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## Craps probability tree

Statistically over thousands of rolls the outcomes will come to the figures above but in an individual game session the results can and will vary widely.

The following table shows each possible total, the net return, the probability of throwing that total, and the average return.There are 4 ways to get a five (1-4, 2-3, 3-2, 4-1) so the probability of getting a five is 4/36.We are then going to record the result of the first roll as "Win "Lose or "Point" in the table where it says "Result of first roll".The fundamental counting principle tells us there are 6*636 ways to roll two dice, all of them equally likely if the dice are fair.So for example while the odds of rolling Snake Eyes (1 and 1) are 1 in 36 this does not means that in 36 rolls you will get one win.

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In the following table the specific number of ways to throw each total and the probability of throwing that total is shown.But, becasue you could theoretically go on forever, finding the probabilities involve an infinite geometric series.The player's loss is the house's gain so the house edge is the product of -1 and the player's return, in this case.0278.78.If the sum is a 2, 3, 7, 11, or 12, go ahead and copy the first roll results into the overall results column and move on to the next game.Note that there are 7 totals that win and only 4 that lose which might cause someone who didn't know better to think it was a good gamble.This bet pays 1:1 (even money) if the next throw is a 3, 4, 9, 10, or 11, 2:1 (double the bet) on the 2, and 3:1 (triple the bet) on the.There is only one way to roll a sum of 2 (snake eyes or a 1 on both dice so the probability of getting a sum of 2 is 1/36.Type of Simulation This is a simulation used to find probabilities.

Total Number of Combinations Probability 2.78 3.56 4.33 5.11 6.89 7.67 8.89 9.11 10.33 11.56 12.78 Total 36 100 The following shows the.

That might not be difficult for you, but since the prerequisite for the applied statistics course is just intermediate algebra, most of the students have never seen an infinite geometric series.

If you roll your point, you win; if you roll a 7, you lose.

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