Simulations

Wizard of Odds,

Thanks for the great site. Being a statistical analyst who is ignorant about real gambling, and being in Las Vegas for the weekend, I really appreciated your discussion of craps, the recursion required to estimate the probabilities, and the confirmation by simulation. What tools do you use for the simulations?

Wizard de la ADs,

Bless you for banning blinking ads!
(I'll try to reach you on the mortgage site.)

Many Thanks

I don't think there's any recursion or scientific method required to calculate probabilities in craps. There are two dice with six sides. The throws of the dice and the outcome are considered two random events, one for each dice. Therefore a total of seven should occur 6 times out of 36 throws because there are six ways to make a seven with two dice.

The results and the probabilities are purely statistical in nature. Standard deviations, variances, etc are approximated using the binomial (Normal) and Poisson approximations, whose theorems have come out and have been proven centuries ago with calculus.

I write my own simulations in C++. I get asked a lot of there is off the shelf software you can buy to test systems. There is none that I know of.

I also agree about blinking ads. You'll never see any on this site either.

Wizard,

I've been studying your analysis of long runs in

You state: The following table shows the probability of being in any of the four possible states in craps before the nth roll. The states are defined as follows:

State 1 = Come out roll
State 2 = Point of 4 or 10
State 3 = Point of 5 or 9
State 4 = Point of 6 or 8

The probabilities are recursive. Let p(x,r) represent the probability of being in state x before roll r. Based on simple dice probabilities, p(x,r) can be expressed... .

Can you add the constraint of a $2,000 bank roll and the best strategy in Casino Royale. What is the distribution of money I could expect to leave with?

Quote: hml48

Can you add the constraint of a $2,000 bank roll and the best strategy in Casino Royale. What is the distribution of money I could expect to leave with?

Before you can calculate the answer you're looking for, you need to answer a few questions:

1) How will you determine when to stop playing? For example, will you play a set amount of time, # rolls, # come bets or will you set win/loss limits?

2) What size bets do you want to make?

3) Do you want to play RIGHT or WRONG (i.e., with or against the shooter).

You may also be interested in this post where I ask a similar question and presented my own betting strategy for craps at Casino Royale.

DK,

Quote: dk

Quote: hml48

Can you add the constraint of a $2,000 bank roll and the best strategy in Casino Royale. What is the distribution of money I could expect to leave with?

Before you can calculate the answer you're looking for, you need to answer a few questions:

1) How will you determine when to stop playing? For example, will you play a set amount of time, # rolls, # come bets or will you set win/loss limits?

2) What size bets do you want to make?

3) Do you want to play RIGHT or WRONG (i.e., with or against the shooter).

***

1)Stop when busted or at $5,000 or above.
2)$1 or $2 at pass and $20 or $40 at point.
3)For the sake of the best odds lets say against the shooter.

Now here as real newbie question: What is laying odds versus buying odds as mentioned in the Craps Faq?

I will look at your other post.

Thanks

I estimate that your outcome distribution will be approximately:

75% lose $2,000
25% win $3,000

This is assuming $3 Don't Pass bets with max odds.

However, I also estimate that it will take you on average about a week of non-stop play to win or lose that much, so my numbers seem suspect, even to me.

Anyone have a better ruin calculator that is set up to take into account the uneven payouts that occur in craps?