The first roll of the dice in a betting round is called the ComeOut roll - a new

Question

The first roll of the dice in a betting round is called the ComeOut roll - a new game in Craps begins with the Come Out roll. ACome Out roll can be made only when the previous shooter fails tomake a winning roll, that is, fails to make the Point or sevenout.

A new game then begins with a new shooter. If the currentshooter does make his Point, the dice are returned to him and hethen begins the new Come Out roll. This is a continuation of thatshooter's roll, although technically, the Come Out roll identifiesa new game about to begin.

When the shooter fails to make his or her Point, the dice arethen offered to the next player for a new Come Out roll and thegame continues in the same manner. The new shooter will be theperson directly next to the left of the previous shooter - so thegame moves in a clockwise fashion around the craps table.

The dice are rolled across the craps table layout. The layout isdivided into three areas - two side areas separated by a centerone. Each side area is the mirror reflection of the other andcontains the following: Pass and Don't Pass line bets, Come andDon't Come bets, Odds bet, Place bets and Fieldbets. The center area is shared by both side areas andcontains the Proposition bets.

Pass bets win when the come out roll is 7 or 11, while pass betslose when the come out roll is 2, 3, or 12. Don't bets lose whenthe come out roll is 7 or 11, and don't bets win when the come outroll is 2 or 3. Don't bets tie when the come out roll is 12 (2 insome casinos; the 'Bar' roll on the layoutindicates which roll is treated as a tie).

Explanation / Answer

Probability of win on first roll is 7 or 11 =6/36+2/36=8/36=22.2%

P loss on first roll is 2,3,12 = 1/36+2/36+1/35=4/36

Later throws depend on the point, need the sample space for4,5,6,8,9,10

COnditional probablity depends on making these points vs makingthe 7, and there are 6 ways to make 7 so...

P 3/9, 4/10, 5/11, 5/11, 4/10, 3/9 respectively for4,5,6,8,9,10

but this is conditional on that number being thepoint,

the P of each number being the point is 3/36, 4/36,  5/36,  5/36,  4/36,  3/36,respectively for 4,5,6,8,9,10

SO multiply the P of each number being the point, times eachnumber coming before 7

3/9, 4/10, 5/11, 5/11, 4/10, 3/9

3/36, 4/36,  5/36,  5/36,  4/36,  3/36

eg 3/39 x 3/36 for the 4 point, etc, total is 27.07%

So .222+.2707=.4929. it is less than 50!

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