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I played 12 1/2 hours of $3-$6 Omaha High-Low Split last night, netting an incredibly massive profit of $8. That was just enough to pay for my meals at the casino.

It's funny how I can get more ticked off at sessions like that than at sessions where I actually lose money.


heihojin
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Aww, don't feel bad. Think of the poor guy who had to go home to his wife and explain how he lost the eight bucks! ;-)

- Jim
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I played 12 1/2 hours of $3-$6 Omaha High-Low Split last night, netting an incredibly massive profit of $8. That was just enough to pay for my meals at the casino.

It's funny how I can get more ticked off at sessions like that than at sessions where I actually lose money.
- heihojin


This may be a manifestation of the same psychological condition referred to in an book I recently read. It concerned sports handicapping. The author stated that 'the man who bets small, hopes to lose.'

If he loses, he gets to "reward" himself by thinking, 'yeah, I knew there was something wrong with that game. It just didn't feel right. Boy, am I glad I only put the $11 down instead of $1100! I dodged the bullet on that one.' He lost but he's happy.

If he wins, he has to punish himself because of the realization that he called it right but screwed up on his money management. 'I was right, I hit it. Damn, the game broke just the way I thought it would. Why didn't I bet the dime on it? Why did I let that stinking injury report scare me off? Damn, damn, damn, damn, damn!!!' He won but he's unhappy.

You said you spent 12 1/2 hours. Your mention of the "1/2" is significant. Who cares 12, 12 1/2? Obviously, you do. Your cost/benefit ratio did you in. 'ALL that time and I walk away with a stinkin' 8 bucks, sheeesh.'

If you had lost 8 bucks, you would have found consolation in 'so I lost, it happens. At least I lost only 8 bucks. Win big, lose small - that's the way the winners do it. I win big, I lose small, I heihojin - winner!'

Hope this helps,
Raken
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This may be a manifestation of the same psychological condition referred to in an book I recently read. It concerned sports handicapping. The author stated that 'the man who bets small, hopes to lose.'

I'm not sure if you're referring to the table limit ($3-$6) or not. My reasons for playing that particular limit of Omaha High-Low Split are really pretty simple: Omaha is my weakest game. Although my bankroll is large enough to consistently play up to $6-$12 Omaha (according to my estimates), I deliberately choose to gain more experience at Omaha by playing in the smaller limits ($3-$6 and $4-$8). Once I have tracked enough time, and determined that I am indeed beating the game at the smaller limits, only then will I make moves to higher limits.

Deliberately choosing to play smaller limits doesn't shield me from the risk of large losses, though. I've lost over $400 in four hours from playing $4-$8 Texas Hold'em before. Fortunately, such catastrophic results are few and far between.


heihojin
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I'm not sure if you're referring to the table limit ($3-$6) or not - heihojin

No, I was referring to your comment:

It's funny how I can get more ticked off at sessions like that than at sessions where I actually lose money.

I provided my comments as a possible explanation for why you would be more "ticked off" at a profit than at a loss.

Every gambler loses bets. What matters is that your play and money mgmt are good. My money mgmt plan last football season was:

1. Make my usual 'lunch money' bets of 20-50 on games that ought to win.
2. Make my usual 'real bets' of 100-300 on the games that I felt confident about.
3. Try a three team parlay of a special nature. Select three games during the year that I felt were stone cold solid. Run a 500-1000-2000 bet sequence on those three games. That would net me 3500 (175% return on my season bankroll).

I selected the games and hit all three with the smallest cover being 15 pts.

So why am I ticked off? Because I didn't jump on those games with both feet. I didn't step up after the first win and bet the dimes on the next two. I'm still angry with myself a year later.

The point I was trying to make in the previous post was a win does not necessarily make you happy and a loss make you sad. It depends on how you played versus the circumstances and your personal goals.

I'm sure you've had nights when you played well but didn't walk away with a lot because the cards were simply not falling for you. But you probably didn't feel too bad because you knew you played smart and tough.

That's the key to beating the gambling game. Play smart and tough.

Raken
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My money mgmt plan last football season was...

This is the first time I've heard you mention that you are a sports bettor, too. Cool - I wasn't aware of that.

Your psychological explanation could be right. I find that twelve hours is about the longest I can play in one sitting, before getting tired. What was really frustrating, though, was that up until the last two hours, I was up over $100, and then POOF! It all vanished in that last two hours.

I did need to play that session, though, because I gleaned some important insights about Omaha. So maybe the 12 1/2 hours wasn't all for naught.


heihojin
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This is the first time I've heard you mention that you are a sports bettor, too. - heihojin

I am primarily, almost exclusively, a sports bettor now. I started out my gambling with blackjack in Atlantic City in the late 70's. It was the only game I knew back then. I've since tried different table games and enjoy craps the most.

In the early 80's I started betting pro football. I did well with that. I did poorly with college hoops for reasons I did not understand then but understand now. Pro hoops went well. Then I started college football in the mid 90's.

