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Dannydoyle
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Quote:
On 2008-04-04 18:35, luvisi wrote:
Quote:
On 2008-03-30 20:41, Dannydoyle wrote:
My understanding is that if you get a casino that lets you take enough free odds bets, you can have a very slight advantage, (DO I MEAN SLIGHT!) over the casino.


Could you explain how this works? How large of an odds bet do you need to be able to make to gain an advantage? 100 times the line bet? 1000 times the line bet?

As far as I can tell, odds bets decrease the overall house percentage by increasing the denominator (average amount of each bet) while keeping the numerator constant (average house take on each bet). I see how arbitrarily large odds bets could make the house percentage arbitrarily small, but I don't see how any size of odds bets could make it go even the tiniest bit negative. What am I missing here?

Andru


For a complete explination, please reference Sklansky/Malmuth's Gambling for a Living, pages 166-169. For fear of being nit picked to death, I refuse. The formula and reference are there. Or PM me.

I will say this though, they do NOT use the term "free odds".
Danny Doyle
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<BR>In a time of universal deceit, telling the truth is a revolutionary act....George Orwell
JasonEngland
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Danny, not to nit-pick, but it's on p. 163-164, at least in my copy. Page 166 is a table about Keno trials. Page 168 begins a discussion on baccarat.

Secondly, Sklansky and Malmuth certainly don't mean that you would have a mathematical advantage at craps, only that you might be able to make a little money at the game by exploiting dealer errors on your strange dollar amounts bet behind the line.

They use the phrase "advantage in practice" to distinguish this from a genuine mathematical advantage. I don't put much stock in this attempt at making money and neither do they - the last sentence in that paragraph is "So we don't recommend [this idea]."

However, I do admire the fact that you dug this out and posted it. It's the kind of mathematical/gambling trivia question that I enjoy and I'd forgotten about this particular example.

I'll give you another:

In Beyond Counting, an excellent and advanced book on advantage play by James Grosjean, he mentions an interesting situation that occurs from time to time in certain craps games under some very special circumstances.

When these circumstances occur, the player or players can actually have a distinct advantage in the game of craps over the house for a very brief period of time.

Can you guess what it is?

I'll give you a few hints:

a. It is a genuine mathematical edge, but as I said, it only occurs under special circumstances that don't apply to all (or even most) craps games.

b. The craps games where this is applicable are run exactly like other casino craps games, with this one exception...and the exception is what provides the edge. The layout and game operation are identical to any craps game in Las Vegas or Atlantic City with this one exception.

c. Yes, these are legitimate casino-style craps games. Nothing illegal or underhanded about them.

Any guesses?

Jason
Eternal damnation awaits anyone who questions God's unconditional love. --Bill Hicks
Mr. Z
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Ooh I remember this but won't spoil it.
"...if you have to say you is, you ain't."--Jimmy Hoffa
JasonEngland
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Greak Marok,

I was traveling last week and couldn't access my copy of Allan Wilson's Casino Gambler's Guide until this evening.

Although I won't retype his entire argument here, the bulk of it is contained within these headings:
The Double-Up Breaks Even in a Fair Game
Stretching Out the Progression Has No Effect
Proof of the Double-up Fallacy in an Unfair Game
Stretching Out the Progression Makes Matters Worse!


All of these sections are bound between pages 237 - 241.

Although Wilson correctly identifies the table limits and non-infinite player bankrolls as reasons the Martingale fails to be a viable playing method in day-to-day casino play (this is on p. 237 as mentioned earlier by Andru), he goes on to demonstrate why the Martingale fails to win money (he uses doubling the player bank as an example but actually any increase in bankroll size works out the same) regardless of the actual size of the player's bankroll.

He does this first using a game of "fair" roulette in which the 0 and 00 have been removed and the player bets only on red/black.

In this situation, he demonstrates that the chances of doubling any bankroll are precisely balanced by the chances of losing everything. Starting with a 31 unit bankroll your chances of doubling before losing everything are 50/50. (This is to be expected since it's a 50/50 proposition to begin with.)

If you started with a bankroll of 1023 units, the specific numbers change but the formula remains essentially the same and the answer is the same also: your chances of doubling your bankroll are 50/50 in a fair game using the Martingale.

If you had a billion units your chances of doubling your bankroll using the Martingale would be: 50/50.

