Bridge Odds for Practical Players

Very detailed analysis of distribution of different combination. Although I'm not very familiar with statistics, it helps to improve your percentage play, defence, and overall game by comparing the percentage of different play lines and advices the best odd. A must read book! Highly recommend!

Both a great introduction and comprehensive exposition on the meaning and value statistices in bridge playing. A MUST read

This book is for advanced players that are willing to make it into the championship level. Describes not only probabilities, but also odd changing, vacant places, chance combination and more. Highly recommended.

While the calculation of the odds is interesting this is a practical book as well as a methematical one. Theer are numerous problems where teh reader needs to improve their chances by combining plays. Such as playing AK of a long suit to see if the Q drops before taking a finesse. Not only is the information useful, its well presented adn enjoyable to read. The math is not especially dificult and if you want to become a good player you should be aware of this. I put it under "knowing your fundamentals" I liked this a lot more than the Vivaldi book. The Terence Reese book "Master the Odds" was ok, this was better.

I've read several of Kelsey's books, and the problems he gives are often rather difficult. Those in this book are usually easy, however. And that is how it should be. Most decisions at the bridge table are pretty easy. You just need to make the right ones consistently. After a brief introduction to basic probability theory, Kelsey tells us about the odds for distributions of missing cards. The next chapter is on how to play various card combinations in a suit. After that, we practice combining chances as a declarer. We learn to play for a drop in one suit before taking a risky finesse in another, and so on. Next is a chapter on care of options. Sometimes, the opponents will remove one of your options. Sometimes, you will remove one of theirs. We learn to make some straightforward plays that take all this into account. Of course, one elementary aspect of bridge is that the odds change as the hand is played. If an opponent shows out of a suit, or gives you other information about the distribution of cards, the odds can change. And Kelsey expresses the change in odds by the number of "vacant places" that remain undetermined. The final elementary concept in bridge odds is generally referred to as "restricted choice." Kelsey finds this term confusing, so he calls it "freedom of choice." A simple example is when you have nine trumps, missing the Queen, Jack, five, and four. With the Ace and King in your hand, you try the Ace. Your left-hand opponent drops an honor! Before that happened, you would have played for the suit to split 2-2. But you now realize that there are only two kinds of hands your opponent could have started with: a singleton honor or both honors. There are two hands where your opponent has a singleton (singleton Queen and singleton Jack). And only one hand where your opponent has both honors. So the odds are nearly 2 to 1 in favor of finessing on the next round of trumps. That's a basic concept one has to know in bridge, and Kelsey gives some more examples of it. This book is easy to read but teaches some valuable lessons. There is only one statement I seriously disagree with in it, and naturally, it is not about bridge. Near the start of the book, Kelsey asks about the probability of a "tossed coin" to come down tails if it has come down heads nine times running. Kelsey is trying to explain that the chance of tails is not greater than 50%. After all, the coin has no memory. It is not going to come down tails just to even the odds! Kelsey says that each toss of the coin is a separate 50% chance. Well, that's not quite true. The chance of it coming down tails is not 50%. After all, there is only one chance in 512 of a fair coin coming down heads nine times running. The chance may be considerably greater if the coin (or the toss) is not fair. If the coin is two-headed, the chance of nine straight heads is 100%. Clearly, the chance of tails on the tenth throw is less than 50%. I recommend this book