To sacrifice means to deliberately bid a contract which cannot be made, hoping that the doubled penalty will be less than the value of the opponent's making contract. A sacrifice is always made in a suit contract, and is mostly likely happen when both sides have found a fit.
Relationship to vulnerability Edit
A non-vulnerable game is about 400 points and a vulnerable game is about 600 points. By comparing these to the doubled undertrick scores:
Therefore, a sacrifice is profitable when the contract is down at most three tricks at favourable vulnerability; two tricks at equal vulnerability; one trick at unfavourable vulnerability. As a result, sacrifice is mostly made when a side has favourable or equal vulnerability, but seldom made at unfavourable vulnerability, unless the contract has some chance to be made.
The scoring method (MP or IMP) greatly affects whether to sacrifice or not because a false sacrifice (made when the opponent's contract cannot be made) costs heavily.
In this case, the sacrificing pair has won 320 points, which is 8 IMPs.
In this case, by falsely sacrificing, EW has lost 400 points, which is -9 IMPs.
This example shows that even at favourable vulnerability, a false sacrifice costs heavily in IMPs, unless the contract is close to making. However, at MPs, this may only be a 50/50 bet on a top or a bottom.
In this case, the sacrificing pair has won 120 points, which is 3 IMPs.
In this case, the sacrificing pair has lost 180 points, which is -5 IMPs.
This example shows that if not enough tricks are available, the loss is greater than the potential gain in IMPs. Therefore, even a contract 3 tricks short is still profitable, the opposing pair may still let go the contract instead of sacrificing unless they are confident that the contract will be short by not more than 3 tricks. However, at MPs, again this may only be a 50/50 bet on a top or a bottom.
To conclude, sacrificing is more common at MP than at IMP.