The Book of Proposition Bets, by Owen O’Shea

November 5, 2021 |

Jeff Watson writes:

Proposition bets have been around since the beginning of time. They capture the greed of the victim and put money in the pocket of the prop hustler. Proposition bets rely on the greed of the victim combined with the ignorance of the real probability of what they are betting on. Most good proposition bets are of the sort that will give the victim at least a small chance of winning, the bets that allow the victim no chance to win aren't really bets, but swindles. Although I'm not a fan of swindles, there are some very elegant swindles out there. The book only mentions a couple of them.

Owen O'Shea has presented 50 different proposition bets, mostly in the card, dice, or numbers categories. The real beauty of his short book is that the author kindly explains the math behind each of the prop bets in easy to follow detail. The math is very friendly to those math challenged individuals who might read the book.. The description of each wager and the subsequent true odds of the outcomes allows the reader to "see" what's under the hood for each bet.

The bets described in the book could be easily modified for different situations. For example, he describes the birthday problem wager, but also describes a wager that is a kissing cousin to the birthday problem. I could think of 15 different scenarios that one could apply the same principles of the birthday problem.. All of the other wagers mentioned the book could be expanded upon in this manner.

O'Shea's book is brand new, July 2021, and I highly recommend it. It is an easy read, which is surprising, considering the level of explanation for each bet. This book should be included on the shelf of every library of those interested in gambling, probabilities, math, cards, dice….and for those with a touch of larceny in their hearts. For the beginning proposition hustler, this book could be a bible.

When I was a young man about to go out into the world, my father says to me a very valuable thing. He says to me like this… "Son," the old guy says, "I am sorry that I am not able to bank roll you to a very large start, but not having any potatoes which to give you, I am now going to stake you to some very valuable advice. One of these days in your travels, a guy is going to come to you and show you a nice, brand new deck of cards on which (Sky snaps fingers) the seal has not yet been broken. This man is going to offer to bet you that he can make the jack of spades jump out of that deck and squirt cider in your ear. Now son, you do not take this bet, for as sure as you stand there, you are going to wind up with an earful of cider."

- Sky Masterson "Guys and Dolls"

The prop bet was whether Mindy's (actually, Lindy's) sold more strudel or cheesecake.

all prop bets on S&P from short side are losers. in sports betting you can win if 52% against the line. is that better or worse than markets? how can you beat the 52%?

Henry Gifford writes:

After hearing about the book on the list, I bought a copy. Thanks for the tip. I particularly looked forward to having the examples explained.

I started reading the introduction, which starts with an explanation of the Monty Hall paradox.

Now let’s get something straight – the problem described in the book is described as being a description of the game that was played on TV. All such explanations I have ever heard also say they describe the game that was played on TV.

A hustler offers a mark the option of choosing which one of three doors (cards in the book) is a winner, with the mark betting \$10 for a chance to win \$10 for choosing the winning door. The three choices are designated A, B, and C.

In the example given, the mark chooses A, then the hustler reveals that C is a losing option, then the hustler gives the mark the option of switching to choice B. The book then explains the mark’s situation as follows:

Here’s the thing. If you do not switch, your choice of picking the [winner] is 1/3, so think of the other unturned card as the “winning card” with probability of 2/3. Therefore, if you switch 2/3 of the time, you switch to the [closed winning door]. Consequently, by switching you double your chances from 1/3 to 2/3 of picking the [winner].

Suppose a con artist is offering this bet to various marks at various locations. At a bet of say, \$10 a round, where the mark wins, they win \$10. About 1/3 of the time the mark will choose the wrong card. If the mark decides not to switch from their original choice, they lose. This will occur about 1/3 of the time. But the hustler wins about 2/3 of the time and therefore for every \$10 the mark wins, the hustler wins \$20. Therefore, the con artist is winning this bet 2/3 of the time and in so doing, is making a tidy profit.

Then the book names a famous mathematician who was fooled by this bet, then changes the subject.

I don’t see any explanation of the paradox, and a lot of other things are not explained in any way I can understand.

For example, if switching improves the odds from 1/3 to 2/3, why would switching 2/3 of the time improve the odds to only 2/3? And what is the assumption of the mark switching 2/3 of the time based on?

And “If the mark decides not to switch from their original choice, they lose.” Huh? They lose all the time by not switching? But the previous sentence says the mark wins 1/3 of the time if not switching.

Another gem is “About 1/3 of the time the mark will choose the wrong card.” Really? I thought that with one choice out of three cards the mark will choose the wrong card 2/3 of the time.

And, at the core of the issue, the claim that switching improves the odds to 2/3 is not explained.

Of course the greatest paradox is that the book is about proposition bets that appear to be better bets than they really are, meanwhile the bet described says the mark is betting \$10 to win \$10 on a choice of one out of three options – a bet which does not appear to me to be a winning bet, as the hustler has a 2/3 chance of winning. Then, after the “paradox” is allegedly explained, the book explains that the hustler enjoys odds of winning of 2/3 because of the paradox. So, the hustler’s odds of winning improve from 2/3 to 2/3. Just how much did the hustler gain by improving his odds of winning from 2/3 to 2/3? This is another thing I don’t understand, and don’t see any explanation of.

This leaves me with zero faith in the accuracy of anything else in the book, and zero faith that anything else in the book will be adequately described. Or, at least, explained in a way I can understand it. My copy is in my garbage can, but I can retrieve it and mail it to any list member who asks for it.

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