Craps In this game an individual rolls two dice if the sum o

Craps: In this game an individual rolls two dice, if the sum of the dice on the first roll is a 7 or 11, the individual wins. If the sum is a 2,3,12 in the first roll the player loses. If the sum of the first roll is any other number the player has set the \"Point\" and continues to roll. So, if a player rolls 9, the \"Point\" is set at 9. The player then continues to roll the dice until one of two things happens:

Player rolls the point again and wins

Player rolls a seven and loses

Double Roulette:

This game involves spinning a ball on a wheel with 38 numbered slots (0,00,1-36). The goal is to bet whether the ball will land on a number or set of numbers. If the ball lands of your number or numbers, you win. You can choose one number or various combinations of numbers for the bet.

Chuck-A-Luck:

This is a simple game that involves a single roll of three dice. The best is that a single value will appear on at least one of the dice in the roll. If your number appears once, you win one times your bet. If the number appears on two dice, you win twice your bet, and if the number appears three times, you win three times the bet. IF the number doesn\'t appear you lose the bet.

Given the rules of the different games of chance described in the sheet you downloaded, think about your odds of winning in each of these three scenarios:

Craps: Either roll or a 7 or 11 on the first roll, OR match the point value on a subsequent roll. What\'s the likelihood of winning after one roll? Explain your answer.

Roulette: You bet on numbers 1-18. What\'s the likelihood of winning after one trial? Explain your answer.

Chuck-A-Luck: To win any money, at least two of your dice must show the same number. What\'s the likelihood of winning anything after one roll? Explain your answer.

To win at these games seems quite easy! Use you knowledge of probability to compute the likelihood of winning each of these games and rank them from best to worst odds. Explain your answer.

How would a probability to win of .42 translate into an expected amount won if you had $5.00? Assume that each time you win, you double your money, and each time you lose, you lose what you bet.

Imagine a scenario where you\'d put one dollar on each of five games, each with a probability of winning of .42, and you do NOT roll your winnings into another game. (Hint: Your expected \"winnings\" would always be negative, but how much would you expect to lose?)

If people win every day in Las Vegas gambling casinos, why do the casinos always take in more money than they pay out? Use a specific probability example to explain your answer.

There are many ways to win each of these games. Some of these \"wins\" are harder and thus provide better payoffs (for example, spinning a number between 1-4 in Roulette is harder, and thus pays better odds, than simply spinning a number between 1-18). Here are two modified game scenarios:

You win if you spin a 3, 13, 23, or 33 in Double Roulette. You lose on any other roll.

You win if you roll two or more of your chosen value (you choose 3 and roll 2+ 3\'s) in a roll of Chuck-A-Luck. You lose with any other combination of the dice.

In which scenario do you have the best chance of winning? In which scenario do you have the worst chance of winning? In which scenario would you be willing to bet the largest amount of money?

Solution

craps

win =sum 7,11 for 7= no of combination 3*2=6, for 11- 1*2=2

point=4,5,6,8, 9,10= 44-6-2-2-2-2= 30

lose- 2,3,12 no of combinations for 1=1*2=2, for 3 ,1*2=2, for 12, 1*2=2

craps- 6/44+38/44*30/44 = 0.735207

odds of winning=1-0.735207 =0.274793

explanation

craps= probability of getting seven in first roll+ getting any other number except 7 in first roll* probability of getting point in 2nd roll

roulette- 18/36=0.5

odds of winning= 1-0.5=0.5

chuck-a-luck= 6*1*1/6*6*6 = 0.0277

                   odds of winning=1-0.0277 =0.9723

best to worst odd of winning= craps>roulettle>chuck -a- luck