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The Roulette Wheel (probability) question


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#41 of 76 OFFLINE   Jeff Gatie

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Posted February 08 2005 - 08:50 AM

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One thing that absolutely galls me is the fact that Vegas can outlaw card counting in Blackjack. Counting cards isn't cheating, anymore than know probabilities in poker.


Vegas casinos (or any other casino) do not "outlaw" card counting. As long as you are not caught, you can count all day long. However, since a Casino is a private business and no one has a "right" to be there, you can be asked to leave and/or be banned for any reason the management wants. They do this in a very professional manner (compared to the old days), often giving a free dinner and room if the counter just stops gambling. This is what happened to some of the MIT team. The MIT team was never arrested or prosecuted for anything and legend has it there is one or another version of the MIT team at work right now (the TV special blacked out the face of a few of the interviewed team members).

#42 of 76 OFFLINE   Greg*go

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Posted February 08 2005 - 09:17 AM

The answer the Casinos have to card counters is to increase the number of cards teh counters have to count.

Apparently A.C. had single deck blackjack tables for a while, until they lost a law suit with a card counter. Now they all have at least 7 decks
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#43 of 76 OFFLINE   Chris Derby

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Posted February 08 2005 - 10:33 AM

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The MIT team used an elaborate scheme that involved in-place counters that played normally but signaled to spotters when a shoe was "hot".


Don't forget to mention that they would have teams that sat at most or all of the spots at the table. Each team member was a "champion" card counter.

Here is a link to the wired article:

http://www.wired.com...9/vegas_pr.html
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#44 of 76 OFFLINE   Lew Crippen

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Posted February 08 2005 - 10:38 AM

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Anyone see "Las Vegas" on TV last night? They had a guy win a lot on Roulette (up to around $4 million before they figured out what was happening). The writers tried to explain the scam by the guy putting bets on 4 "sectors" of the board AFTER the ball was in play, and the guy had an accomplice to help with triangulation, throw in an offsite PC doing the number crunching, and a cell phone to tell him which sector to bet, you get a guy winning on a roulette table. (this was glossed over rather quickly, so I may have some of the details wrong)

Of course, much was just sloppy writing, but I guess it might be possible to predict the outcome of the ball given certain factors that could be measured. Mike (the resident guru) said it'd take some heavy computing power to get the right sector for each tumble of the ball around the wheel.
Aside from the fact that the timing necessary for this to work would involve instant computing and betting (I don’t really think that you can get bets down after the ball is in play), Chaos Theory would seem to much make this kind of prediction not possible (chris mentions the bounce—caused by raised diamonds on the wheel).

Put briefly, the ability for computers to predict the outcome based on the initial vectors, is deterministic. A deterministic system might be thought of as something like Newtonian mechanics, (why we can get to the moon). However the fly in the ointment here is that (so far) no one has been able to actually prove the stability of the solar system.

Chaos Theory has to do with the effects of a butterfly in Brazil causing a toranado in Oklahoma. Chaotic systems are typically so complex, that, though they in fact might be deterministic, but (nearly) impossible to predict. This has to do with our inability to find a variable that has a ‘repetition of values’ as the system changes.

In simple terms, this basically means that if one drop of water hits an edge it will continue on either to one side or the other—but the next drop may or may not follow the same direction.

It cannot be predicted.

In terms of a roulette wheel, with the very many number of diamonds (and also the ridges of the slots themselves) produce a system for which it would not be possible to predict the outcome at all, much less in a very limited time.

In terms of CSI, much of their investigation is based on deterministic outcomes, some of them, likely outcomes that are not predictable. This does not lessen my enjoyment of the show.
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#45 of 76 OFFLINE   Greg_R

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Posted February 08 2005 - 11:06 AM

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If you have already flipped a coin 9 times and all 9 times it comes up heads, then the probability of the 10th time being heads is still 50/50. But, if you have yet to flip the coin, the probability of coming up with heads 10 times in a row is extremely low.
Another way to look at it is that the probability of 10 heads in a row occuring is the same as HTHTHTHTHT occuring with a single coin (in that exact order). Note that this is totally different than flipping 10 coins at the same time and seeing a result or flipping a coin 9 times and then (attempting to) predict the outcome of the 10th flip.

