Craps players
who wager on Pass and Come can increase or decrease the amount they "take"
as Odds during the point phase of a roll. But they must leave the initial
"flat" part of the bet as-is. Solid citizens who wager on Don't
Pass and Don't Come can change what they "lay" as Odds and also
lower or remove their flat bets.
Pass and Come are restricted
because bettors have an edge on the casino during come-out rolls. Then,
these wagers pay even money on sevens or 11s and lose on twos, threes,
or 12s. Out of 36 possible dice combinations, that's eight ways to win
and four to lose so bettors are favored 8-to-4 (2-to-1) to win 1-to-1.
When any of the 24 other dice combinations appear on the come-out, the
money shifts to the "point" and players become underdogs. They
fight chances of 6-to-3 on fours and 10s, 6-to-4 on fives and nines, and
6-to-5 on sixes and eights. Casinos won't let anyone have an 8-to-4 hammer
at the start and not face the music later.
Conversely, Don't Pass and
Don't Come lose on sevens or 11s and win on twos or threes during the
come-out. That's eight ways to lose and three to win 1-to-1, a serious
hurdle. However, if the barrier is overcome and the money goes to the
point, the compensation is that the bet has an advantage during the second
phase equal and opposite to the Pass/Come situation. Players have already
paid their dues, so to speak; if they want to take down bets on which
they have an edge, the casino will happily oblige.
Some doyens of the darkside
routinely take Don't Come wagers off sixes or eights. They're figuring
these aren't robust enough favorites and prefer to go through another
come-out, hoping for a point with a greater shot at winning. This is false
logic because the exposure during the come-out swamps any gain they can
hope to achieve on a new point. Also, their "conditional" edge
over the casino for money positioned behind the six or eight through the
Don't Pass or Don't Come is not chicken feed. Every such flat dollar has
an expected value slightly over $1.09.
Money moved to the other numbers
through the Don't Pass or Don't Come has even greater edge for the player.
A flat dollar behind a five or nine has an expected value of $1.20. Behind
a four or 10, it's $1.33. Odds, regardless of the point, have no edge
either way. A dollar in Odds has an expected value of $1.00.
Given that a bet has survived
a come-out roll on the Don't side and has a statistical worth exceeding
its face value, probability theory militates against taking it out of
action under any conditions. But, were the laws of probability the only
criteria to be considered, the issue would be immaterial because nobody
would gamble in a casino anyway. Pretend, for instance, you'd gone through
a Don't Pass and two Don't Come come-outs and had $10 each behind the
four, five, and six. Say you don't lay Odds. On a seven, you'll recover
your $30 and grab $30 profit, adding $60 to your rack. On any of your
numbers, you'll lose $10 but not change the stack in your rack. If you
take down your bets, your rack will grow by $30.
The expected value of the $30
at risk is $10.91 + $12.00 + $13.33 or $36.24. Imagine further that the
shooter has been on a tear, but happily for you it's involved only eights,
nines, and 10s.
Taking down your bets sacrifices
a theoretical $6.24. But it adds a sure $30 to your rack. The alternative
for the next throw is 12 ways to lose $10 (one of your numbers hits) versus
six ways to win $30 (the seven pops). Are you wrong to give up the advantage?
How would you answer if you had $500 in your rack? What about $5?
The decision you make is in
the realm of what economists call "utility theory." It hinges
on the strength of your aversion to losing $10 and the value you place
on winning $30, subject to the 2-to-1 chance of feeling the pain and not
the pleasure. Other salient factors are that the $6.24 is theoretical
not real, and the advantage is based on averages not the here and now.
Sumner A Ingmark caught much the same conundrum in his canto:
Your prosperity
looks great on paper,
But you can't buy groceries with vapor.