Restricted choice
Two Equals
| North | ||
| AJT | ||
| West | East | |
| ??? | ??? | |
| South | ||
| xxx |
Before the play the odds are:
| A priori | ||
| West | East | % |
| KQ | - | 24 |
| K | Q | 26 |
| Q | K | 26 |
| - | KQ | 24 |
| South makes 2 tricks = 76% | ||
South plays small to the ten east takes with the K or Q. The odds are now:
| A posteriori | |||
| West | East | % | |
| KQ | - | 0 | 0 |
| K | Q | 26 | 34,2 |
| Q | K | 26 | 34,2 |
| - | KQ | 24 | 31,6 |
| South takes 2 tricks = 68.4% | |||
When a defender wins a trick with one of two equals, the probability of him having both cards is halved.
| North | ||
| AT9862 | ||
| West | East | |
| ??? | ??? | |
| South | ||
| K53 |
South plays the king west follows with the four and east takes the jack.
In the next trick south plays small and west plays the 7.
West has 11 vacant places east has 12.
But with QJ east will win the jack half of the time and half of the time he will win with the queen.
Meaning that the odds will be west 11 against east 12/2=6.
Play west for the queen.
The a priori probability of east having a singleton honneur = 12,44% and east having QJ sec = 6,78% (11 against 6) gives the same result.
Three equals
| North | ||
| AT98 | ||
| West | East | |
| ??? | ??? | |
| South | ||
| 432 |
South ducks the first round and east takes the jack.
On regaining the lead south plays small to the ten east takes the queen.
Finally south plays small west follows:
West has 10 vacant places east has 11.
If east had KQJ he could have taken the first 2 tricks with another combination of cards. (KJ or KQ instead of QJ)
So west has 10 vacant places against east 11/3 conclusion west has the king is 30 against east 11.
Finessing is almost 75%.
If one defender takes two tricks with two out of three equavalent cards, the probability of him having all three cards is reduced to one third.
It looks as if you always have to finesse in these situations however in extreme cases this is not true.
If one suit is very unevenly diveded over the defenders you may have to play for the drop. An example:
Game all dealer east.
| North | ||
 Q 7 6 4 | ||
 A Q 9 | ||
 K 6 | ||
 A 8 7 6 | ||
| West | East | |
| ??? | ??? | |
| South | ||
| - | ||
| K J 2 | ||
| A 10 9 7 5 4 3 | ||
| K Q 4 |
East opens 3 spades and desparate for points you end up in seven diamonds.
You ruff the spade lead and play a diamond to the king west drops the queeen and east follows.
You continue with a small diamond from north east follows.
It seems likely that east has seven spades leaving west with two.
East has 4 vacant places (13 - 7 spades - 2 diamonds) west has 10 (13 - 2 spades - 1 diamond)
However if west had QJ he could have played either one so, correcting for that:
East has 4 and west has 10/2=5 vacant places so west is favorite for the jack.
You should play for the drop.
From the book:
Bridge odds for practical players
Hugh Kelsey and Michael Glauert.
Home
| W3C XHTML 1.0 | W3C CSS 2.0 |
Page top