In other words, the Martingale is no better than a coin-flip when it comes to doubling your bankroll! Another way of looking at this is to realize that it simply does NOTHING.

Well, actually that isn't entirely accurate. It does do something. It redistributes your wins and losses. The Martingale provides a lot of tiny wins that are almost a certainty. But the infrequent catastrophic losses occur just often enough to make the whole thing a wash.

This is true regardless of table limits and regardless of your bankroll size (as long as it's finite).

And of course, all of the first part of Wilson's examination is predicated on a FAIR game. Once you start paying off at the actual casino payoff odds the Martingale's performance begins to perfectly match the age-old formula for how much money you'll win or lose at a given game in the long run: expectation times action.

In other words, at the pass line the Martingale will cause you to lose ~ 1.41% of all the money you put into action. At roulette, it'll cause you to lose 5.26%, etc.

In Edward Thorp's The Mathematics of Gambling on page 116, you find this statement, referring to a situation where a player has a certain chance of winning one unit versus losing everything on his eleventh spin.

Quote:
We are going to find out that the "house percentage advantage" on Red is not changed in the slightest by the doubling-up system. In fact, the disaster of the eleventh spin is exact compensation to the casino for the high chance the player has of winning $1 per cycle.


All italics emphasis is in the original quote.

Granted, Thorp mentions (as does most every other gambling author) the table limits and bankroll considerations. I've never disputed the reality that those things get involved in stopping Martingale players on a day-to-day basis. I'm just making the point (reporting it, really) that you don't actually need to consider those elements to prove that the Martingale fails as a winning system in the long run.

On page 32 of Practical Casino Math by Hannum and Cabot, we find this statement (after the obligatory comments about table limits and bankroll issues):

Quote:
While the probability [of a long sequence of losses] is relatively small, these losing streaks will sometimes occur and when they do, the money lost will more than compensate for the one-unit profits gained when the system "works".


Actually, as Wilson showed, the money lost will exactly compensate for the money won in a fair game, and will compensate and then some in an unfair game.

One last quote, this time from Richard Epstein's phenomenal The Theory of Gambling and Statistical Logic:

Quote:
No one [of the betting systems] can affect the mathematical expectation of the game when successive plays are mutually independent.


Hey, what do you know, we're right back to "the Martingale doesn't change your expectation." In a dead-even game like flipping a coin, your odds of winning with the Martingale are 50/50. In a game like roulette, you'll lose money at a rate exactly matched by your expectation (-5.26% for most bets) times your action. At craps it's -1.41% for pass and come bets.

Extract the essence of what Wilson, Epstein, and the others are saying and you get this:

The Martingale does nothing to your bottom line in the long run (it neither helps it nor hurts it), regardless of table limits or the size of your finite bankroll.


Jason
Eternal damnation awaits anyone who questions God's unconditional love. --Bill Hicks
Dannydoyle
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Quote:
On 2008-04-05 04:33, JasonEngland wrote:
Danny, not to nit-pick, but it's on p. 163-164, at least in my copy. Page 166 is a table about Keno trials. Page 168 begins a discussion on baccarat.

Secondly, Sklansky and Malmuth certainly don't mean that you would have a mathematical advantage at craps, only that you might be able to make a little money at the game by exploiting dealer errors on your strange dollar amounts bet behind the line.



If I have too I can scan my copy of the pages. It is the EXACT pages I said. I have the Second edition first printing September 1998. Page 164 is on Roulette. Thank you for asking in a civilized manner.

Here is the quote in question. Mr. Z can nit pick David if he likes.

"When you take 100x odds, (in deferance to Z he does not say "free odds) your disadvantage is so minuscule (about 1/`00 of 1 percent, even less if you are a don't better) as to be almost irrelevant. That does not mean you could start playing craps for a living. But the truth of the matter is if you made only pass, don't pass, come don't come bets and constantly took 100x odds you actually would have a small advantage in practice.

Now the next line is interesting. "This is true as long as you were willing to take the money when the dealer made a mistake in your favor and point it out when he made a mistake in his favor. If you are astute enough not to make any errors yourself and complicate matters by using odd amounts you would ALMOST certainly have the best of it when playing craps at one of those 100x odds places. (Capitals added by me for emphasis) Still, that edge would be very small and would involve giant swings. So we don't recomend it."

