My new MathHammer trick.

Do you remember this post, if not go back and read it.

OK here some thing new; so for my lovely assistant I will use turn three with four units waiting in the wings to come on. Remember on each roll that a 66.7% chance of a successful dice roll.

1.2%   chance that zero will come on.
9.9%   chance that one will come on.
29.6% chance that two will come on.
39.5% chance that three will come on.
19.6% chance that four will come on.

Well that come out to an average 2.7 units will come on given this set up.  How does .7 of a unit come on, you ask, or even were does this number come from?  Well think of it this way, let say that you have to make this roll 100 times.  This means you will get zero units on 1.2 times out of the 100. One unit 9.9 times out of a 100, 29.6 of 100 rolls will get you two units, 39.5 of 100 three units come on, and finally four units will come on 19.6 times out of the 100 dice rolls. 
Then we need to see home many total untis come on for the 100 rolls.
(0 x 1.2) + (1 x 9.9) + (2 x 29.6) + (3 x 39.5) + (4 x 19.6) = 266 unit* coming on to the board if you rolled this out 100 times.  Well you rolled the dice 100 times so if you divide 266 by 100 you get an average of 2.7 units per roll.

Still confused yet me know an I see if I can explain in another way. 


* statically, results may vary in actual game play.