Last year I focused on college football and hung up a win % that blew my mind. Unfortunately, my money mgmt sucked big time. This year I am going at the books hard. There's going to be blood on the streets before this season is over and it's not going to be mine.

What was really frustrating, though, was that up until the last two hours, I was up over $100,

Do you play for a set time or until you've won a certain amount of money? What is your money goal?

I did need to play that session, though, because I gleaned some important insights about Omaha.

Do you keep a dairy of what you have learned and do you read poker books for insights? I've found as I've gotten older, the handicapping factors that used to come to mind automatically no longer do so. A checklist for me to review as I handicap a game is helpful.

Aside: If anyone knows of some boards for college football handicapping, I would really appreciate some links. Thanks.

Raken
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Do you play for a set time or until you've won a certain amount of money? What is your money goal?

Neither. I play until I either have other commitments, or until I am not playing well (such as when I get tired), or until the game is no longer any good. I don't set a money goal for any session.

Do you keep a dairy of what you have learned and do you read poker books for insights?

I don't keep a diary beyond the tracking of my results by the half-hour. Keeping a diary is a pretty good idea, though, and a number of top players suggest keeping one.

I have read many of the books on the market. There is, however, a great deal of misinformation in print about Poker strategy.


heihojin
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I just got back from 4 days in Las Vegas, where I met up with a group of 14 Fools from various boards. It was a social gathering, and excluding the time I spent teaching others to play craps, I was only able to spend a little over 14 hours at the tables. I started with a $500 stake which I never upped, and came home with $620 above that. All this really came on 3 long rolls, of course, spread over the 14 hours. One of these rolls came on Sunday afternoon, when my buddy kept if going for 15 minutes. That seemed long, but the guy next to him had been there since midnight before. We were still doing fine until I popped one of the die off the table, then we all packed it in, including the midnight guy.

I found a little casino that allowed $2 minimums at the craps table, with 100X odds. Still, me and another guy were the only ones betting high odds bets. Everyone else was playing regular. I don't get that. Playing straight odds like that for high stakes, I don't understand how the casino makes money if people bet right. I guess they do, because people don't bet right.

I don't think there is a better game in town than 100X odds. I can leave when I want, but the casino has to play. Play long enough, the worst I do is even, but get one good win and I am up at least $200. Where is the gamble?

Rick
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Rick,

Play long enough, the worst I do is even, but get one good win and I am up at least $200. Where is the gamble?

My understanding of odds is that your pass bet (or whatever) is a "buy-in" for the even-money you get on your odds bet. The house gets its 1.4something percent on your pass bet in the long run no matter what odds you play -- that's the gamble.

Obviously, you want to play as high odds as possible to minimize the house's overall percentage. But you couldn't play 100x odds -- $200 on the table you described -- right away because your $500 stake could have been blown in no time. So eventually you'll be ahead enough to risk those 100x odds -- but then you're risking an equal probability of losing $200 as winning it!

I dunno, I like odds too because you can bring the house percent way down, but unless you've got a gigunda bankroll and can go for the 100x play each time, it seems to me playing odds are just as much (or almost as much) of a gamble as other casino games.

- Jim
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I started with a $500 stake which I never upped, and came home with $620 above that.

Cool - congrats on a good session. I'm looking forward to going to Vegas again, which will probably be sometime in October.

Still, me and another guy were the only ones betting high odds bets. Everyone else was playing regular. I don't get that. Playing straight odds like that for high stakes, I don't understand how the casino makes money if people bet right. I guess they do, because people don't bet right.

You're right in that the casino makes more from people not taking full advantage of the odds bets. The casino still makes its money though, because the pass and come line bets all have negative expectation for the player - even with 100x odds.

In which casino did you play, by the way?


heihojin
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Heyho said:
You're right in that the casino makes more from people not taking full advantage of the odds bets. The casino still makes its money though, because the pass and come line bets all have negative expectation for the player - even with 100x odds.

Miniscule, really. They take 1.4% of a 1% bet, so the risk is fractional. Bet $2, back it with $200 and you are as close to even as you can get, without quite getting there. Since I have the option to quit at any time, you need to factor that in too. I don't see this as negative expectation.

In which casino did you play, by the way?

Many. I stayed at Harrah's, also played at Mirage, Casino Royale (the 100X odds place) Flamingo, Bally's, Rio, Frontier, Venutian (what a place!), Stardust, Circus Circus, Barbary Coast, a few others I can't recall now.

Rick
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Since I have the option to quit at any time, you need to factor that in too. I don't see this as negative expectation.

The expectation of the game has nothing to do with whether or not you have the choice of playing. By backing up your pass line and come line bets with maximum odds, you are reducing the house edge as much as you possibly can, but you are still playing with a negative expectation.

Not that there's anything WRONG with that...just don't quit your day job. :-)


heihojin
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The expectation of the game has nothing to do with whether or not you have the choice of playing. By backing up your pass line and come line bets with maximum odds, you are reducing the house edge as much as you possibly can, but you are still playing with a negative expectation.

