if relative vulnerability is equal where both sides are vulnerable against a small slam in a major or notrump four tricks if relative vulnerability is equal where both sides are vulnerable against a small slam in a minor four tricks if relative vulnerability is equal where both sides are not vulnerable against any small slam three tricks if relative vulnerability is unfavourable against any small slam Sacrificing against grand slam contracts When the opponents are likely to make a grand slam contract, a sacrifice bid which is doubled is viable if one can go down no more than eight tricks if vulnerability is favourable seven tricks if both vulnerable six tricks if both not vulnerable five tricks if vulnerability is unfavourable. Strategy A sacrifice most often occurs when both sides have found a fit during bidding (eight cards or more in a suit), but the bidding indicates that the opponents can make a game or slam contract. Also, it is possible to perform an advance sacrifice, when it is more or less clear that the opponents have a fit somewhere and greater strength. For example, after the partner opens 1 and RHO doubles, the following hand is suitable for a bid of 5, outbidding opponents' major suit game in advance: As seen in the table above, vulnerability significantly affects the sacrifice: success is most likely if the opponents are vulnerable but the sacrificing side is not. At equal vulnerabilities, sacrifices are less frequent, and vulnerable sacrifices against non-vulnerable opponents are very rare and often not bid deliberately. Also, the specific duplicate scoring method affects the tactics of sacrifice – at matchpoint scoring, −500 or −800 (down three or four) against −620 is a 50/50 probability for a top or bottom score, but at international match points (IMPs) it can gain 3 IMPs (120 difference) but lose 5 (180 difference), making it less attractive. However, if it turns out that the sacrificing side misjudged, and that the opponents' contract was unmakeable (or unlikely to make), the sacrifice is referred to as a false or phantom one. A false sacrifice can cost heavily, as the sacrificing side has in effect turned a small plus into a (potentially large) minus score. The Law of total tricks can be a guideline as to whether the sacrifice can be profitable or not. Sacrifices are practically always made in a suit contract; sacrifices in notrump are