[Swammerdam]

There are various arithmetic rules to guide early bidding decisions. I mention three of them:
1. Rule of 20. Open when HCP + two longest suits sum to 20 or more
2. Open 2C with 4 or more QT and 4 or fewer losers
3. Open 4th hand if and only if spade length + HCP is at least 15.

With one (interesting?) exception Rule 1 is equiv to *Open with 13 or more Goren points." Opening with 12 or 12½ Goren points is condoned by aggressive bidders: the opening threshold is a matter of scoring method, style and agreement. Conservative players from circa 1960 might want 14 Goren points, or at least 13½.

The one exception is THREE-Suiters, where Goren overrates distributional value compared with "Rule of 20" scoring. For example KJ9xx Axxx QTxx (void) has 13 Goren points, but only 19 "Rule of 20" points. With such a three-suiter the Rule of 20 will often give the better result. Details matter: With the hand shown open 1S and bid a red suit if partner answers 2C. Reverse clubs and spades however and 1S response to 1C is rather unpleasant so the hand shouldn't open at all. Players who reckon with QT and losers, will be pleased that the example hand has only 6 losers, but unhappy about only 1½ QT.

Rule 2 seems pretty good.

Rule 3 -- "Open in the pass-out chair if you have 15 points or more, with spades counting as one point each." IOW open with 13 points and at least 2 spades or 10 points if you have 5 spades. With a void in spades Pass unless you have 15+ HCP.

I've been following this Rule and it seems to work out well. BUT I'm not as intuitively clear on its application as I am with Rule 1 or 2. For starters, it seems unlikely that the optimal function mathematically would have slope of exactly 45 degrees, i.e. with spades == hcp everywhere. Do you open with a "good 14"? With a "bad 15"?
MY QUESTION IS: How do experts interpret the "Rule of 15"? Do thy tilt toward 14½ or 15½?

[jdiana]

I'm sure someone will tell you that experts don't use these rules - they use their judgment. But I'll leave that to them.

I would just say that the Rule of 15 is used when deciding whether to open or pass with a borderline hand. If you have a full opener, you would open in 4th seat just as you would in first or second seat, regardless of how many spades you hold. The logic behind it is that HCP are likely to be more or less evenly distributed so, if you open, you're probably going to be in a battle for part score. You don't want to give the opponents the opportunity to come in and outbid you if they have spades. No idea how that relates to your mathematical question.

(P.S. I had to look up Goren Points. Kind of interesting. A quick glance suggests that it's quite conservative by modern standards, which doesn't mean it's not good bridge but likely to be anti-field in a lot of settings, I think. I seem to be among the last people who still care about having defensive tricks ("quick tricks") when opening.)

[Stephen Tu]

Swammerdam, on 2025-January-03, 14:17, said:

I've been following this Rule and it seems to work out well. BUT I'm not as intuitively clear on its application as I am with Rule 1 or 2. For starters, it seems unlikely that the optimal function mathematically would have slope of exactly 45 degrees, i.e. with spades == hcp everywhere. Do you open with a "good 14"? With a "bad 15"?
MY QUESTION IS: How do experts interpret the "Rule of 15"? Do thy tilt toward 14½ or 15½?

Generally, open anything 4th chair that you'd happily open in 1st/2nd, ignoring the spade length entirely. (You think you probably have enough hcp/playing strength to buy the contract successfully or will have enough defense against say 3 spades). Only apply the 15 pt Pearson guideline as like a final tiebreaker with borderline stuff that you'd pass 1st/2nd, or at least strongly consider passing.

[pescetom]

Stephen Tu, on 2025-January-03, 15:01, said:

Generally, open anything 4th chair that you'd happily open in 1st/2nd, ignoring the spade length entirely. (You think you probably have enough hcp/playing strength to buy the contract successfully or will have enough defense against say 3 spades). Only apply the 15 pt Pearson guideline as like a final tiebreaker with borderline stuff that you'd pass 1st/2nd, or at least strongly consider passing.

Somewhere inbetween IMO.
It's more like 2nd than 1st, spades do count when you hope to buy the contract, your partner's opening style counts too.
Rules are guidelines for beginners, not straightjackets.