What About the Come

This is a game you will lose at Period Here in lies the crust of the proof. There are needless to say 36 outcomes of the Dice each having 6 sides, hence 6 ² = 36 all things being equal etc

So, on the Come out when the Puck is White only the Seven and the Eleven are winners, for Come players this holds true on each subsequent roll, Total winners of 8, 6-7's and 2-11's. 8 ways to win and of course 4 ways to lose, for a total of 12 .

So, you think it is clear bet against the dice, but wait the twelve and the initial disadvantage on the come out roll, does it out weigh the other. Let's look at that odds the number comes and apply our observation to both methods of play. Firstly, the frequency the number comes is proportional to the number of ways it can happen for instance the four can come 3 ways and the number of ways the seven can come is 6. one would think that the "Don't Come" player's have the advantage, but they had to go through the come out roll. And now that the puck is black the number and the Seven are the only two numbers that mean anything to anybody's bet, right. So ,the meld of the probability must take it to consideration the frequency of the come out roll's result as well as their probability.

Hence one out of 3 times the decision is made right there, on the first roll. Due to the notion of conditional probabilities. which applies 2 out of 3 times the probabilities are as follows: you win, 8 of 36 or 22.2 % And you lose, 4 of 36 or 11.1 % With of course the two ,three or twelve. That means that 24 of 36 rolls you get a number, 4,5,6,8,9 or 10. each of these number has you at a disadvantage as depicted below.

Again, there you have it, with the Don't Come 1/3 of the time you are 2.666666 times as likely to lose. and 2/3's of the times your advantage is at most, with the 4 or 10, merely 40,0 % Meaning that even after you past the come out roll you could lose 33.33% of the time. and the math is easy 2/3 times 2/3 = 4/9 less than half at it's best, when you don't go down on the come out. At the come out your 1/3 of the times that your decision is made times .0857142 your chance of winning = .0285714, exactly 1/35 of the times add that to 4/9 and you have .47301587301 amazingly still less than 1/2, you lose.

What About the Don't Come

Here is where you bet the come out roll on the dark side, that is on the Come Out Roll when the Puck is White only the Two and the Three are winners, for Don't Come players . 3 ways to win and of course 8 ways to lose, for a total of 11 . Here the twelve is held out of play and no action is taken, you push Hence eleven to 35 that the decision is made right there, The actual probability for a win in the come out roll is ¹¹ / ₃₅ times ³ / ₁₁
Or, ¹¹ / ₃₅ x ³ / ₁₁ = ³³ / ₃₈₅ = .085714285 you win
And ¹¹ / ₃₅ x ⁸ / ₁₁ = ⁴⁸ / ₄₃₂ = .228571428 you lose With of course the seven or eleven. Since one thing or the other must happen 24 of 36 rolls you get a number, 4,5,6,8,9 or 10. each of these number has you at an advantage as depicted below.

Yeah Sure but what if
I Bet on the Come

Therefore ¹ / ₃ of the time you have a 2 out of 3 chance of winning and ² / ₃ 's of the time you get a number, "to make", in order to win, of which, the best odds 5/11 is less than 1 out of 2, hence you lose .