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Should you prefer the four four fit over the five three?

I’ve come across a completely free dealer program called Deal 3.1 that lets you control what hands you deal and the analysis which is done on the hands. It is particularly useful since it has a built-in double dummy solver so you can check, for instance, how many tricks you can make in a particular contract. Here's an example of its use.

I’ve often been told that if you can play in a 5-3 fit or a 4-4 fit on a particular hand then you should chose the 4-4 fit since you may make more tricks. Here’s an example:

S AKQ84 962 H AKJ2 Q765 D T5 A98 C K2 A93


Playing in spades on a 3-2 break you make 5 spades, 4 hearts, 1 diamond and 2 clubs which is 12 tricks. Playing in hearts, however, you can probably ruff a club in the left hand and hence make 5 heart tricks generating 13 tricks in all. It doesn’t help to ruff a club playing in spades because you have to ruff in the long trump hand. Alternatively, you could discard two diamonds on your long spades and ruff a diamond in the right hand. Ruffing in either hand generates an extra trick when playing in hearts.

This takes no account of bad breaks and overruffing etc. so I wanted to investigate whether it was generally true that you make more tricks in the 4-4 fit and how often following this advice would be of benefit. I dealt hands similar to the one above where one partner has 5 spades and four hearts and the other had three spades and four hearts. So that you would probably be playing the final contract, I wanted the hands to have more than 20 points in total.

The way you control the dealer program is by writing routines in ‘Tool Control Language’ or TCL. Below is the routine that describes what hands you want to generate. Basically you deal random hands, reject the ones you don’t want and accept the ones you do want. The symbols != mean not equal to and hcp is the number of high card points in a hand.

main { reject if {[spades north]!=5} reject if {[hearts north]!=4} reject if {[spades south]!=3} reject if {[hearts south]!=4} set hcpN [hcp north] set hcpS [hcp south] set points [expr {$hcpN + $hcpS}] accept if {$points > 20}

}

For simplicity, I’ve only considered the case where spades are 5-3, since the hearts case would presumably be the same. In 10,000 accepted deals the total number of tricks that could be taken was 96,936 playing in spades, the 5-3 fit, but 98,119 playing in hearts, the 4-4 fit. That’s 1183 more tricks or an extra trick every 8.5 accepted deals. (N.B. that’s deals fulfilling the above criteria, not random deals!) It’s worth having the extra trick by itself but it might be the difference between making game or not. Playing in spades you could make 5427 games but playing in hearts you could make 5703 games. That’s an extra game bonus every 36 accepted deals.

What really matters, however, is how often would we encounter this situation in real life. By doing away with the double dummy analysis we can select suitable deals extremely quickly. In a million deals I determined that there were 2612 deals where you would have the majority of the points and be 4-4 in one major and 5-3 in the other. That’s 383 random deals per accepted deal so you make an extra trick every 3236 deals and an extra game every 13871 deals. Playing 24 boards per session as much as 3 times per week that’s an extra trick every 10 months and an extra game every 3.7 years. This knowledge won’t change your NGS grade a great deal!

So, we’ve confirmed the advice, it is generally better to play in the 4-4 fit than the 5-3 one but Deal 3.1 has allowed us to see that we won’t benefit from this very often, even if you apply it to minors as well!

The home page for Deal 3.1 is https://bridge.thomasoandrews.com/deal/ . It is not a modern program with a slick graphical interface but is driven from a command line interface so you will need some appropriate computing experience.

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