I do love profit, I am still certainly risk averse. That being said, however, would you really be ready, willing, and able to risk a million dollars to win my hundred?

[raiders72001]

Ganchro- What do you want to bet? What's the minimum and maximum amount of picks that I can make and I'll prove it to you.

[Ganchrow]

Ganchro- What do you want to bet? What's the minimum and maximum amount of picks that I can make and I'll prove it to you.

You first tell me the terms that you want.

[natrass]

By playing a game with player input and playing badly. You might have favourable blackjack rules and have a player advantage of 0.5%. However, if you don't play the cards the right way then you can turn a player advantage into a house advantage.

How is that relevant to the unlimited bankroll versus limited casino question?

Are you talking about bringing in the players ability to judge black or red here?

I am sorry ... how is it relevant to this?

[tacomax]

How is that relevant to the unlimited bankroll versus limited casino question?

Are you talking about bringing in the players ability to judge black or red here?

I am sorry ... how is it relevant to this?

Raiders said "It's also statistically impossible to turn a player advantage into a house advantage". I was just highlighting that this is not true.

He also thinks that "Theoretically the martingale system is a 100% winning system". I think the less said about this one the better.

[raiders72001]

You first tell me the terms that you want.

That I will win using the martingale system with an unlimited bankroll and limit. You can tell me the minimum and maximum amount of plays that I can make.