I think we've been down this road before. Hehehe...

Rick
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I stayed at Harrah's, also played at Mirage, Casino Royale (the 100X odds place) Flamingo, Bally's, Rio, Frontier, Venutian (what a place!), Stardust, Circus Circus, Barbary Coast, a few others I can't recall now.
- Rick


If you had gone downtown to play, you could probably have found a 50 cent table at the El Cortez. The Casino Royale used to have a 50 cent game a few years ago when I lived in Vegas. It was a good place to experiment. The problem was you usually had a lot of rookies and jerks playing there. My favorite place was the Desert Inn. Very serious, very professional game. Almost all the shooters were guys 40-70 who knew what they were doing.

Did you notice any differences in the way the dice reacted at the different casinos? I shot several times at Treasure Island but did not like the bounce the dice took. I don't know if it was the composition of the dice or the table surface that was odd. I do know those little puppies bounced real high off the surface even when gently thrown.

Raken
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Miniscule, really. They take 1.4% of a 1% bet, so the risk is fractional. Bet $2, back it with $200 and you are as close to even as you can get, without quite getting there. Since I have the option to quit at any time, you need to factor that in too. I don't see this as negative expectation.

I assume this is old ground on this board (never been here before) based on your(Rick's) comment a few posts up, so I won't ramble on in opposition. But I may have to go back and try and find the earlier discussion, because I'm can't imagine what debate there could be over heijohin's point.

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But I may have to go back and try and find the earlier discussion, because I'm can't imagine what debate there could be over heijohin's point.

I'll shorten your search. The question is whether "negative expectation" is a valid concept for anything other than, say, a million rolls. It's not, of course, it's only valid of the rolls generate a normal distrubution, and on a craps table, it's unlikely to happen for anything under, say, 100 rolls.

That's been my whole point all the way through this discussion, and I'm not sure if I am not making my point clearly, or people are too stuck to the idea of looking at things from the casino perspective, where tables run 24/7. With 100X odds, I will always get even (minus my 1% if I lose it), but since I can walk after I go up, it does not fit the definition of negative expectation. A wrench is thrown into this plan if I can't use a large bankroll to support my waiting to get even, but assuming I have this bankroll, or assuming I will have the occasional loss, this isn't a scenario where the definition of negative expectation fits.

Rick
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(never been here before) - howardroark

Then I invite you to check out posts 152-4 wherein Raken presents the opportunity to test your clever mind by attempting to discover a betting system for baccarat using numbers provided by one Lyle Stuart.

You can start here:
http://boards.fool.com/Message.asp?mid=13103948

When Jim Korenthal gets a little time he promises to run a computer simulation to test what Stuart claims is a mathematically valid system to win at baccarat.

Good luck,
Raken
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When Jim Korenthal gets a little time he promises to run a computer simulation to test what Stuart claims is a mathematically valid system to win at baccarat.

Get in line. Jim's got numbers to run for me!



rnik



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RAKEN,

When Jim Korenthal gets a little time he promises to...

LOL, I haven't forgotten. We're in crash development mode at the office right now. Today (Saturday) and tomorrow I'm taking a much-needed rest and it's back to the grind on Monday. I'll get a round tuit at some point, though. :-)

- Jim
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rnik,

Ditto. ;-) Gotta stop making those promises online. Well, at least I can weasel out of the ones I make in email. Or can I? Heheeeeeeeeeeeeeeee!

- Jim (looking forward to two days of <*>NOTHING<*>!)
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The question is whether "negative expectation" is a valid concept for anything other than, say, a million rolls. It's not, of course, it's only valid of the rolls generate a normal distrubution, and on a craps table, it's unlikely to happen for anything under, say, 100 rolls.

?

Tell me you're kidding. Expected outcomes do not derive validity from the number of trials. Trials impact the distribution of results around the expected outcome, but the expected outcome remains the same, with or without normal distributions or the central limit theorem. If I gave you a jar of 51 green marbles and 49 red marbles, green I win and red you win, and asked you to pick once at even odds, how would you decide whether to play? Is the distribution of marbles (expected outcome) irrelevant for a single trial? Mind if I add a few more green then?

That's been my whole point all the way through this discussion, and I'm not sure if I am not making my point clearly, or people are too stuck to the idea of looking at things from the casino perspective, where tables run 24/7. With 100X odds, I will always get even (minus my 1% if I lose it), but since I can walk after I go up, it does not fit the definition of negative expectation. A wrench is thrown into this plan if I can't use a large bankroll to support my waiting to get even, but assuming I have this bankroll, or assuming I will have the occasional loss, this isn't a scenario where the definition of negative expectation fits.

Neither the perspective nor the ability to walk away is relevant. If you walk into MGM an play one roll of craps you are more likely to lose than win. On that roll. Just because the variance is enormous, doesn't mean the odds shift. Your option to walk away from the table is equally unhelpful, except that walking away from a negative expectation game is always economically beneficial. The only exception would be if we lived in the land of ininity - inifinite bank rols, bets and time - and then Martingale like progression would allow the ability to walk away to matter. Since we don't, Martingale is bogus, and so is the idea that the option to cease trials impacts expected ex ante outcome.

And, Raken, you cannot beat baccarat (a negative expectation game) by counting sequences. I don't know anything about what this Lyle Stuart thinks, but I'm certain it's mathematically inaccurate if it relies on sequences of bank, player or tie. The only way to get a positive expectation in baccarat is to perfectly count cards, to perform combinatorial analysis with the capacity of a department of defense computer, all while finding the one game in the country that charges only 4% on bank wins.
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HR said:
If I gave you a jar of 51 green marbles and 49 red marbles, green I win and red you win, and asked you to pick once at even odds, how would you decide whether to play? Is the distribution of marbles (expected outcome) irrelevant for a single trial? Mind if I add a few more green then?

As I said, my knowledge of statistics comes from my experiences in quantum mechanics, the real statistical machine of the universe. In this world, an expectation value, is what the average will be in a huge number of trials. What's a huge number? It varies, but it has to be enought to regenerate the distribution used to calculate the expectation value. For example, if I want to guess the speed of one of the molecules buzzing around my flask, the expectation value does me no good. If I measure the speeds of all the molecules, the average will be the expectation value. Maybe your definition is different.

That said, I will tell you I have no idea whether I will pick a green marble or a red one from your jar. And it doesn't matter to me if you do add more greens, I still won't play unless I feel lucky. The fact that I will pick 2 more greens than reds if I go all the way through your jar has nothing at all to do with each individual pick. Right?

So, if I am at a table with 100X odds, I have the option of "picking through all of the marbles" if I get down, I do know that the average of my wins will approach the expectation value if I keep going and generate enough rolls to approach the statistical limit. That's to my advantage. I *know* I will get there, I just keep rolling, and I can always keep going. It's also to my advantage if a collection of wins come up before a collection of losses. Here too, if I keep going, I will give back those wins, but since I can walk away, I can keep my wins, and it's obviously to my advantage. Right?

If I am missing something in practice, please correct me.

Rick
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Raken, you cannot beat baccarat (a negative expectation game) by counting sequences... I'm certain it's mathematically inaccurate if it relies on sequences of bank, player or tie...

The only way to get a positive expectation in baccarat is to perfectly count cards, to perform combinatorial analysis with the capacity of a department of defense computer... HR


I try to keep these discussions simple due to the enormous variation in the ways people use words and concepts. So please bear with me as I set a few ground rules for this thread.

1. I do not claim you can beat baccarat. Stuart presents numbers which he claims are accurate. IF his numbers are accurate AND his 95 shoes are not an aberration, then his method is mathematically valid.

2. Please, please, please let us not return to that swamp of probability theory that we went through on the amzn board with beating roulette. If you want to assign terms like positive and negative expectation and central limit theorm in your own mind, find. But, like any disgusting sexual practices you may favor, please keep them to yourself, not on this board, not on this thread, thank you.

3. You do not need any cipher crunching Cray from the NSA to work his system. I did not even need my $2.98 Staples calculator. I did not even bother with pencil and paper when I went back just now to check the method. I did the numbers in my head, it's that simple. Just look at the numbers presented in post 152 and see if you can determine how to beat baccarat, assuming the numbers hold for other shoes.

4. The entire system revolves around the single question, 'what do you do when either 3 player or 3 banks wins occur in a row.

http://boards.fool.com/Message.asp?mid=13103948&sort=postdate

Raken
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Thanks for your response. My qualification, which will soon become obvious, is that I am not a physicist.

That said, I will tell you I have no idea whether I will pick a green marble or a red one from your jar. And it doesn't matter to me if you do add more greens, I still won't play unless I feel lucky. The fact that I will pick 2 more greens than reds if I go all the way through your jar has nothing at all to do with each individual pick. Right?

It has everything to do with each individual pick. Your extended distribution - say 100 picks - is nothing but a compilation of individual picks. There's no emergent property at the hundredth or millionth picks that changes the nature of the constitutent expected outcomes. Each individual pick is a losing bet. What would you do if I kept adding green balls? Say I was willing to give up my green ball fetish and unload my entire collection of 341 trillion green balls, against your 49 red balls. Would you ignore that distribution in making your decision on whether to play a single trial, or defer to whether you felt lucky?

Why do you hit the brakes when you see a red light? Regardless of whether you see the world deterministically, we know that no driver can be certain that brakes will function properly at any given time. The probability is something like 99.999...% that John Doe's brakes will result in the car stopping. Does this estimate impact your behavior in a single trial, or is it meaningless to apply brakes unless you have a series of applications to reduce your expected variance to a normal distribution of outcomes? Should you only apply the brakes if you feel lucky, and otherwise turn on the radio?

