Roulette Theory

[Special K]

Originally posted by: alkemyst

Originally posted by: jman19

Originally posted by: alkemyst

Originally posted by: Special K
It may have worked for you, but I'm saying if you analyzed the probabilities associated with your strategy, I doubt the expected value of the winnings would be in your favor.

It sounds like another case of the gambler's fallacy to me - i.e. let's say you roll a dice 100 times and never roll a single 6. The gambler's fallacy would say "I haven't rolled a 6 in 100 rolls! That means I'm more likely to roll one in the future!"

I am not thinking you understand the way odds and probablities work.

Self ownage.

How do you figure? I know I am very right here.

to the other poster your chance to roll a 6 on a six sided dice is 1/6 yes, but the chances of getting a 6 in x number of rolls is not 1/6 at all.

I would think our members would understand basic statistics/probability a little better.

If one never hits a 6 on a 6 sided die in 100 rolls I would bet that die is fixed.

I was not talking about the probability of getting one six in X rolls. I was talking about the probability of getting a six on roll 101, given that the previous 100 rolls were not sixes. This probability is 1/6. Each roll of the die is an independent event.

And to say I don't understand probability:

Let A = probability of getting a 6 on roll 101
Let B = probability of not getting a 6 on rolls 1-100

Now P(A|B) = P(AB)/P(B)

P(AB) = (5/6)^100*(1/6)^1
P(B) = (5/6)^100

Therefore, P(A|B) = 1/6

To answer your other question - the rolling of exactly one six in 100 rolls is a binomial random variable with n = 100 and p = 1/6. Let X = number of sixes rolled. Now:

P(X = 1) = nCr(100,1)*(1/6)^1*(5/6)^99, which is approximately 0, as you said

I am not sure what about my reasoning is incorrect.

 

[alkemyst]

Originally posted by: Special K
I was not talking about the probability of getting one six in X rolls. I was talking about the probability of getting a six on roll 101, given that the previous 100 rolls were not sixes. This probability is 1/6. Each roll of the die is an independent event.

And to say I don't understand probability:

Let A = probability of getting a 6 on roll 101
Let B = probability of not getting a 6 on rolls 1-100

Now P(A|B) = P(AB)/P(B)

P(AB) = (5/6)^100*(1/6)^1
P(B) = (5/6)^100

Therefore, P(A|B) = 1/6

To answer your other question - the rolling of exactly one six in 100 rolls is a binomial random variable with n = 100 and p = 1/6. Let X = number of sixes rolled. Now:

P(X = 1) = nCr(100,1)*(1/6)^1*(5/6)^99, which is approximately 0, as you said

I am not sure what about my reasoning is incorrect.

That wasn't your statement though...

You stated 6 has not come up in 100 rolls and it would be wrong that it'd be more likely to roll one in the future.

for every x rolls your chances of getting a '6' improve if it has not happened yet.

The formula you'd want is 1 - (N-1/N)^R N= number of sides, R=number of rolls.

At roll 101 you'd be at over nine 9's probability.

On your second way of presenting the problem (after 100 rolls, what is the chance of getting a 6 on roll 101...then I believe that would be a simple 1/6 like rolling from scratch. There is no need to consider the previous 100 rolls. Odds in gambling don't work like that though. They work like you originally presented.

I am not sure how the odds work on guaranteeing only one roll of 6 comes up or that out of 100 rolls the chance of a 6 being hit on roll X....but those can be computed.

A lot of this is why statistics / gambling odds give people the wrong sense of their real chances.

This is why bet caps are usually placed, otherwise you just keep raising your bet each time to cover your previous losses and ensure a profit (given an unlimited wallet in theory)...you'd have to be extremely unlucky not to win.

This doesn't work for fixed prizes only ones that always score a payout higher than the bet amount.

 

[vital]

i tried this in yahoo blackjack and i end up always losing all my money

 

[Eeezee]

This really doesn't work. You have less than a 50% chance of getting black or red (due to 00). Play enough times and you will always lose money.

Statistically speaking, play an infinite number of times on just red/black and you'd break even if not for the 00. That's the kink in your plan.

Blackjack FTW

 

[gorcorps]

This theory blows... the odds are 50/50 every time, so you have the same chance of losing every single spin as you do hitting one.

 

[Special K]

Originally posted by: alkemyst

Originally posted by: Special K
I was not talking about the probability of getting one six in X rolls. I was talking about the probability of getting a six on roll 101, given that the previous 100 rolls were not sixes. This probability is 1/6. Each roll of the die is an independent event.

