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Aces are good for suit contracts because they represent "first round" control. In a trump contract, there might only be one or two rounds of a side suit played before trumps are used to control the suit.

If you are playing it a major suit trump contract, declarer and dummy will likely have a mid-twenties (Work) point count. That would average to 2.5 aces, pro rata.

As a practical matter, most such hands will have either two aces (below average) between them or three aces (above average). A few will have one or four.

Studies have been done that show that the chances of making a major suit contract are positively correlated with rising point counts, with 25 points being the closest to "50-50."

Have these or other studies shown that hands with three aces are more likely to make than hands with two aces (holding point count constant at 25, 24, 26, or any other number)?

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  • Are you asking about aces being considered four points in standard 4321 system? Are you considering length and distribution or just HCP?
    – Joe
    Jun 19, 2021 at 18:16
  • @Joe: I referred to the "work" system. so it would be HCP. But the real question is, if you make everything ELSE equal and focus only on the number of aces, does three beat two? So you can equalize length, distribution, Work points, and everything else and the question would still hold.
    – Tom Au
    Jun 19, 2021 at 18:24
  • So you’re saying has anyone done a study if the identical hand but AT vs KJ which is better?
    – Joe
    Jun 19, 2021 at 18:40
  • @Joe: You could put it that way. It has been shown that AT beats KJ in "hold 'em" poker.
    – Tom Au
    Jun 19, 2021 at 18:51

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Aces are definitely undervalued in standard (Work) points. In Work points aces are 4/10 of total points in a suit (40%). In most recent systems, they’re worth more; how much more varies. Tysen points for example judge them as 6/13 (nearly half).

The best source I’ve seen for the kind of data you are looking for is Thomas Andrews who has some really thorough data on what each card is worth in each distribution. His stats seem to confirm that A is worth more than KJ (even AT vs KJT for example). Not a ton more - but slightly more tricks taken on average, in that example it is 8.82 vs 8.66.

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  • I'm experimenting with a system where A= 4.5, K= 3 Q=1.5, J=.75, and T=.25. Yes, AT is worth more than KJ, 4.75 vs. 3.75 in this system. As a "standalone," the A is worth 45% of the suit's total (10), and A, K, Q stand in the relationship 3, 2, 1, as in the Tysen system. It's my treatment of Js and 10s (1/10 between the two of them instead of 1/13) that differ from his. But it takes both J and T to equal this "1/10." Put another way, it takes the T to make up the difference between 1/13 and 1/10.
    – Tom Au
    Jul 1, 2021 at 6:31

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