As I said, my knowledge of statistics comes from my experiences in quantum mechanics, the real statistical machine of the universe. In this world, an expectation value, is what the average will be in a huge number of trials. What's a huge number? It varies, but it has to be enought to regenerate the distribution used to calculate the expectation value.

I'm not sure I understand your application of quantum indeterminism to single trial verus multi-trial events that don't take place on a quantum scale. Why would you use Heisenberg uncertainty to say that a single roll of a die can be conceptually differentiated from thousands of rolls? I've never heard a physicist apply quantum probability to something at the level of classical probability (i.e. gambling). Classical probability measures our ignorance, while quantum probability purports to measure inherent uncertainty. To the extent that there is inherent uncertainty in the the outcome of a single die roll, it is no different from the inherent uncertainty in million of such rolls, since neither take place at the supposed qunatum level. Using quantum physics to differentiate the two circumstances seems odd.

I don't know if God plays dice or not, but I do know that to the extent that sub-atomic particles play dice, they impart identical affects on non-quantum scale single trials as non-quantum scale multiple trials.

So, if I am at a table with 100X odds, I have the option of "picking through all of the marbles" if I get down, I do know that the average of my wins will approach the expectation value if I keep going and generate enough rolls to approach the statistical limit. That's to my advantage. I *know* I will get there, I just keep rolling, and I can always keep going. It's also to my advantage if a collection of wins come up before a collection of losses. Here too, if I keep going, I will give back those wins, but since I can walk away, I can keep my wins, and it's obviously to my advantage. Right?

Actually, you don't know you will get there, since you can't play to infinity. Additionally, your probabilities for the entire data set change after each roll. The antithesis of this, is known as the Gambler's Fallacy: the idea that past independent trials impact future results so that the entire set will equal original probability. Once you have a result, you have new information, and you expected outcome for a set that includes that new information is forever changed, while your expected outcome for future events is always the same.

Say you walk up to the craps table and win your first ten rolls. Then I walk up next to you to play. Who has a better chance of winning the next roll? Neither one of us. The minute you win or lose a roll, it's pocketed forever. So you beat the odds for those ten rolls for all time, and the probability for your entire night in Vegas is forever changed to incorporate that new information. Your future rolls and probabilities remain unaffected, so your ability to quit does you no good. Sure, you can now walk away and say you beat a negative expectation game. But you can only say that ex post, and an ex post advantage is no advantage at all.

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I am going to try an suppress my long winded nature and follow your rules.

Just look at the numbers presented in post 152 and see if you can determine how to beat baccarat, assuming the numbers hold for other shoes.

If the numbers posted in 152 held for other shoes, there would be multiple ways to beat baccarat. For example, I could watch 95 shoes until there was a sequence of 13. Then, knowing that there were no sequences of 13-18, and only one of 19 I could bet six consecutive times on the sequence, and once against it. 7-0.

BTW, the numbers don't seem to add up, since the sequences indicate 6842 rolls resulting in a bank/player win, while the raw numbers say there were 6832.

Either way, it's all based on the premise that those sequential results will persist in the future, which is absurd. Future sequences will follow the probably inherent in the odds of the game, not the results of a set of 95 shoes.

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Just a question for HowardR:

Do you know what 100X odds means? If you don't play craps, this is all esoteric, and I'd like to stay focused on the game.

I also want to say something about your discussion of quantum mechanics and I will tomorrow when I have no time. It's important though, you mention Heisenberg, and I never did. Heisenberg is a cosnequence of the physics, it's a physical principle that introduces a set amount of "error" into very specific conditions, two sets of measurables that have commuting operators. Heisenberg does not always apply, and in most cases does not. Statistics in microscopic systems always do, however, and that is why I used that to talk about expectation value. Expectation value is a defined quantity, and is really the average value when a set of measurements gives a distribution that was used to calculate the value. 10 measurements will not produce an average that is the expectation value, just like ten rolls of the dice will not produce the average predicted. That is the basis for my argument that expecation values in small numbers of trials is unimportant.

More tomorrow. Thanks for your comments.

Rick
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BTW, the numbers don't seem to add up, since the sequences indicate 6842 rolls resulting in a bank/player win, while the raw numbers say there were 6832. - HR

Sorry, my typo. The raw numbers should be:
bank - 3539 (not 3529)
player - 3303
tie - 698 (ignore for counting sequences)

If the numbers posted in 152 held for other shoes, there would be multiple ways to beat baccarat. For example, I could watch 95 shoes until there was a sequence of 13. Then, knowing that there were no sequences of 13-18, and only one of 19 I could bet six consecutive times on the sequence, and once against it. 7-0.

Whoa, I did not mean to imply that this exact pattern of sequences would repeat every 95 shoes. That would, indeed, be as you stated, "absurd." Rather, I would expect some similar distribution of sequences based on the probabilities inherent in the rules of the game.

Let us look at the sequences you selected, 13-19. There were 4 seq of 12 and 1 seq of 19. You said bet the seq 6 times for and 1 time against. You rightfully consider that absurd. But, look at this bet:

When there are 12 consecutive bank or player wins, bet the next hand the opposite of the sequence.