And to say I don't understand probability:

Let A = probability of getting a 6 on roll 101
Let B = probability of not getting a 6 on rolls 1-100

Now P(A|B) = P(AB)/P(B)

P(AB) = (5/6)^100*(1/6)^1
P(B) = (5/6)^100

Therefore, P(A|B) = 1/6

To answer your other question - the rolling of exactly one six in 100 rolls is a binomial random variable with n = 100 and p = 1/6. Let X = number of sixes rolled. Now:

P(X = 1) = nCr(100,1)*(1/6)^1*(5/6)^99, which is approximately 0, as you said

I am not sure what about my reasoning is incorrect.

That wasn't your statement though...

You stated 6 has not come up in 100 rolls and it would be wrong that it'd be more likely to roll one in the future.

for every x rolls your chances of getting a '6' improve if it has not happened yet.

The formula you'd want is 1 - (N-1/N)^R N= number of sides, R=number of rolls.

At roll 101 you'd be at over nine 9's probability.

On your second way of presenting the problem (after 100 rolls, what is the chance of getting a 6 on roll 101...then I believe that would be a simple 1/6 like rolling from scratch. There is no need to consider the previous 100 rolls. Odds in gambling don't work like that though. They work like you originally presented.

I am not sure how the odds work on guaranteeing only one roll of 6 comes up or that out of 100 rolls the chance of a 6 being hit on roll X....but those can be computed.

A lot of this is why statistics / gambling odds give people the wrong sense of their real chances.

This is why bet caps are usually placed, otherwise you just keep raising your bet each time to cover your previous losses and ensure a profit (given an unlimited wallet in theory)...you'd have to be extremely unlucky not to win.

This doesn't work for fixed prizes only ones that always score a payout higher than the bet amount.

I guess it depends on how you want to view the events. If you consider each die roll separately, then the outcome of the previous rolls have absolutely no bearing on the outcome of the next one. This is the situation I meant to describe.

On the other hand, if you take a fixed number of rolls, you can compute the probability of not rolling a six in any of them, and your formula was correct.

I guess we were just referring to different scenarios, although now I am confused - let's say a gambler wins if he rolls a 6, and loses otherwise. So he keeps rolling the die, hoping to get a 6. Let's say the first 20 rolls are not 6's. If we look at it the way I broke it down, then his probability of rolling a 6 on the 21st roll is 1/6, because each roll is independent. On the other hand, if we ask "what is the probability of not rolling any sixes in 21 rolls", the answer is (5/6)^21, or 0.0217.

Would anyone else like to comment?

 

[her209]

Here's a better gambling strategery. Every time you lose, bet 3x the original amount. Here how the math works out.

Bet amount $1 - Result Lose
Bet amount $3 - Result Lose
Bet amount $9 - Result Lose
Bet amount $27 - Result Lose
Bet amount $81 - Result Win!

$81 - ($27 - $9 - $3 - $1) = $41

w00t!

 

[spidey07]

All you math guys...

Have you ever gambled? Have you ever laid out a bet based on feel? Have you ever played?

It's fun to play with math, but call me a sucker again, you can feel it and react accordingly. Ever been around a hot craps table?

Honestly for those that are playing math...Have you EVER been at a hot craps table? If so, the what was the outcome?

 

[alkemyst]

Originally posted by: spidey07
All you math guys...

Have you ever gambled? Have you ever laid out a bet based on feel? Have you ever played?

It's fun to play with math, but call me a sucker again, you can feel it and react accordingly. Ever been around a hot craps table?

Honestly for those that are playing math...Have you EVER been at a hot craps table? If so, the what was the outcome?

Playing by feel usually wins out and screws up any math involved. It's the 'heat' that gets people throwing money at the table without a real hand....much like ebay when people bid up a $50 item new to $100 used.

It's the pros that use math to their advantage whether they are admitting it or not.

 

[hehatedme]

Originally posted by: Thorny

Originally posted by: Fritzo

Originally posted by: hehatedme

Originally posted by: Fritzo

Originally posted by: JC86
Actually, the dealer once told me the safest best in roullete is to bet 1-18, which has a 1-1 payoff and bet the 3rd 12 (which has a 2-1 payoff). Bet the same amounts on both bets and you've covered all the numbers on the table except the zeroes and 19-24. If you hit the numbers between 1-18, you break even and if you hit the 3rd 12, which is 25-36, you win the amount you bet since the payoff is 2-1 and you only lost the amount you bet on 1-18. You can of course, bet the other way around too and bet the 1st 12 and then 19-36. which would leave only 13-18 uncovered by your bets. Obviously, the dealer still has the edge because of 0 and 00 and the numbers not covered in the middle but your odds of losing are the lowest under this betting method. I've tried it myself and came away up nearly a thousand dollars betting $40 per round. By my rough count, I was able to break even or come out on top 5 out of six times. It took me all afternoon at the table to win the amount I did and for those seeking instant gratification, this isn't the way to go but if you want to play it safe, I don't know if there is anything safer than this method.

