situation -1- Probability is : 1 - (5/6)^6 = 0,67
situation -2- Probability is : 1 - (5/6)^12 - 12*(1/6)*(5/6)^11 = 0,62
situation -3- Probability is : 1 - (5/6)^18 - 18*(1/6)*(5/6)^17 - 18!/2!*(1/6)^2*(5/6)^16 = 0,60


I had to use the symbol "!" to denote the mathematical operation of faculty, which means :

18! = 18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1

As such the expression 18!/2! denotes

(18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1) / (2*1) = 18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3


Now some people will say, hey look the difference between situation -1- and -3- is quite large as it is comparing 0.67 to 0.60, we could have just found the answer by just simulating it (actually throwing the dice and counting the number of times the statements are satisfied !)

In reality the difference is really not that large and actually simulating the results would require 1000's throws to have the variance of the averaged experimental results be smaller then the probabilty difference of 0.67 - 0.60 = 0.07. It requires a good number more experiments to have a sifficiently high accuracy level assigned to your conclusion to make the conclusions dependable that one situation is more likely to happen then another WHILE ASSUMING LABORATORY LIKE CONDITIONS (tightly controlled) during the whole time you are simulating.

All that for a simple problem as stated above.

Now try the same statistical simulating strick in an environment where the conditions can change each 10 minutes and where the overal problem is a 1000 times more complex as we have in sail boat racing. Now try to discover which change to the design has actuall improved the performance of the boat. And now we know why the aging Hobie Tiger is still just as fast in capable hands as the nacra Infusion when both are using similar suits of sails.


Back to the original topic now.

Wouter