That is the bet I would make. I would win 4 times and lose 1 time. Net win 3 units minus comm. This is Stuart's method. He does it after a 3 seq. He says 'after 3 of one side, bet that side the next hand.' The reason is that there are more seq of more than 3 than of 3's. It works best on the bank side according to the numbers in the book. But I have to check out a game on TV right now, so I will post them later.

In summary, just add up the number of sequences longer than any particular sequence and you have your bet for or against the seq continuing. That is, assuming that his numbers are both accurate and not an aberration.

Raken
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Do you know what 100X odds means? If you don't play craps, this is all esoteric, and I'd like to stay focused on the game.

I know what 100X odds is. In fact, I happened to be in Vegas (I don't go all that often) soon after the Horseshoe debuted 100X odds. I saw a guy take in more money that IPET spends on advertising backing the Pass Line at huge multiples. Now, I never backed at 100X, despite it being the optimal economic decision, because I don't play craps to win money. Craps is a negative expectation game, even with 100X odds (-0.02% in total), so when I do play, I do it with strict capital limits and lots of alcohol.

That is the basis for my argument that expecation values in small numbers of trials is unimportant.

I am willing to agree to disagree. But if you're ever in the Atlanta area, let me know, because I've got a jar full of green marbles with your name on it.

Whoa, I did not mean to imply that this exact pattern of sequences would repeat every 95 shoes. That would, indeed, be as you stated, "absurd." Rather, I would expect some similar distribution of sequences based on the probabilities inherent in the rules of the game.

Yeah, I figured that's what you meant, but I don't know how to respond to the larger point without invoking all those words that you specifically outlawed. If I did, I might say that you can calculate the odds of getting Stuart's results with a multinomial distribution (give or take a tiny bit). Because the trials are more or less independent, both the dispersion of hands (bank, player, tie) and sequences (1,2...n) will distribute around the expected values. The probability inherent in the game (bank-45.96%, player-44.62%, tie-9.52%), produces sequences that stem directly from their individual probabilities and thus - since they are not significantly correlated - if the individual games don't provide and advantage, the sequences don't either. It'd be tossing a coin 10,000 times and thinking you can benefit from the number of sequences of heads or tails, despite independent trials and a losing original expectation (assume a vig).

There's a reason casinos spend money on scorecards so players can record Bank, Player or Tie sequences in Baccarat, but don't for Blackjack players to record card counts.

I offer one more thing, because this applies to both discussions in this post. It's from a book that I highly recommend, "The Theory of Gambling and Statistcal Logic," by Richard Epstein:

Theorem II: No advantage accrues to the process of betting only on some subsequence of a number of independent repeated trials forming a complete sequence.

Corollary: No advantage in terms of mathematical expectation accrues to the gambler who possesses the option of discontinuing the game after each play.


Okay, I'll shutup now.



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HR said:
Craps is a negative expectation game, even with 100X odds (-0.02% in total), so when I do play, I do it with strict capital limits and lots of alcohol.

Yeah, I was going to get around to calculating that, thanks. I'll take -0.02%, and because of my ability to walk away, I still believe I will win over the course of my life, going once or twice a year.

And I agree about agreeing to disagree. It's important to me, though, that you know I do understand what you are saying about expectation value, and I am not claiming to have any evidence that the definition should be changed. I just don't think it works well as a predictor under certain conditions.

I guess the way I look at it, is that if I came to Atlanta 100s of times over the next 10 years, and I bet you $10 I'd pick a red marble (the 49 marble color) from your jar each time, I imagine you'd take that bet. I know I wouldn't, because I'd be doing it enough for stats to work. If I visited only once, would you be as confident? As I think you understand by now, I don't see these as similar betting oportunities, but I believe you do. Right?

Thanks again.

Rick
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As I think you understand by now, I don't see these as similar betting oportunities, but I believe you do. Right?

No! I completely agree that the number of trials makes a significant difference in the overall characteristics of the bet. But where we disagree, I think, is that I think they differ because of differing variances, and not differing expected outcomes! If you popped down to Atlanta and bet me a beer that you'd pick one of the 49 red in my 51G/49R jar, I would take the bet, because my expected outcome is positive, and because the massive variance in that trial is diversified by the rest of my "invested" capital (assuming I have more than $4.50 to my name). In finance academic lingo, the bet would have high idiosyncratic risk but a low market risk (actually, market risk would be zero, since there's no correlation between you picking marbles and the rest of my capital, unless you happen to be my boss).

But if you bet me everything I had, I wouldn't make the bet, because despite the positive expectation, that massive single trial variance (risk) would overtake the utility of the favorable odds (for me). Now, if you came down and wanted to bet everything I had on a single trial using my jar with 341 trillion green and 49 red, I would do it in a heartbeat, because my expected outcome is so high as to make even the high single trial variance favorable (to me).