Quote:
It cannot be predicted.
Of course you can't predict exactly. However, computer models can reasonably guess which sector the ball will land in and improve your chances of winning. This can tilt the odds in your favor (enough to win). The episode of Las Vegas made it appear that the guy was winning every hand. In real life, he'd win slightly more than 50% of the time (thus ensuring that he'd make money as long as he kept playing). Also, you wouldn't need a lot of computer power for this method... a look-up table of ball speed decay to wheel position (pre calculated or determined) would be all you'd need. Of course, casinos look for these types of cheating methods and devices.

#46 of 76 OFFLINE   Jeff Gatie

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Posted February 08 2005 - 11:18 AM

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In terms of CSI, much of their investigation is based on deterministic outcomes, some of them, likely outcomes that are not predictable. This does not lessen my enjoyment of the show.


Lew, I feel the same way. Ever since I saw CSI:Miami blow up a low res photo taken from a traffic camera to view the reflection of a perp off the lens of the eyball of a pedestrian crossing nearby, I have ceased to even look at the science/technology in use and just go for the ride. It is not possible to blow up a 4x4 pixel eyeball and get a hi res photo of a reflection in the lens, just as it is not possible to predict a roulette wheel (due to chaos theory and the butterfly effect, just as you explained).

Quote:
The answer the Casinos have to card counters is to increase the number of cards teh counters have to count.

Apparently A.C. had single deck blackjack tables for a while, until they lost a law suit with a card counter. Now they all have at least 7 decks


It is not really the amount of decks in the shoe, it is the frequency of shuffling into the shoe. The MIT team was so good they were able to count the entire shoe, no matter how many decks there were, and signal a "hot shoe" when the shoe was starting to run out. Casinos can fight this by reshuffling before the shoe is out, but many dealers do not do this because it interupts the game and pisses off the players who think their hot hand would have been next.

#47 of 76 OFFLINE   Lew Crippen

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Posted February 09 2005 - 02:58 AM

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Also, you wouldn't need a lot of computer power for this method... a look-up table of ball speed decay to wheel position (pre calculated or determined) would be all you'd need. Of course, casinos look for these types of cheating methods and devices.

It is much more complex than that Greg. For starters (and just off the top of my head), since you believe this to be a deterministic system, you need be able to accurately measure the ‘initial conditions’. These initial conditions are many more than the two you cite: you need the speed (and exact point in its rotation when the ball entered the system, of the roulette wheel (it varies every spin), the speed (actually the vector) of the ball and the way the ball bounces when it hits the raised diamonds on the wheel (which will completely change the vector of the ball). These variables (and many others) won’t fit in a ‘simple’ look up table. The speed of the ball and the speed of the wheel are not nearly enough. Very precise starting points for the wheel must be instantly determined (how would a look-up table translate the pictorial information into the wheel’s starting position (taken when the ball entered the system). This does not even take into account things that seem small, but which would drastically affect the outcome, like the ball bouncing when it hits the wheel on its initial entry. Put another way, the measurements of the ball must include not only the speed and direction (vector) in two dimensions, but must account for the angle that the ball hits the wheel (or the third dimension as well). Since we have a human spinning the wheel and tossing the ball, it varies every time.

Not only that, the measurements need to be taken accurately and immediately. And, as you know (I noticed that you are an engineer), a there is a core principle of science that you cannot make, even in a laboratory with controlled conditions, exact measurements. All measurements have a degree of uncertainty. Now it may be true that a measurement can be small enough for a particular, practical purpose, but I would suggest that in this case it is not possible with current devices—most especially those that would be available via some poorly placed (for measurement purposes) in a casino.

I did not go into Chaos Theory as to why you can’t make accurate enough measurements, but if you are really interested, you might check out What is Chaos. This is all descriptive and very easy to understand.