That's the idea actually. You place bets in zones that cover each other, and odds are your winnings will cover your losses. Also, play European wheels instead of American style. European wheels do not have a 00...only a single 0, so there's more black and red.

That strategy is no different than just picking red or black. Regardless of how you bet on a roulette table, its a fixed probability of winning and losing. Its also why over a lifetime's worth of gambling the casino will be up against any individual at least 3 standard deviations out.

Funny how I use this strategy and end up winning at least $500 everytime I go to Vegas. How about that.

I also use this method. 4 out of 5 times I come home with more than I started with, and thats after a night out on the town. There have been at least 5 times in the last couple of years that I ended up ahead over $1000, never have I ended up down over $500 for the night. I've never seen a european wheel though, everyone around here is american.

I'm not denying that you guys have won money, but that fact doesn't prove that the strategy is no less or more advantageous than simply betting on red or black, picking a number or many numbers, or any other bet on the roulette table (except betting 0,00,1,2,3: which does have an even lower edge). What your stratgey entails is just a more aggressive approach to the same outcome.

 

[alkemyst]

Originally posted by: her209
Here's a better gambling strategery. Every time you lose, bet 3x the original amount. Here how the math works out.

Bet amount $1 - Result Lose
Bet amount $3 - Result Lose
Bet amount $9 - Result Lose
Bet amount $27 - Result Lose
Bet amount $81 - Result Win!

$81 - ($27 - $9 - $3 - $1) = $41

w00t!

Been discussed already...doesn't work when the bet is capped.

 

[her209]

Originally posted by: alkemyst

Originally posted by: her209
Here's a better gambling strategery. Every time you lose, bet 3x the original amount. Here how the math works out.

Bet amount $1 - Result Lose
Bet amount $3 - Result Lose
Bet amount $9 - Result Lose
Bet amount $27 - Result Lose
Bet amount $81 - Result Win!

$81 - ($27 - $9 - $3 - $1) = $41

w00t!

Been discussed already...doesn't work when the bet is capped.

It was a facetious post.

 

[Special K]

Originally posted by: Thorny

Originally posted by: Fritzo

Originally posted by: hehatedme

Originally posted by: Fritzo

Originally posted by: JC86
Actually, the dealer once told me the safest best in roullete is to bet 1-18, which has a 1-1 payoff and bet the 3rd 12 (which has a 2-1 payoff). Bet the same amounts on both bets and you've covered all the numbers on the table except the zeroes and 19-24. If you hit the numbers between 1-18, you break even and if you hit the 3rd 12, which is 25-36, you win the amount you bet since the payoff is 2-1 and you only lost the amount you bet on 1-18. You can of course, bet the other way around too and bet the 1st 12 and then 19-36. which would leave only 13-18 uncovered by your bets. Obviously, the dealer still has the edge because of 0 and 00 and the numbers not covered in the middle but your odds of losing are the lowest under this betting method. I've tried it myself and came away up nearly a thousand dollars betting $40 per round. By my rough count, I was able to break even or come out on top 5 out of six times. It took me all afternoon at the table to win the amount I did and for those seeking instant gratification, this isn't the way to go but if you want to play it safe, I don't know if there is anything safer than this method.

That's the idea actually. You place bets in zones that cover each other, and odds are your winnings will cover your losses. Also, play European wheels instead of American style. European wheels do not have a 00...only a single 0, so there's more black and red.

That strategy is no different than just picking red or black. Regardless of how you bet on a roulette table, its a fixed probability of winning and losing. Its also why over a lifetime's worth of gambling the casino will be up against any individual at least 3 standard deviations out.

Funny how I use this strategy and end up winning at least $500 everytime I go to Vegas. How about that.

I also use this method. 4 out of 5 times I come home with more than I started with, and thats after a night out on the town. There have been at least 5 times in the last couple of years that I ended up ahead over $1000, never have I ended up down over $500 for the night. I've never seen a european wheel though, everyone around here is american.

Just because you have been able to win with this method does not mean the math is in your favor. The probability of hitting the jackpot on a slot machine is very low, yet someone will eventually win it.

 

[spidey07]

Originally posted by: alkemyst

Originally posted by: spidey07
All you math guys...

