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

SBR Founder Join Date: 9/7/2005

2. Originally Posted by natrass
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.

Originally Posted by natrass
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.

Originally Posted by natrass
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.

SBR Founder Join Date: 8/28/2005

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

SBR Founder Join Date: 7/21/2005

4. Originally Posted by Mudcat
From what I have read, Ganchrow is 100% correct on every single point here.
But natrass is better looking.

SBR Founder Join Date: 8/28/2005

5. Originally Posted by Mudcat
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?

SBR Founder Join Date: 9/14/2005

6. Originally Posted by natrass
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) .

SBR Founder Join Date: 8/28/2005

7. Originally Posted by ganchrow
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.

SBR Founder Join Date: 9/14/2005

8. 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.

SBR Founder Join Date: 8/10/2005

9. Originally Posted by raiders72001
It's also statistically impossible to turn a player advantage into a house advantage.
I wish Id thought of that!!

SBR Founder Join Date: 9/14/2005

10. Thanks natrass

SBR Founder Join Date: 8/10/2005

11. Originally Posted by natrass
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:
Originally Posted by ganchrow
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.

SBR Founder Join Date: 8/28/2005

12. Originally Posted by jjgold
Casinos have limits only because of MArtingale system
100% incorrect.

SBR Founder Join Date: 8/28/2005

13. 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

SBR Founder Join Date: 8/10/2005

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

SBR Founder Join Date: 8/10/2005

15. 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.

SBR Founder Join Date: 8/11/2005

16. Originally Posted by raiders72001
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.

SBR Founder Join Date: 8/10/2005

17. 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.

SBR Founder Join Date: 9/14/2005

18. Originally Posted by tacomax
No, it's perfectly possible to turn a player advantage into a house advantage.
How?

SBR Founder Join Date: 9/14/2005

19. Originally Posted by raiders72001
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.

SBR Founder Join Date: 8/28/2005

20. Originally Posted by ganchrow
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?

SBR Founder Join Date: 9/14/2005

21. Originally Posted by natrass
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.

Originally Posted by natrass
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.

Originally Posted by natrass
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.)

SBR Founder Join Date: 8/28/2005

22. Originally Posted by 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
Thanks, Taco. Great link, by the way.

SBR Founder Join Date: 8/28/2005

23. 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.

SBR Founder Join Date: 8/10/2005

24. Originally Posted by natrass
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.

SBR Founder Join Date: 8/10/2005

25. Originally Posted by natrass
Yes, but its not an infinite universe.

That fact alone is crucial.
Huh?

Originally Posted by natrass
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.

SBR Founder Join Date: 8/28/2005

26. 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.

SBR Founder Join Date: 9/14/2005

SBR Founder Join Date: 8/28/2005

28. 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.

SBR Founder Join Date: 8/10/2005

29. Originally Posted by 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.
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.

SBR Founder Join Date: 8/28/2005

30. Originally Posted by raiders72001
Theoretically the martingale system is a 100% winning system..

Originally Posted by raiders72001
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?

SBR Founder Join Date: 8/28/2005

31. 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.

SBR Founder Join Date: 8/10/2005

32. Originally Posted by 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.
You first tell me the terms that you want.

SBR Founder Join Date: 8/28/2005

33. Originally Posted by tacomax
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?

SBR Founder Join Date: 9/14/2005

34. Originally Posted by natrass
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.

SBR Founder Join Date: 8/10/2005

35. 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.

SBR Founder Join Date: 8/10/2005

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