[Wainfleet]

Suppose I am playing in 3NT and there are five missing clubs. Vs. a 4-1 split I can secure my contract by ducking a club, but if they split a more likely 3-2 I won't need to duck and will make an overtrick, but if they split 4-1 I will go off. Am I right in thinking that playing duplicate pairs the percentage play is to not duck and risk going off, but in Teams it is better to duck and secure the contract unless the clubs split 5-0.

[mycroft]

At MPs, you will gain 1 MP against the pairs who make the safety play ~68% of the time (*) and lose 1 the rest of the time. You will share that gain/loss with everyone who makes the same decision as you. So, it's worth doing if everyone is going to be in 3NT and you don't expect to be 63-ish% on the field with your normal play.

Note the other caveat, though - "everyone is in 3NT". If you get to a good contract relative to the field, don't risk +400 going for +430. You've already won the board, and -50 will lose to not only those who made the same good judgement in the bidding (and played safe) but also those who are in the inferior partscore contracts (that make).

Similarly, if you're in a bad contract relative to the field, you should be playing for the "good contract" to fail on bad breaks or the like. So play safe in 3NT by hoping that 4♠ only makes 9 tricks on the same bad break (if the 3-2 would allow 4♠ to make 5, +430 is the same loss to +450 as +400; -50 ties when you could have a win if 9 tricks is the limit of the hand).

Now, as always, "everyone" means "the large majority". There are nearly no hands where in a decent size field, absolutely every pair is playing the same contract. And you have to have a pretty good judge of "the field" to make these judgements.

At IMPs - provided it's team-of-four (less so IMP pairs, then "the field" comes back, but not much less so), the odds are:
NV: 430 is +1 IMP vs 400, -50 is -9 IMPs vs 400
V: 630 is +1 IMP vs 600, -100 is -12 IMPs vs 600.
Playing for anything less than a 90% chance is wrong in the long run NV, and VUL, they pretty much have to show your their cards (or you get a complete count) for it to be worth it.

You can see from the length of the two discussions why matchpoints is such a fascinating game. You can also see why people will say "but it's not bridge".

(*) all numbers a priori, obviously your hands and the knowledge you get from the other suits (in the auction and the play) will change them.

[AL78]

This somewhat depends on the standard of the field you are playing in. In general with your example you want to be playing for the 3-2 break as if you take the safety play and everyone else doesn't, the safety play has to be right at least two out of three times to show a profit in the long term, assuming the safety play always loses a trick. At teams, your priority is to make the contract and the maths (in general) says that giving up an overtrick is the best play if doing so increases your chance of bringing in a game.

There is a difference between expert fields, which is what many contributors on here have experience of and where people are playing bridge to a standard where one can make a decent judgement about what is likely to happen across the field, and what seems to be typical club bridge in my part of the UK which consists of quasi-randomness at times and it is near impossible on many hands to accurately judge what will happen. One example would be where I was playing with a scratch partner, I showed slam interest, she showed no interest despite having a golden card in my primary suit, and we played in 4S+3. I was expecting a bottom but we got 50% because everyone else up to that point had played in game. In a decent field it would have been a bottom. The primary reason I am not a fan of matchpoints is because you have no influence over your true opponents and what those opponent's scores can be all over the place due largely to random chance sometimes, but imps is rare in club bridge around here.

[thepossum]

Play to score postive and try not to second guess a field. Game theory works fine in theory