The bet I would never make (unless I considered it paying for entertainment), however, is on picking one of the 49 red chips. Not for 1 trial or a billion trials. That's why I've never bought a lottery ticket.

If expected value did not apply to single trials, what advice would give this prisoner who is offered two guns by his captors with which he's got to play Russian Roulette. In the first gun 11 of 12 bullets fill the chamber. In the second, only 8 of 12 bullets are loaded. He only has to fire once, and he can go free if he survives. (Assume there's no trickery by the captors.) Pick a gun. Is expected outcome irrelevant for this single trial?

Sorry. I said I'd shut up. I will. I think. It's a sickness.
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HR said:
Sorry. I said I'd shut up. I will. I think. It's a sickness.

No! Now I think we are getting somewhere. So, how would you decide of the 0.02% loss at 100X odds is a reasonable bet (given variance and all that, I don't know those terms) since you have the ability to walk away at any time? Or do you only bet on things with a positive expectation? So if it were positive 0.02% would that make a difference? Isn't the variance so large it doesn't matter if there is a very slim preference for or against?

All this is about you the bettor, of course, not the casino. I fully understand they will always win. But maybe not against me.

Let's say the gun you mention has 72 chambers. If the doomed man had a choice between two guns, on with 3 bullets in the chamber and another with 4, would he really be that better off to pick the 3 bullet gun? If I did 10 tries with each gun, is it really a good bet to guess that the 4 bullet gun is safer? In a lot of tries, yes, but not in a few. If you were to pay me cash, lots of it, to use the 4 bullet gun rather than the 3 bullet gun, assuming I had to use one or the other, I would do it for the right amount. That's the key, what is the right amount?

The fact still remains, in nature's statistical machine, microscopic physics, if I want to guess the speed of an individual molecule picked from a million molecules, I would be just as likely to guess right picking the <average value + 1> as I would the <average
value>. In my language, the most likely value will equal the expectation value only after a huge number of samples. It's impossible to guess the most likely value correctly if I only pick 10 molecules. Expectation value is no help in picking the most likely result of a small number of trials. Is this what you mean by large variance? I think if I understood exactly what you mean by variance, I could talk about this better. Sorry about that.

Rick
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So, how would you decide of the 0.02% loss at 100X odds is a reasonable bet (given variance and all that, I don't know those terms) since you have the ability to walk away at any time? Or do you only bet on things with a positive expectation? So if it were positive 0.02% would that make a difference? Isn't the variance so large it doesn't matter if there is a very slim preference for or against?

You're right. We are getting somewhere. Knowing that expected value is relevant for a single trial, doesn't tell you how relevant it is. In fact, with an expected value close to zero (or even not so close), your single trial result is dominated by the second moment (volatility or variance) and not expected value (the first moment). In the case of a single -0.02% craps bet (assuming you could do it in a single trial, which is complicated a bit by the rules of craps), we don't need things like variance or standard deviation to make a decision. Those things are only used to condense information about entire distributions, but here, the distribution doesn't need to be condensed.

Betting $20, you either win $20 or lose $20 (simplifying craps again for the sake of the discussion). You have around 49.99% chance of the former and a 50.01% chance of the latter. That's it. That's all probability can tell you for a single trial. So, you are welcome to conclude that you would like to perform a single trial at those odds. It might be a "reasonable" decision for the gambler whose utility function was not risk averse. However, it would clearly be an inferior decision to the inverse single trial bet (the one made by the casino). Just because the difference in expected outcome is miniscule compared to the volatility, doesn't mean it is invalid or irrelevant. That becomes clear in the single trial case as expected value moves away from zero, and you are looking at a jar with a ratio of 341 trillion:49. In both cases, the rational choice is to pick the bet with the higher expected value, but it makes a much bigger difference in the second instance.

Sure, the casino might not win against you while still winning overall, and the volatility of your returns(luck) will dominate the expected value. The casino might also leave you with a -100% return (0 for 1), which it also won't achieve overall. Does the ability to walk away help you here? No! That's the same myth that supports the bogus Martingale progression betting systems. Why would the ability to walk away help you? It only helps you if you first buck the fractional odds against you and win. But it's not the walking away that helps you, it's the bucking the odds part! Whatever you do after that is independent of your past results. If your strategy is to continue playing until you're ahead, you are playing partial Martingale, but you do not have inifinite trials or inifinite capital, so for all times you win under this strategy, you will likely have big losses commensurate to those winnings plus some for the negative expectation.

Finally, it doesn't take all that many trips to casinos playing negative expectation games to create a 68% (1 Standard Deviation in a normal distribution) aggregate probability that your outcome will fall within a range that is completely negative. In other words, it doesn't take much for the first moment to dominate.

Let's say the gun you mention has 72 chambers. If the doomed man had a choice between two guns, on with 3 bullets in the chamber and another with 4, would he really be that better off to pick the 3 bullet gun? If I did 10 tries with each gun, is it really a good bet to guess that the 4 bullet gun is safer? In a lot of tries, yes, but not in a few. If you were to pay me cash, lots of it, to use the 4 bullet gun rather than the 3 bullet gun, assuming I had to use one or the other, I would do it for the right amount. That's the key, what is the right amount?

