When to double?
This makes certain simplifying assumptions that won't hold in practice:
- the contract will either make exactly or go off by one trick;
- the opponents will not redouble or run to another contract;
- the act of doubling won't change the number of tricks made;
- in pairs or teams scenarios, all pairs / the other team are facing the same decision.
Probability of beating contract needed for double to be profitable
|
Non-vulnerable |
Vulnerable |
When to redouble?
Probability of making contract needed for redouble to be profitable
|
Non-vulnerable |
Vulnerable |
When to bid game?
Probability of making game needed to make bidding it profitable
|
Non-vulnerable |
Vulnerable |
When to bid small slam?
Probability of making small slam needed to make bidding it profitable
|
Non-vulnerable |
Vulnerable |
When to bid grand slam?
Probability of making grand slam needed to make bidding it profitable
|
Non-vulnerable |
Vulnerable |
When to sacrifice over making game?
Required probability of going only n off vs. n+1 off
|
Green (n = 3) |
White (n = 2) |
Amber (n = 2) |
Red (n = 1) |
When to sacrifice over making small slam?
Required probability of going only n off vs. n+1 off
|
Green (n = 5) |
White (n = 4) |
Amber (n = 4) |
Red (n = 3) |
As you can see, six of the cases above have 0% probability requirement. This is due to 1370 and 1430 (or 1440) lying on either side of 1400 (6 off doubled non-vulnerable or 5 off doubled vulnerable). This leads to different n values as shown in the following table:
Required probability of going only n off vs. n+1 off
|
Green (n = 6) |
White (n = 4) |
Amber (n = 5) |
Red (n = 3) |
When to sacrifice over making grand slam?
Required probability of going only n off vs. n+1 off
|
Green (n = 8) |
White (n = 6) |
Amber (n = 7) |
Red (n = 5) |