The way I understand it, you win on a 2 or 3; lose on a 7 or 11; push on a 12; go to point phase for 4-6 8-10. So that means you can win on 2 numbers, lose on 2, push on 1, and go to 50:50 odds with the others. Seems like the house doesn’t have an advantage. (As opposed to the Pass, where you lose on 3 and win on 2 in the come out.)
In: Mathematics
It isn’t the number of possible numbers that show why the house has the advantage. It is the number of possible combinations to get those numbers. There is only one way to roll a 2, whereas a seven can be reached multiple ways, meaning you are more likely to roll a 7 than a 2, so they do not cancel each other out.
each number combination has a different probability of occurring.
A 2, for example, can ONLY occur when both dice show 1.
But a 7 can occur on a 1/6, 2/5, 3/4, 4/3, 5/2, or 6/1 combo. So a 7 is 6 times as likely to occur than a 2.
Similarly, an 8 can be a 2/6 or a 3/5, 4/4, 5/3, or 6/2. Less likely than a 7, but more likely than a 2.
7 is the most likely, 6 and 8 are equally likely, more than 5 and 9 which are equally likely, more than 4 and 10 which are equally likely. 2, 3, 11, and 12 are the least likely possibilities.
So it’s not a 1 in 12 chance of any number occurring. In fact there are 36 possible outcomes when rolling 2 dice (6 for die A and 6 for die B, 6*6=36)
a 7 can occur in 6 of those or 16.7% chance (1/6, 2/5, 3/4, 4/3, 5/2, 6/1)
an 8 in 5 of them or 13.9% chance (2/6, 3/5, 4/4, 5/3, 6/2)
a 9 in 4 or 11.1% chance (3/6, 4/5, 5/4, 6/3)
a 10 in 3 or 8.3% chance (4/6, 5/5, 6/4)
etc.
7 is the most common combination of 2 dice. There are 11 possible outcomes from a roll of 2 dice (2 through 12.) But there’s only one way to make 2 – by rolling a 1 on each die. There’s also only one way to make 12 – by rolling a 6 on each die.
There are 36 possible combinations and only 11 outcomes. There are 6 possible ways to make 7, which means it’s 6 times as likely to roll a 7 as it is to roll a 2.
If you look at your outcomes listed above…
You win on a 2, which is 1/36, or on a 3, which is 2/36. You lose on a 7 or 11 – 6/36 or 3/36. You go to points on all other rolls. At the outset, you have a 3/36 chance of winning, a 9/36 chance of losing, and a 24/36 chance of moving on to the point phase.
> So that means you can win on 2 numbers, lose on 2, push on 1, and go to 50:50 odds with the others.
Not exactly. You win on three rolls (1:1, 1:2, 2:1), lose on eight rolls (1:6, 2:5, 3:4, 4:3, 5:2, 6:1, 5:6, 6:5), and push on one (6:6). You are over twice as likely to lose than win.
The odds are complicated, but a pass line bet has about a 49.3% chance of winning, where a don’t pass bet has about a 47.9% chance of winning and about 2.8% chance of pushing (getting their bet back).
The house advantage is slightly lower for the don’t pass bet, but both are quite low for a casino game.
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