For a bit more check out: Chaos Theory and Fractal Phenomena . The second paper is only about 40 pages and can be easily understood even without much of a math background (though it helps to know the calculus if you really want to follow his reasoning).
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#48 of 76 OFFLINE   Jeff Gatie

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Posted February 09 2005 - 04:57 AM

Lew is correct. Three dimensional vectors require some sophisticated measuring devices, certainly not ones that can be smuggled into a casino. This premise (excluding the fact the human factor adds chaos to the system), plus the given fact that a person is never allowed to place a bet after the ball is in motion, makes this CSI moment about as probable as the hi res picture of a reflection off the eyeball of a pedestrian in a traffic camera, which is to say not possible at all.

Anyone looking to CSI for an example of current science would have about as much insight into the subject as a person viewing Star Wars. Even the pattern recognition of fingerprints is a little over the top, given the computing power needed and the database required for a search.

#49 of 76 OFFLINE   AjayM

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Posted February 09 2005 - 09:29 AM

It may not be a deterministic system, but look at the odds on the table. There's what, 38 spots on the wheel and the payoff is 35 to 1. You have to eliminate 3 spots on the table to put bets down in order to come out even. Winning a few bucks a spin isn't going to make you rich, but I bet it's at least "technically possible" using the right computing equipment.

Granted I don't think any ultra-portable computing equipment exists that can do those types of calculations so fast, let alone tell you which spots to put bets down before they call no more bets. Next you're going to spend a lot of time and money on building this device to do this, and what is the best you can hope for in terms of winnings before the casino catches you using this device?

#50 of 76 OFFLINE   Jeff Gatie

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Posted February 09 2005 - 10:43 AM

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Granted I don't think any ultra-portable computing equipment exists that can do those types of calculations so fast, let alone tell you which spots to put bets down before they call no more bets.


As I said above, there are no devices that can analyze the 3-d vector (direction and velocity) of the ball at the time of release, never mind computing equipment that can do the impossible (due to chaos theory) non-linear analysis that is required to eliminate even a few spots. A roulette wheel is certified by the state gaming commision to adhere to very strict analysis of its randomness. A random event is by definition unpredictable.

Also, the "analysis" of simply measuring the 3-d input vector while not taking into account the thousand of other inputs into the system (temperature, humidity, air pressure, altitude, sweat on the hand that throws the ball, imperfections in the ball itself, air movement, friction on the wheel, etc, etc, etc) is akin to predicting the weather in New York by observing butterfly wings in China (i.e. small, infinitessimal variations in any input(s) to a complex system increase randomness exponentially), which is far worse than predicting the weather by normal means.

#51 of 76 OFFLINE   Greg*go

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Posted February 11 2005 - 02:41 PM

Ahh, it took me a couple days, but here's the pic that can easily prove your thoery shot to shit. Notice that in the last 14 rolls were all the same color.

This happens fairly often. The only reason we took a picture of this table's outcomes is becuase a friend of ours lost most of his money during this unfortunate turn of luck and we like reminding him of it...

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#52 of 76 OFFLINE   george kaplan

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Posted February 11 2005 - 06:39 PM

here's the pic that can easily prove your thoery shot to shit. Notice that in the last 14 rolls were all the same color.

This happens fairly often.
Sorry to be dense, but...

Which theory does this shoot down?

How can you tell the last 14 rolls were all the same color? In that picture it looks to me like there were a couple of greens in there. I don't see 14 of one color in a row.
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#53 of 76 OFFLINE   Jeff_CusBlues

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Posted February 12 2005 - 12:48 AM

