The Unsinkable Titanic Thompson. Question about odds on page 142

[h_ven]

A friend of mine introduced me to a book called "The Unsinkable Titanic Thompson" A true story of a world super star: golfer, gambler, hustler, con man. He won millions in fascinating schemes that stagger teh imagination.

The book refers to Lee Trevino and Johnny Moss. Would recommend this book to any gambler.

Anyways, on page 142 they start talking about some odds:

"Throw up one coin and it's even money you'll call it right. Throw up three coins and the odds of calling them correctly goes to five-to-three. Throw up three at once, call two heads and one tails, and you're looking at six-to-one odds. Call five coins and it's eleven-to-five the side you call will come up.

Odds of throwing an ace on the first roll of the dice are eight-to-three. Your best bet is throw the dice four times. To roll a 12 with the dice takes 24 throws..."


If I'm not mistaken, if you throw up three coins, wouldn't the odds of calling them correctly be .5*.5*.5 = .125? What percentage is 5:3

The other probabilities don't look right either, thoughts and comments?

[yellowjack]

If you call the three coins simultaneously, they are indistinguishable. So if you called 1 heads and two tails, any of the following outcomes is a win for you: HTT, THT, TTH. Hence 3 winning outcomes and 5 losing bad outcomes.

I'm not sure if this works out nicely to the other cases described, but it should.

[pzhon]

It looks like several of these are wrong or stated so poorly that you have to guess at the context. Editors usually don't know math.

[ QUOTE ]
Odds of throwing an ace on the first roll of the dice are eight-to-three.

[/ QUOTE ]
When you roll two dice, 11 rolls out of 36 have at least one ace. That's not close to 8:3 against. It's not too far from 7:3.

[ QUOTE ]
Your best bet is throw the dice four times. To roll a 12 with the dice takes 24 throws

[/ QUOTE ]
Those propositions are close to 1/2. Rolling no ace in 4 rolls happens 625 out of 1296 times ~ 48.2%. Rolling no 6-6 in 24 rolls happens (35/36)^24 ~ 50.9% of the time. I'm not sure why those would be called the best bets.

[MtDon]

Is the section you quote a quote of what Thompson said, or is it the author's explanation of the corrsct odds?

If it is a quote of what Thompson said, then some of the odds should be incorrect, in Thompson's favor. That is one of the ways a con man makes money betting.

It would also explain the odd statement that "Your best bet is throw the dice four times."