Reply to thread

Message: <blockquote data-quote="guachi" data-source="post: 7411287" data-attributes="member: 6785802">Aside from having a Monte Carlo simulation up and ready I also wanted to do it to see the distribution. Sometimes people find it easier to grasp probabilities using large, whole numbers instead of decimals, fractions, or percentages. In this case, the math is actually fairly straightforward as you showed, but a distribution also visually shows the nonexistence of getting 4-6 hits and the sharply reduced number of 3 hits in a way that simple average won't. However, since we have it both ways I hope readers get a better understanding of probability.To be even mathier the calculations for the possibility of achieving any number of hits are as follows. Find the number of possible combinations for each outcome. In our example it's 6!/(X!*(6-X)!). Where the 6 is the total number of attacks and the ! means factorial and that means to multiply 6*5*4*3*2*1 = 720 possible outcomes. The X is the number of hits you achieve. For example, for two hits the formula is (6*5*4*3*2*1)/((2*1)*(4*3*2*1)) = 15. So there are 15 possible ways to get four hits. Specifically, there are this many ways to get each of 0 to 6 hits.0: 11: 62: 153: 204: 155: 66: 1Then, calculate the probability of getting a certain number of hits. So zero hits is 0.8^6 and six hits is .2^6. Two hits is 0.2^2*0.8^4 and so forth. Then multiply this probability by the number of combinations. The results:0: 26.214%1: 39.322%2: 24.576%3: 8.192%4: 1.536%5: 0.154%6: 0.006%Which is, not surprisingly, quite similar to the results I got above.If you don't care a lick about what the distribution looks like then UngeheuerLich showed you just how much easier it is to compute the average.One positive I will say about Monte Carlo is that as the number of variables increases (like, if you wanted to simulate 20 attacks of various types each with different hit probabilities and damages) it doesn't get much harder to simulate the distribution. Just hit a button and let the computer do the math for you.</blockquote>

Verification