When I go to the casino I tend to play the penny slot machines. I will...

When I go to the casino I tend to play the penny slot machines. I will bet a penny per line until I've lost several rounds in a row. Then I feel like I must be about due for a win and increase my bet until I do win.

See if you can explain why this is faulty reasoning.

Expert Solution

Penny slot machine

When you place a bet on the penny slot machine, you have a small probability of winning.

Each subsequent bet on the penny slot machine does not change this probability.

For example, let us assume this probability is 1%.

When you play for the first time, the probability of you winning is 1%,

When you play for the second time, the probability of you winning remains unchanged at 1%.

Every subsequent play is independent of any previous play i.e. losing/winning on the first try does not influence the probability of losing/winning in any subsequent try. (This is a Markov chain exhibiting memoryless property)

Feeling that you are due for a win after multiple losses is a flawed argument since your probability in each play of winning and losing remains constant. You would not have a higher chance of winning just because you lost in multiple previous plays.

If satisfied, please do upvote! Let me know in the comments if anything is unclear. I will reply ASAP

orchestra answered 2 years ago

Among gamblers playing the slot machines and winning at a certain time (at a certain casino),...

Among gamblers playing the slot machines and winning at a certain time (at a certain casino), the following was determined to be true about one hour later: 45% were still winning; 25% were losing; 10% had switched from the slots to table games (blackjack, roulette, etc.); and 20% had left the casino. Similarly, among gamblers playing the slots and losing at a certain time, the following was determined to be true about one hour later: 32% were winning; 47% were...

Suppose you go to a local casino to gamble using a slot machine. The following probability...

Suppose you go to a local casino to gamble using a slot machine. The following probability distribution characterizes your net earnings on a single play. Assume each play is independent of the other and every play has this same distribution for earnings. Net earnings ($) Probability -1.00 0.90 -0.50 0.07 5.00 0.0285 500.00 0.0015 You play this slot machine one hundred times. Assuming the central limit theorem, what is the chance that you will come out of the casino with...

I am going to install a slot in the VIP lounge of my casino. A coin...

I am going to install a slot in the VIP lounge of my casino. A coin is inserted and a button is pressed. The screen reveals 3 colored circles (on the left, middle, and right side respectively). Each of the colored circles will be purple, red, blue, black, white independently with P[purple]=P[red]=P[white]=P[blue] = 0.5P[Black]. The payoff is as follows: circles reward (coins) 3 white 5000 3 blue 1000 3 purple 100 3 red 6 2 red/1 non-red 4 1 red/2...

Research in the gaming industry showed that 8% of all slot machines in the United States...

Research in the gaming industry showed that 8% of all slot machines in the United States stop working each year. Short’s Game Arcade has 70 slot machines and only 5 failed last year. Use the five-step hypothesis-testing procedure at the 0.05 significance level to test whether this data contradicts the research report. (a) State the null hypothesis and the alternate hypothesis. (Round your answers to 2 decimal places.) H0: π = H1: π ≠ (b) State the decision rule for...

The mean age of a random sample of 25 people who were playing the slot machines...

The mean age of a random sample of 25 people who were playing the slot machines is 55.3 years and the standard deviation is 6.8 years. The mean age of a random sample of 35 people who were playing roulette is 49.7 years with a standard deviation of 4.2 years. Find the 99% confidence interval of the true difference in means. Would you reject the null hypothesis that there is no difference in the mean ages of slot machine players...

What are the pros and cons of using a revenue share strategy while placing slot machines...

What are the pros and cons of using a revenue share strategy while placing slot machines on a casino floor?

1. Slot machines are the favorite game at casinos throughout the U.S. The following sample data...

1. Slot machines are the favorite game at casinos throughout the U.S. The following sample data show the number of women and number of men who selected slot machines as their favorite game. Women Men Sample size 320 250 Favorite game-slots 256 165 Test at a 5% level of significance whether the difference between the proportion of women and proportion of men who say slots is their favorite game is statistically significant. (Please use both confidence interval approach and standard...

If the probability of winning a slot machine is 5% and you are going to play 500 pulls.

If the probability of winning a slot machine is 5% and you are going to play 500 pulls. Using a normal approximation. What’s the probability that you win less than 40? What’s the probability that you win 30?

Problem 1 Slot machines have three drums with the same number of positions on each drum....

Problem 1 Slot machines have three drums with the same number of positions on each drum. Each position contains a symbol. When you pull the lever on the machine, the drums spin. Assume that each drum is equally likely to stop in any position, and that the positions in which the three drums stop are independent of each other and independent from spin to spin. Suppose a particular slot machine has 9 positions on each drum, and that each position...

Slot machines are the favorite game at casinos throughout the United States (Harrah’s Survey 2002: Profile...

Slot machines are the favorite game at casinos throughout the United States (Harrah’s Survey 2002: Profile of the American Gambler). A local casino wants to estimate the difference in the percent of women and me who prefer the slots with a 95% level of confidence. Random samples of 320 women and 250 men found that 256 women prefer slots and 165 men prefer slots. 1- -Hypothesis test for one population mean (unknown population standard deviation) 2-Confidence interval estimate for one...

Question