PROBABILITY GUIDE - how likely are you to win at Seven/Eleven?
--------------------------------------------------------------

Table of throwing two dice:

      1    2    3    4    5    6        Hence the probability of throwing
   +----+----+----+----+----+----+      the following numbers is:
1  |  2 |  3 |  4 |  5 |  6 |  7 |      2:  1/36
   +----+----+----+----+----+----+      3:  2/36
2  |  3 |  4 |  5 |  6 |  7 |  8 |      4:  3/36
   +----+----+----+----+----+----+      5:  4/36
3  |  4 |  5 |  6 |  7 |  8 |  9 |      6:  5/36
   +----+----+----+----+----+----+      7:  6/36
4  |  5 |  6 |  7 |  8 |  9 | 10 |      8:  5/36
   +----+----+----+----+----+----+      9:  4/36
5  |  6 |  7 |  8 |  9 | 10 | 11 |      10: 3/36
   +----+----+----+----+----+----+      11: 2/36
6  |  7 |  8 |  9 | 10 | 11 | 12 |      12: 1/36
   +----+----+----+----+----+----+ 


When throwing for the first time, the probability of an INSTANT WIN (7 or 11) is 8/36 and an INSTANT LOSS (2, 3 or 12) is 4/36, and going on to make a target number is 24/36.

When trying to roll the target number, the probability of doing so is:
- 3/36 if the target is 4 or 10
- 4/36 if the target is 5 or 9
- 5/36 if the target is 6 or 8
The probability of a loss (rolling 7 or 11) is 8/36 in all cases.

This is probably a gross oversimplification - but over all the possibilities of the target number, the average probability of rolling it is 4/36, i.e. half the probability of rolling 7/11 and losing.

Hence (in this simplified context) the overall chances of a win are:

8/36 + (1/3 * 24/36) = 16/36 = 4/9

And the overall chances of a loss are:

4/36 + (2/3 * 24/36) = 20/36 = 5/9


Remember: THE HOUSE ALWAYS WINS. 
