A correction to evaluating two craps bets

Dear Readers:

It's nice to have friends that are smart. In the article "Evaluating Two Craps Bets," I misread the question (translation: totally screwed up) and gave the wrong answer to the proposition. Then I received the following e-mail from Skinny putting it right (note how delicately Skinny handles telling me I screwed up -- what are good friends for?):

Frank,

I think there is an omission in the article entitled "Evaluating Two Craps Bets."

You left out the place bet on the 4 and 10 in your analysis of Proposition #1. It changes your conclusion since you left out two of the bets.

Proposition #1 - Bet $64 across as follows with the corresponding loss due to the house edge:

$10 place the 4 - loss of 67 cents
$10 place the 5 - loss of 40 cents
$12 place the 6 - loss of 18 cents
$12 place the 8 - loss of 18 cents
$10 place the 9 - loss of 40 cents
$10 place the 10- loss of 67 cents

Proposition #1 has a total expected loss of $2.50.

Proposition #2 - Wager $66 as follows:

$20 place the 5 - loss of 80 cents
$18 place the 6 - loss of 27 cents
$18 place the 8 - loss of 27 cents
$10 on the field - loss of 56 cents (note you said 55 cents in the article but HA is 5.56% which rounds to 56 cents - less important than the omission)

Proposition #2 has a total expected loss of $1.90.

Proposition #2 is the better of the two propositions offered by the gambler.

Skinny