Have you ever gambled? Have you ever laid out a bet based on feel? Have you ever played?

It's fun to play with math, but call me a sucker again, you can feel it and react accordingly. Ever been around a hot craps table?

Honestly for those that are playing math...Have you EVER been at a hot craps table? If so, the what was the outcome?

Playing by feel usually wins out and screws up any math involved. It's the 'heat' that gets people throwing money at the table without a real hand....much like ebay when people bid up a $50 item new to $100 used.

It's the pros that use math to their advantage whether they are admitting it or not.

Sure, but I never said I was a pro. Gambling is a hobby of mine.

 

[jman19]

Originally posted by: alkemyst

Originally posted by: jman19

Originally posted by: alkemyst

Originally posted by: Special K
It may have worked for you, but I'm saying if you analyzed the probabilities associated with your strategy, I doubt the expected value of the winnings would be in your favor.

It sounds like another case of the gambler's fallacy to me - i.e. let's say you roll a dice 100 times and never roll a single 6. The gambler's fallacy would say "I haven't rolled a 6 in 100 rolls! That means I'm more likely to roll one in the future!"

I am not thinking you understand the way odds and probablities work.

Self ownage.

How do you figure? I know I am very right here.

to the other poster your chance to roll a 6 on a six sided dice is 1/6 yes, but the chances of getting a 6 in x number of rolls is not 1/6 at all.

I would think our members would understand basic statistics/probability a little better.

If one never hits a 6 on a 6 sided die in 100 rolls I would bet that die is fixed.

That's not what he said.

 

[alkemyst]

Originally posted by: her209
It was a facetious post.

I see, ...this was exactly what someone presents though when they think they beat the system ... heh.

 

[jman19]

Originally posted by: spidey07
All you math guys...

Have you ever gambled? Have you ever laid out a bet based on feel? Have you ever played?

It's fun to play with math, but call me a sucker again, you can feel it and react accordingly. Ever been around a hot craps table?

Honestly for those that are playing math...Have you EVER been at a hot craps table? If so, the what was the outcome?

In a limited number of games, the variability away from the true probability of an event can be rather large - that is the "heat" you are talking about. It's not some magical entity.

 

[alkemyst]

Originally posted by: spidey07

Originally posted by: alkemyst

Playing by feel usually wins out and screws up any math involved. It's the 'heat' that gets people throwing money at the table without a real hand....much like ebay when people bid up a $50 item new to $100 used.

It's the pros that use math to their advantage whether they are admitting it or not.

Sure, but I never said I was a pro. Gambling is a hobby of mine.

I was agreeing with what you stated. No matter how strict many think they are...the frenzy of a hot round does them in 9 times out of 10 .

 

[alkemyst]

Originally posted by: jman19
That's not what he said.

It sounds like another case of the gambler's fallacy to me - i.e. let's say you roll a dice 100 times and never roll a single 6. The gambler's fallacy would say "I haven't rolled a 6 in 100 rolls! That means I'm more likely to roll one in the future!"

That statement to me is saying your odds of getting a 6 in 100 rolls is no different than 101 rolls. In reality your odds get better each time. This question is fundamentally flawed as only in theory would you ever see someone NOT get at least one 6 in 100 rolls of a 6-sided die assuming no trickery is involved.

How would you do the math on this presentation?

 

[Special K]

Originally posted by: alkemyst

Originally posted by: jman19
That's not what he said.

It sounds like another case of the gambler's fallacy to me - i.e. let's say you roll a dice 100 times and never roll a single 6. The gambler's fallacy would say "I haven't rolled a 6 in 100 rolls! That means I'm more likely to roll one in the future!"

That statement to me is saying your odds of getting a 6 in 100 rolls is no different than 101 rolls. In reality your odds get better each time. This question is fundamentally flawed as only in theory would you ever see someone NOT get at least one 6 in 100 rolls of a 6-sided die assuming no trickery is involved.

How would you do the math on this presentation?

I chose the number 100 somewhat arbitrarily. It really doesn't matter which number you pick - my point was that the outcome of the next die roll is not influenced by the previous ones.

However, as I said in a previous post:

Originally posted by: Special K
I guess we were just referring to different scenarios, although now I am confused - let's say a gambler wins if he rolls a 6, and loses otherwise. So he keeps rolling the die, hoping to get a 6. Let's say the first 20 rolls are not 6's. If we look at it the way I broke it down, then his probability of rolling a 6 on the 21st roll is 1/6, because each roll is independent. On the other hand, if we ask "what is the probability of not rolling any sixes in 21 rolls", the answer is (5/6)^21, or 0.0217.

