# BBO Discussion Forums: Question about percentages - BBO Discussion Forums

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### #1NemoJames

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Posted 2019-July-17, 00:48

I tried googling this but the answers gave me a headache and it is bridge related.

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.
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### #2Tramticket

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Posted 2019-July-17, 01:27

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

I tried googling this but the answers gave me a headache and it is bridge related.

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?
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### #3NemoJames

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Posted 2019-July-17, 14:26

This was a casual game on one table with friends and it was the last game of the day so a bit of fun really. We had between 33 an 35 points with a long spade suit. After asking for control cards I correctly assessed that if partner had the king or the king was with east we would have 7NT and it made no difference what other cards the opps held. Needless to say West had the king of spades.

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 .
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### #4smerriman

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Posted 2019-July-17, 16:07

The probability really heavily comes down to the hand you have and exactly what the auction was (eg if you asked for keycards I'm not sure how you knew you might be missing the king of spades but no ace, and knowing the point range partner showed and what the missing high cards are impacts the probability he has the king.)
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### #5dsLawsd

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Posted 2019-July-18, 12:26

You need to be able to combine chances to come up with exact odds.
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.
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### #6barmar

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Posted 2019-July-18, 14:51

Another reason the two situations aren't analogous is that coin flips are independent of each other, but card locations in the same deal are related. You can have two heads in a row, but the king of trumps can't be in two hands.

### #7pullelam

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Posted 2019-July-18, 18:58

I use a system combining number of controls and loosing tricks count.In this system if you have 11 controls and 11 loosing tricks count you can bid grand slam, and not otherwise.
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### #8sfi

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Posted 2019-July-18, 19:07

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

You need to be able to combine chances to come up with exact odds.
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 ...

Bridge Odds for Practical Players
, by Hugh Kelsey and Michael Glauert. Definitely worth a read.

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.
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### #9msjennifer

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Posted 2019-July-19, 06:35

Sir,I have read both KELSEY and RUBENS books and no doubt they can make one an expert in no time.However the mathematics can give you only a better way of declarer play .IF THE OPPONENTS ARE SILENT THROUGHOUT the mathematics will only help marginally.But certainly its importance is very much there.One can not depend upon opposition to help oneself .They will always try to mislead you by false carding.I wish you all the best luck in your percentages play.
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### #10NemoJames

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Posted 2019-July-20, 01:18

in the spirit of keeping it simple:
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.
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### #11smerriman

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Posted 2019-July-20, 02:13

In that case I agree with 75%.

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
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### #12nige1

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Posted 2019-July-20, 05:37

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

I tried googling this but the answers gave me a headache and it is bridge related.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.
75% seems about right, so you were correct, in theory, to bid the grand. You might have 12 s between you which would make 7N a certainty.
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