Please help me with the Math

I am trying to understand the math on the Field bet in craps.

Can someone tell me how to figure the odds on hitting the field on back to back rolls vs the number of times I would roll 5, 6, 7, or 8 in the same turn?

Sample rolls 4/7/6/9/5/10/8/3/7/12/8/11/2 that is 13 rolls but only 6 losers of (5,6,7,or8)

Please help.

The easiest way to work it out is list all the combinations of 2 3 .... 11 12. Simply put there is one way to make a 2, two ways to make a 3... up to six ways to make a 7, back to one way to make a 12; total thirty-six ways to roll the two dice. Using this info can be used to look at multiple rolls.

So you should get 16 winners and 20 losers, which simplifies to 4/9 and 5/9. Two wins = 4/9 * 4/9, whereas two losers = 5/9 * 5/9.

Also remember the field bet pays double/treble for 2/12 (depends on casino), so while you only win 16 times every 36 rolls, assuming the 2 and 12 pay 2/1 and 3/1 in some order, the House Edge is about 1/36.