How to do an excel simulation for gambling; In a casino there are two gamblers p

Question

How to do an excel simulation for gambling; In a casino there are two gamblers playing a game and they play until the time anyone of the gambler ruins himself completely i.e. either of them becomes bankrupt. One game is played at a time and the money left with a gambler at the end of the game depends upon the result of the game. Each gambler looses or wins 1 dollar at the end of the game. Each gambler starts with 10 dollars at the start of the game and the game continues till any one of the gamblers becomes bankrupt. Probability of gambler 1 loosing is 60% and gambler 2 loosing is 40%. Starting conditions for both is $10. What are the probabilities and average number of plays before either player becomes bankrupt?

Explanation / Answer

Ans:

Money with gambler 1 after playing first game =10-0.6*1+0.4*1=9.8

Money with gambler 2 after playing first game =10-0.4*1+0.6*1=10.2

Money with gambler 1 after playing second game=9.8-0.6*1+0.4*1=9.6

Money with gambler 2 after playing second game=10.2-0.4*1+0.6*1=10.4

Now we simulate the above 2 terms in excel for gambler 1 and gambler 2 respectively

As we observe from above simulation,after 50 number of plays,gambler 1 becomes bankrupt and gambler 2 will never become bankrupt as probability(0.4) of his loosing money is lesser than probability(0.6) of winning the money(i.e if we simulate for gambler 2 for more number of plays he will accumulate more and more money and will never become bankrupt.I simulated for gambler 2 for 500 plays,then he accumulate=$110).

Number of plays gambler 1 gambler 2 0 10 10 1 9.8 10.2 2 9.6 10.4 3 9.4 10.6 4 9.2 10.8 5 9 11 6 8.8 11.2 7 8.6 11.4 8 8.4 11.6 9 8.2 11.8 10 8 12 11 7.8 12.2 12 7.6 12.4 13 7.4 12.6 14 7.2 12.8 15 7 13 16 6.8 13.2 17 6.6 13.4 18 6.4 13.6 19 6.2 13.8 20 6 14 21 5.8 14.2 22 5.6 14.4 23 5.4 14.6 24 5.2 14.8 25 5 15 26 4.8 15.2 27 4.6 15.4 28 4.4 15.6 29 4.2 15.8 30 4 16 31 3.8 16.2 32 3.6 16.4 33 3.4 16.6 34 3.2 16.8 35 3 17 36 2.8 17.2 37 2.6 17.4 38 2.4 17.6 39 2.2 17.8 40 2 18 41 1.8 18.2 42 1.6 18.4 43 1.4 18.6 44 1.2 18.8 45 1 19 46 0.8 19.2 47 0.6 19.4 48 0.4 19.6 49 0.2 19.8 50 0.0 20

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