The Question: In Bridge, when in a game forcing hand, is it better to be in 3 No Trump or 4 of a Major? Better here is defined as the odds of making the contract or better.

My Hypothesis: At around 25 High Card Points, even with an 8 card fit, it is better to be in 3NT because one can afford to lose one more trick compared to 4 Spade or 4 Heart.

The Result:  With an 8 card or better fit at 24 High Card points and higher it is better to play in 4 of a Major.

Comments & Methods

I think for most folks the above is what they care about, the results.  The raw data used in the analysis was generated using a Python program that generated 200,000  hands. From each of the hands the Double Dummy analysis was taken using the DDStable Python library.  Lastly, the hand shape, suits, and high card points were extracted from each hand.

There's a human factor of Bridge not accounted for here. A wise Bridge player once said, "Defense is hard." Often times I've heard from players much better than myself that the Double Dummy analysis of a hand favors the defending side. It assumes the defense finds the perfect lead.  While that factor will certainly change ones real life percentages, I hold it doesn't materially affect these results but is worth acknowledging.

From the 200,000 hands, 400,000 actual attacks were analyzed. I took every combination regardless of shape & HCP and pulled the resulting makeable No Trump contracts & Major suited contracts possible according to Double Dummy.  Even though a contract can be played from either side, the lowest value was used to determine what contract was makeable. For example, if North could make 3NT if they were declarer but South could only make 2NT as declarer the whole hand was deemed to make only 2NT.

Raw Bridge Data

Excel Analysis