## Question about percentages

### #1

Posted 2019-July-17, 00:48

If I flip a coin once I know the odds of it being heads are 50%

What are the odds if I flip it twice and I win if either flip comes up heads?

So I have two chances of making a grand slam, one if my partner (north) has King of spades, or if he doesn't I also win if East has king of spades.

### #2

Posted 2019-July-17, 01:27

NemoJames, on 2019-July-17, 00:48, said:

If I flip a coin once I know the odds of it being heads are 50%

What are the odds if I flip it twice and I win if either flip comes up heads?

So I have two chances of making a grand slam, one if my partner (north) has King of spades, or if he doesn't I also win if East has king of spades.

The mathematics of the coin first: you win if the first coin is heads (probabilty = 0.5) and also in half of the occasion when the first coin is tails (half of 0.5 = 0.25). Adding these together gives 0.75.

The bridge situation is not the same. There are three other hands (partner + two opponents) and you win if the king of spades is in either of two chances. This gives you a two out of three chance = 0.6667.

But this should be wrong too, Why couldn't you find out more about partner's hand from the bidding?

### #3

Posted 2019-July-17, 14:26

If it had been in a tournament I would have signed off at 6nt but afterwards I was wondering what the odds were and assuming they were 75% whether it would be worth taking a chance although I doubt if I would ever have the courage .

### #4

Posted 2019-July-17, 16:07

### #5

Posted 2019-July-18, 12:26

Then it becomes a matter of how much to risk given the stakes.

Two good books on this are 1) By Kelsey Glauert I forget the exact title as I loaned it out, the 2) By Jeff Rubens "Expert Bridge Simplified".

Both available at The Bridge World website.

I would love to see the actual or approximate hand.

### #6

Posted 2019-July-18, 14:51

### #7

Posted 2019-July-18, 18:58

### #8

Posted 2019-July-18, 19:07

dsLawsd, on 2019-July-18, 12:26, said:

Then it becomes a matter of how much to risk given the stakes.

Two good books on this are 1) By Kelsey Glauert I forget the exact title as I loaned it out ...

*, by Hugh Kelsey and Michael Glauert. Definitely worth a read.*

Bridge Odds for Practical Players

Bridge Odds for Practical Players

If you're getting bogged down in the probabilities presented in the early chapters, you can skip forward to the more practical sections later on.

### #9

Posted 2019-July-19, 06:35

### #10

Posted 2019-July-20, 01:18

My partner has either king of clubs or of spades. There is a 50% chance of one of those kings being a king of spades.

If it isn't then an impasse has a 50% chance of working. The percentage for those two events must be correct and not dependent on what anyone else holds. Being 50% they are the same as the toss of a coin.

For the sake of argument, if I am certain that 7NT will make if either event is true then what are the percentages if you combine those two events. I had assumed it would be 75% which is what has been suggested.

With that in mind would it be wise to try for 7NT when there is a 75% chance of success. Personally I wouldn't but I have seen other players bid on much lower percentages than that.

### #11

Posted 2019-July-20, 02:13

Whether or not you should bid it depends on how likely you think the other tables are to find a slam.

Someone else can check my numbers, but I believe:

- in MPs, you should bid grand as long as you expect half of the field to find at least the small slam

- in IMPs, non-vulnerable, you only need 9.5% of the field to find at least a small slam

- in IMPs, vulnerable, you only need 4.4% of the field to find at least a small slam

### #12

Posted 2019-July-20, 05:37

NemoJames, on 2019-July-17, 00:48, said: