How does this apply to the game of roulette?

Quote:EvenBob"Conditional probability is the probability of some event A, given the occurrence of some other event B."

How does this apply to the game of roulette?

I suppose you could ask a problem like this:

What is the probability that last number was 23, given that it was red? The general formula for the answer would be pr(red and 23)/pr(red) = (1/38)/(18/38) = 1/18.

Quote:WizardI suppose you could ask a problem like this:

Empirical probability estimates probabilities from experience and observation. Empirical means: 'Relying on experience or observation alone without due regard for system and theory.' Empirical Probability of an event is an estimate that the event will happen based on collecting data. It is based specifically on direct observations. I'm wondering if this and conditional probability can be applied to roulette in picking the next outcome for the even chances.

Quote:EvenBobEmpirical probability estimates probabilities from experience and observation. Empirical means: 'Relying on experience or observation alone without due regard for system and theory.' Empirical Probability of an event is an estimate that the event will happen based on collecting data. It is based specifically on direct observations. I'm wondering if this and conditional probability can be applied to roulette in picking the next outcome for the even chances.

You would need to generate a hypothesis before going out and collecting your data, and the sample size large enough to prove your hypothesis is so large that it wouldn't be worth your time. Moreover, unless your hypothesis is that the wheel is sufficiently random, it's likely to be disproven anyway.

Quote:SolidAUYou would need to generate a hypothesis before going out and collecting your data, and the sample size large enough to prove your hypothesis is so large that it wouldn't be worth your time. Moreover, unless your hypothesis is that the wheel is sufficiently random, it's likely to be disproven anyway.

"Empirical probability estimates probabilities from experience and observation. Empirical means: 'Relying on experience or observation alone without due regard for system and theory."

My Vegas friend claims to win at roulette using experience and observation, I'm trying to figure out how he does it. Intuitive Probability is used as well.

Quote:dwheatleyIntuitive Probability? Um... no.

Intuitive Probability is a legitimate branch of probability science, books have been written about it.

But, in Roulette, you know EXACTLY what the odds of the ball landing on a particular number are (1/38). And it has NOTHING to do with what past balls have done.

Have you ever read any of those books about intuitive probability? Here are some questions that are in mine (M. Gardner, The Colossal Book of Short Puzzles and Problems, W. W. Norton & Company, 2006)

Which situation is more likely after four bridge hands have been dealt: you and your partner hold all the clubs or you and your partner have no clubs? (A game of bridge is played by two pairs of players, with players on a team sitting opposite each other) [Gardner, p. 39].

A secretary types four letters to four people and addresses the four envelopes. If she inserts the letters at random, each in a different envelope, what is the probability that exactly three letters will go into the right envelope? [Gardner, p. 39].

A pencil with pentagonal cross-section has a maker's logo imprinted on one of its five faces. If the pencil is rolled on the table, what is probability that it stops with the logo facing up? [Winkler, p. 1].

(saved on typing and used the examples available at http://www.cut-the-knot.org/Probability/IntuitiveProbability.shtml#Gardner)

I highly recommend the book. It's fun, and presents a variable degree of difficulty. I used my copy for in-flight amusement for about 6 months before I exhausted the interesting problems.

Intuitive probability is the logical sense that keeps a person from falling for a trick question. That doesn't really apply to Roulette in any way that I can see.

You never did answer the question about your friend's betting amount. Does he just increase his bet when he loses? That is a very simple way to ensure that the majority of sessions are winning ones (with some big losing sessions).

*EDIT* I just noticed that the 3rd example from the website was from a different book. Here is the full cite for that question: P. Winkler, Mathematical Mind-Benders, A K Peters, 2007