None of these is the
rationale you hear most often, however. The honor here goes to "a
number only has to show once to win on a Place bet; it has to hit
twice to pay on a Come." This argument differs because it's
not based on faith, which nobody can really gainsay; it implies
logic, but is more pseudo than scientific.
Temporarily ignore the
payoffs for the various options and consider only the chance of
winning one or another of the wagers.
Place bets on the six
or eight have five ways to win and six to lose, so the probability
of winning is 5/(5+6) or 45.45 percent. The five and nine each boast
four ways to win and six to lose so the likelihood of euphoria is
4/(4+6) or 40 percent. And on the four or 10, it's three ways to
win and six to lose, providing a prospect of profit equal to 3/(3+9)
or 33.33 percent.
Figuring Come bets gets
a bit tougher. The bets win on come-out rolls of seven or eleven;
that's eight ways out of 36, and 8/36 is 22.22 percent. Money moves
to the four three ways out of 36, then subsequently has three ways
to win and six to lose; overall, the chance of reaching then winning
on a four is (3/36)x(3/(3+6)) or 2.78 percent. For a five, it would
be (4/36)x(4/(4+6)) or 4.44 percent. The six is (5/36)x(5/(5+6))
or 6.31 percent. Eight, nine, and 10 mirror six, five, and four,
respectively. Adding it all up, winning on the come-out or establishing
and repeating the possible points, gives a probability of 49.29
percent.
Taking the complete cycle
into account, a Come bet is more apt to win than any Place bets.
Its success rate is 49.29 percent versus 45.45, 40, and 33.33 percent
for Place bets on six or eight, five or nine, and four or 10, in
that order. This, despite Come bets requiring the number to hit
twice. Solid citizens who rely on recurrence theory are forgetting
instances when a Come bet scores before getting to a point, especially
those involving a seven when the Come bet wins but Place money would
lose.
Dauntless dice
doyens doubtless discern that the chance of winning isn't the whole
story in comparing strategies. Place bets pay more than even money:
7-to-6 for the six and eight, 7-to-5 for the five and nine, and
9-to-5 for the four and 10. Come bets without odds pay only 1-to-1
regardless of the point.