That's an interesting and complicated question, partly because it requires that you assign a monetary value to your life. But that isn't what we've been talking about. In my jar game, you had the choice to pick the positive or negative expectation for free! At the craps table, people pick the negative expectation for free, less entertainment and alcohol. If you are getting paid to pick the negative expectation, the expected outcome changes, and it's a wholly different question. For example, if MGM paid me $0.50 for every $100 I bet playing basic strategy BJ, my expectated value would be zero, no -0.5%.

Most numbers are “transcendental.” Very informally, this means that they lack a simple definition. Most numbers with names are not of this variety, so 2, Ö3, and 7/5 are not such numbers. Indeed, most people only know the names of one or two transcendental [number]s: the best known is p, the second is e. So many numbers are transcendental that if all the numbers were put in a barrel, it is good as certainty that the first number pulled out would be so. (In such a lottery always bet on the transcendental [number]s.)

Peter Borwein, Science (1994).

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Because the trials are more or less independent, both the dispersion of hands (bank, player, tie) and sequences (1,2...n) will distribute around the expected values. HR

That "distribution around the expected value" is exactly why I feel that betting on whether a sequence will end is a valid method.

The probability inherent in the game... produces sequences that stem directly from their individual probabilities and thus... if the individual games don't provide [an] advantage, the sequences don't either.

I disagree. The expectation for any result (eg bank) is independent of whether the trial follows 12 player wins or 12 bank wins. HOWEVER, if my study of 1,000,000 baccarat shoes tells me that only 20% of the times a bank seq hits 12 does it go beyond 12, then I am putting my money on player when I see 12 consecutive bank wins.

The house pays on results of trials, not mathematical expectations of trials. That is why I say if Stuart's numbers are accurate and not an aberration, then it is possible to overcome the negative expectation of the game of baccarat.

Theorem II: No advantage accrues to the process of betting only on some subsequence of a number of independent repeated trials forming a complete sequence.

Obviously, I disagree.

Corollary: No advantage in terms of mathematical expectation accrues to the gambler who possesses the option of discontinuing the game after each play.

Strawman argument. I am not trying gain an "advantage in terms of mathematical expectation." I am trying to overcome the negative expectation by good money mgmt and smart play. Rick the Trick's option of walking away from the table is extremely important. It's just like sports betting. The player decides which games (subsequences) and how much to bet. The house has to hang a number on every game. Advantage - player.

But if you're ever in the Atlanta area, let me know, because I've got a jar full of green marbles with your name on it.

Ummmm, could I get my name on that jar, too? I've only been to Atlanta on fly-through (Hartsfield ?). But, if you ever get up to Wash. DC, I would consider it an honor to take you to dinner and I would consider it a pleasure to whip your marble jar game between appetizer and entree.

I am willing to agree to disagree

Amen.

Raken
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The expectation for any result (eg bank) is independent of whether the trial follows 12 player wins or 12 bank wins. HOWEVER, if my study of 1,000,000 baccarat shoes tells me that only 20% of the times a bank seq hits 12 does it go beyond 12, then I am putting my money on player when I see 12 consecutive bank wins.

In any small sample there are patterns that don't represent the population, and if you look long enough you'll find them. However, then you have a multiple hypothesis problem in that you don't know whether 20% is real or just a likely outcome of being able to chose the best among a variety of strategies. Now, if you don't know the grand model that generates the population a small sample is the best you can get and you really have to take the data mining into account before you are able to judge the 20%. This is the typical problem we face in designing mechanical investing strategies. However, in this particular case when studying baccarat shoes we know the true population return generating model. That model implies independence between trials. Therefore, we can learn absolutely nothing from a small sample of trials. We know that any pattern we see is bogus. Howardroark is 100% right. Also, the right to walk away is worthless because the trials are independent.

By the way if you don't believe me collect another 1,000,000 trials and you'll see that the probability is not 20% I can't believe you are discussing this!

Datasnooper.
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Therefore, we can learn absolutely nothing from a small sample of trials. We know that any pattern we see is bogus. Howardroark is 100% right. Also, the right to walk away is worthless because the trials are independent.

Yeah, OK. Sure, way cool. Whatever. Statistics, semantics, probability theory - all very neat stuff. Yep, it sure do tickle my grey cells. But, it is really time to reallocate my neural networks to a subject of more immediate consequence - handicapping foo'ball.

So, I must excuse myself from this thread. If I find some of my old baccarat scorecards, I'll check them out to see if there are any bogus patterns we could examine. Until then, you might want to consider something Josh Billings wrote:

It is better to know nothing than to know what ain't so.

Raken
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AFter 5 trips to Vegas I have never noticed any difference in the dice used on the tables for the different hotels. I do know that I always win at T Island and Tam O Sheas, and lose at Monte Carlo like the worst sucker ever, however...

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