This is very interesting. I want to interject to make sure everyone has the statistical terms correct. Odds are defined as Chances Favoring/Chances Not Favoring. Probability is defined as Chances Favoring/(Chances Favoring + Chances Not Favoring). The Odds of a heads result on any coin flip are 1 to 1. The probability of a heads coming up is .5 or 50%. If you use odds to determine your chance of winning, please come and bet at my house. I will cover all your bets. In the craps example, people always believe they are on equal footing with the house because the house compensates you for riskier bets by giving you better odds i.e paying off 2-1 for a point of 4 or 10, 3-2 for a point of 5 or 9 and 6-5 for a point of 6 or 8. The fact is, the probability of hitting a 4 on any roll is 8.3% (91.7% prob. of loss), a 5 on any roll 11.1%(88.9% prob. of loss) and a 6 on any roll 13.9% (86.1% prob. of loss). This doesn't even take into account the risk you took to get the privilege of making a come bet. You definitely are not being fully compensated for your risk as many craps people will tell you. If you buy the bets, the odds are even lower, but the probability is the same. Don't get me wrong though, craps is a fun game and if you don't mind the speed which you win or lose, you can have a great time. I play this game often, but never delude myself into thinking that it is the game that pays back for your risk. When determining gambling risk, odds are for suckers...use probabilities.

#54 of 76 OFFLINE   george kaplan

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Posted February 12 2005 - 01:17 AM

I'm no expert on craps, but can't you bet for or against whoever's rolling the die?
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#55 of 76 OFFLINE   Jeff_CusBlues

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Posted February 12 2005 - 01:19 AM

Oops. After rethinking my post, I found I made a huge error in my craps probabilities. I made the mistake of including non-7 rolls as losers when trying to make a "point". The probability of wining a 4 point is 33% (67% prob. of loss), 5 point is 40% (60% prob. of loss) and 6 point is 45.5% (54.5 % of loss). The probabilities are higher, but you still are not being compensated for your risk...hence the name gambling. Sorry for the confusion.

#56 of 76 OFFLINE   Jeff_CusBlues

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Posted February 12 2005 - 01:25 AM

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I'm no expert on craps, but can't you bet for or against whoever's rolling the die?


You can make opposite bets Come / Don't Come, etc. but right now, I can't remember how these bets are played and never play them myself (not saying they are wrong, just not my preference). If somebody else understands these bets, I'll let them figure the probabilities (not the odds).

#57 of 76 OFFLINE   george kaplan

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Posted February 12 2005 - 04:42 AM

You can make opposite bets Come / Don't Come, etc. but right now, I can't remember how these bets are played and never play them myself (not saying they are wrong, just not my preference). If somebody else understands these bets, I'll let them figure the probabilities (not the odds).
Well I'm sure I'm oversimplifying this, but if the odds of a roller 'winning' are not 50/50, then if you could bet for or against his winning, then wouldn't you just bet whichever way has the better odds? I realize that casinos probably do something to prevent this, but in the floating crap games, you see people betting both ways, and I don't understand why there wouldn't be a winning strategy to betting there (leaving aside things like loaded dice).
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#58 of 76 OFFLINE   Cees Alons

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Posted February 12 2005 - 06:45 AM

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I realize that casinos probably do something to prevent this
They do: they don't pay you enough if you win.

There's another term you need to define: expectation. It's the probability to win on a given bet times your gain if you do. In roulette your expectation on a bet of $37 is $36.

In your example (I'm not familiar with that game) if the odds of one case are less than 50/50, then either they can make it certain that the other case is less than 50/50 too (by introducing another possible outcome), or they can simply pay less than twice your wager in that case.


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#59 of 76 OFFLINE   george kaplan

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Posted February 12 2005 - 09:46 AM

expectation. It's the probability to win on a given bet times your gain if you do. In roulette your expectation on a bet of $37 is $36.
Actually the expected value is (amount you get if you win)*Prob(win)-(amount you're out if you lose)*Prob(loss).
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#60 of 76 OFFLINE   george kaplan

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Posted February 12 2005 - 09:52 AM

Again, I have no familiarity with how Vegas deals with craps (I fully understand that they set the odds to favor the house, I just don't know the details), but when a bunch of soldiers or mafia guys get together and start throwing the dice, and throwing down bets on a shooter which someone else covers, doesn't someone (either the guy betting on the shooter or against the shooter) have a positive expected value on their bet? I mean it's got to be a zero sum game, and if there's no casino taking a portion of that, and it's just a straight bet between two people, that zero sum game means that one has an advantage, unless the odds are set somehow to be completely 50/50. Or am I missing something about a "friendly" crap game (as opposed to a Vegas one)?
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