To me, just to clarify I am not a fan of a strategy which requires the dealer to make mistakes, and for you to make 0 for you to have an edge.

Mind you my whole point in the first post, before we got all high and mighty about verbage, was simply that it is possible to have a SLIGHT, and I emphasised SLIGHT advantage if you take the (free)odds bet at 100x. As it works out I was right, and if you google the stupid term it is there.

Oh and I have ego problems LOL.

It was more as Jason said one of those "fun facts".
Danny Doyle
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<BR>In a time of universal deceit, telling the truth is a revolutionary act....George Orwell
Dannydoyle
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Jason my only guess is "crapless craps" with 12 times odds and I know NOTHING of the game.

I don't know if Stupak even has the casino any more or if he does offers it on the floor.

This is also covered VERY briefly in "Getting the Best of it" by Sklansky.

Other than this I have no guess. I do not stand by the claim by the way LOL. As I said I know NOTHING about it. It is only my guess.
Danny Doyle
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gadfly3d
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Hey guys just a suggestion for those of you who don't want to do math. When the house has the edge the house has the edge. No magic or math tricks will change that.

Gil Scott
Dannydoyle
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Edit above.

2/100 of 1 percent, even less if you are a don't better.
Danny Doyle
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<BR>In a time of universal deceit, telling the truth is a revolutionary act....George Orwell
JasonEngland
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Danny,

I have a first edition, first printing of Gambling for a Living. That explains the page number difference.

The craps question I referred to involves craps games that have to close at a certain time. Consider a game on a cruise ship or riverboat that absolutely must close before crossing into state waters where gambling is illegal, or before docking (when gambling is illegal on the land).

In spots like this, the craps games were often closed by having the dealers/floorpersons announce: "Three more rolls!"

As soon as you hear this, it becomes favorable for you to start making come/passline bets. The reason is because if you establish a point and the three rolls expire, your pass/come bet is returned to you.

This allows you the benefits of the "front" half of the pass/come bet (where a 7 or 11 wins for you), but you don't have to buck the "rear" half of the bet (where after establishing a point the 7 out loses for you).

The positive player edges are small, but real.

Interesting trivia, nothing more.

Jason
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Dannydoyle
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I had NO Idea and was only on one of those cruises in Key Largo.

Interesting.
Danny Doyle
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<BR>In a time of universal deceit, telling the truth is a revolutionary act....George Orwell
The Great Marok
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Jason,

thanks for the info in your post and the interesting references. I'm not going to go back and quote myself, but I'm pretty sure that I said before that you are right in the case your bankroll has a limit, and that I've advised people not to use this system.

The thing about martingales in gambling is that someone (like the original poster in this thread) can mention a 'system' that at first glance looks perfectly logical and it seems to win money. Then you can ask the question of what's wrong with that system. Someone here (I think silverking) said that the problem is the same as for all the martingales, and that is that you come across either you personal bankroll limit or the table limits. Since no one mentioned any particular person, this would mean that it applies no matter who you are, and hence for any finite bankroll. And this is certainly the typical answer from the point of view of mathematics, when you're presented with a question of what's wrong with a martingale system - you don't have infinite capital. (See for example Rosenthal, p.78

Quote:

In words, with probability one we will gain $1 with this gambling policy, for any positive value of p, and thus "cheat fate". ...
... On the other hand, we may need to lose an arbitrarily large amount of money before we win our $1, so "infinite capital" is required to follow this gambling policy.



The quotation marks weren't added by me. Or Billingsley, p. 97

Quote:

...the gambler must have a patron of infinite wealth and generosity from whom to borrow and so must in effect have infinite capital.



or p. 106

Quote:

Infinite capital is again required.



Note that in the first quote I provided from Billingsley he is not talking directly about martingales but more general systems of which martingales is a type, so I've also included the second quote which is directly about a martingale.)

You objected to the answer that personal bankroll limits/ table limits are the real reason that systems like this fail to win money. But then you gave a proof that if you do have a bankroll limit you will fail to win money - which is saying the same thing that the other person said, plus the proof. There are many proofs that a martingale system fails in real life, but they all either have to use some sort of a stopping event that prevents you from placing your next bet (which is what Allan Wilson does) or to use the bounded convergence theorem, which is the mathematically more elegant method (ibid.).

As a summary, I finally think that we all agree here - any martingale system with unfair odds will fail to win money on average in real life.
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