Would anyone else like to comment?

 

[spidey07]

Originally posted by: jman19

Originally posted by: spidey07
All you math guys...

Have you ever gambled? Have you ever laid out a bet based on feel? Have you ever played?

It's fun to play with math, but call me a sucker again, you can feel it and react accordingly. Ever been around a hot craps table?

Honestly for those that are playing math...Have you EVER been at a hot craps table? If so, the what was the outcome?

In a limited number of games, the variability away from the true probability of an event can be rather large - that is the "heat" you are talking about. It's not some magical entity.

So, what was your outcome on a hot craps table? Did you make thousands?

-edit-
Call me stupid, call me what you will. But I'll keep up this hobby of mine and have a good time doing it.

 

[preslove]

I saw a history channel or discovery channel show on a spanish math professor and his family who realized that roulette tables developed statistical tendencies because of the particular warping of their wheels. By analyzing the results of specific tables, the mathemetician could develop betting strategies that could beat the tables. He used it all around europe with his family, using the single 0 tables, making tons of $. He came to vegas and it was harder because of the 00, but it still worked, until casino watchdogs kicked them out and banned them.

 

[alkemyst]

Originally posted by: Special K

Originally posted by: alkemyst

Originally posted by: jman19
That's not what he said.

It sounds like another case of the gambler's fallacy to me - i.e. let's say you roll a dice 100 times and never roll a single 6. The gambler's fallacy would say "I haven't rolled a 6 in 100 rolls! That means I'm more likely to roll one in the future!"

That statement to me is saying your odds of getting a 6 in 100 rolls is no different than 101 rolls. In reality your odds get better each time. This question is fundamentally flawed as only in theory would you ever see someone NOT get at least one 6 in 100 rolls of a 6-sided die assuming no trickery is involved.

How would you do the math on this presentation?

I chose the number 100 somewhat arbitrarily. It really doesn't matter which number you pick - my point was that the outcome of the next die roll is not influenced by the previous ones.

However, as I said in a previous post:

Originally posted by: Special K
I guess we were just referring to different scenarios, although now I am confused - let's say a gambler wins if he rolls a 6, and loses otherwise. So he keeps rolling the die, hoping to get a 6. Let's say the first 20 rolls are not 6's. If we look at it the way I broke it down, then his probability of rolling a 6 on the 21st roll is 1/6, because each roll is independent. On the other hand, if we ask "what is the probability of not rolling any sixes in 21 rolls", the answer is (5/6)^21, or 0.0217.

Would anyone else like to comment?

I was replying to Jman to find out his take on it.

I don't know why you are now adding in the probability of not picking a 6...you are diluting your own question and making it overly complex.

The probability of not rolling a 6 in 21 rolls would be your 0.0217 result which would give about 98% probably to roll a 6 in 21 rolls.

If you really want to test it rolling a dice 21 times and recording the results over say 20+ times, 100 iterations at most; you should see close to this result. Use a real die and not a computer, many people mistakenly try to reproduce these questions in code, but computers don't really do random numbers so well with the methods most use.

There are some examples that work like this that are easily tested in a small group.

One of them is how many people have to be asked before two people in the room have the same birth month/day.

many will say 180ish...but in reality it's at 23 people you have the same odds of heads or tails...50% IIRC.

 

[alkemyst]

Originally posted by: preslove
I saw a history channel or discovery channel show on a spanish math professor and his family who realized that roulette tables developed statistical tendencies because of the particular warping of their wheels. By analyzing the results of specific tables, the mathemetician could develop betting strategies that could beat the tables. He used it all around europe with his family, using the single 0 tables, making tons of $. He came to vegas and it was harder because of the 00, but it still worked, until casino watchdogs kicked them out and banned them.

This is why even with lotteries they change the balls time to time.

The physical devices tend to add their own variables to the odds.

 

[Ns1]

Originally posted by: alkemyst

Originally posted by: preslove
I saw a history channel or discovery channel show on a spanish math professor and his family who realized that roulette tables developed statistical tendencies because of the particular warping of their wheels. By analyzing the results of specific tables, the mathemetician could develop betting strategies that could beat the tables. He used it all around europe with his family, using the single 0 tables, making tons of $. He came to vegas and it was harder because of the 00, but it still worked, until casino watchdogs kicked them out and banned them.

This is why even with lotteries they change the balls time to time.

The physical devices tend to add their own variables to the odds.

in the same history channel special, they claimed the casinos pwned them by changing the tops. the oldest guy had a heart attack IIRC