calculating probability for slot machines

Slot Machine 2: (101+2-1)/(168+2+2-2) = 102/170 = 60%īAM! Unlike the intuition, estimated winning probability θ by MAP for these two slot machines are exactly same. The formula and results are as given below: So, he tries to use MAP because he has got some Data and also prior belief that winning probability of each slot machine follows Beta distribution with hyperparameters α=β=2.Īssuming that the results (k wins out of n plays) follow binomial distribution with the slot machine’s winning probability θ as its parameter. He has an access to frequentist (MLE) approach and Bayesian Point Estimator approach (MAP).īeing a Mathematician, he knows that MLE will not work because of very small size of the observed Data. Now, how to prove mathematically if the intuition is Correct? But “ Slot Machine 2” data doesn’t look like happening by chance. Slot Machine 2: Won 101 times when played game for 168 times.īy intuition, not only him but anybody would also think “ Slot Machine 2” is the special one, because getting 2 wins out of 3 plays on “ Slot machine 1” could just happen by chance. Slot Machine 1: Won 2 times when played only 3 Games. In order to compute MLE or MAP, he asks for Some data and somebody on the casino floor shares a small set of data with him as follows: Now if he gets some observed data D, he can estimate probabilistic model’s parameter θ (Winning Probability of Slot Machine) by using MLE (Maximum Likelihood Estimation) OR MAP (Maximum as Posteriori) as follows: 50%, then he will assume that winning probability θ of each slot machine follows Beta distribution with hyperparameters α=β=2 as a Prior Belief. He will have no choice but to assume that winning probability of each slot machine is equal i.e. He doesn’t have any prior information about the Math implemented by games developers in slot machines. For the purpose of illustration, we have picked a casino example:Īssume a Mathematician goes to Casino floor. In this tutorial, I would like to show you how the methodology can help us answer some of these questions. Unfortunately, designing such a strategy is difficult because it involves making very complicated decisions about when to pull the handle.

On the other hand, if you understand how these machines work exactly, you could design a strategy to maximize your chance of winning. How do you win at slot machines? From one point of view, it is random whether you win or lose on each pull of the machine’s arm.

Calculating probability for slot machines