Why is an eight card fit considered the holy grail in partnership trump holdings? To at least partially answer this question we need to detour into another "rule" founded firmly in probability.. Odds split even and Evens split Odd.

Evens split odd and Odds split even, what does that mean? If your partnership possesses an even number of cards in a suit, the remaining, odd number of cards, in the opponents' hands are more likely to be evenly distributed between their two hands. Conversely, if your partnership holds an odd number of cards and the opponents hold an even number, their holdings are more likely to be skewed or unbalanced rather than evenly split. This concept is particularly important in understanding why an eight-card fit is desirable and why a seven-card fit, despite being over half the suit, may present significant difficulties.

The odds of a given suit distribution in the opponents’ hands is mathematically shown using Pascal’s Triangle.  Starting from the top if you hold 12 cards then opponents hold 1. It is either held by your LHO or RHO 50-50; Second line if you hold 11 cards and there are 2 cards held by your opponents, they are either 2-0 1-1 or 0-2 held by LHO, Both or RHO and the odds are 1:4, 2:4 and 1:4 respectively   ​​    

.  . . . .     ​​  1 1

. . .  . . .   ​​1 2 1

             1 3 3 1

 ​          1 4 6 4 1

​      1 5 10 10 5 1     you hold 8 cards; opponents hold 5.

 ​   1 6 15 20 15 6 1   you hold 7 cards; opponents hold 6.

The 6th and 7th rows of the Triangle represent the opponents holding 5 cards and 6 cards respectively. (you are holding 8 or 7)  The possible distributions expressed as probability percentages are:

6th row: 3.13%, 15.63%, 31.25%, 31.25%, 15.63%, 3.13% which correspond to distributions of 5-0  4-1 3-2 and then 3-2  1-4 and 0-5  on the other side.
7th row: 1.56%, 9.38%, 23.44%, 31.25%, 23.44%, 9.38%, 1.56% which correspond to distributions of 6-0 5-1 4-2 3-3 etc.

In a nutshell, if you hold 8 cards the outstanding cards will split 3-2 or 2-3 62.5% of the time. (Odds split evenly!) However, if you only hold 7 cards and opponents hold 6 they are split 3-3 only 31.25% of the time. The card split  4-2 or worse 68.75% of the time.   (Evens split Oddly.)  This is why an eight-card fit is considered beneficial maybe even magical.  Bridge bidding systems are designed to find an eight-card fit whether it be 4-4, 5-3 or 6-2.

Why is an eight card fit considered the holy grail in partnership trump holdings? To at least partially answer this question we need to detour into another "rule" founded firmly in probability.. Odds ..........

To bid or not to bid that is often the question.. When you are in the fourth seat you are in a unique position.   You can Pass for a zero.. A zero is better than going set and a zero is better than opening the door for opponents' making a part score by out bidding you.. How do they out bid you?  With the spade suit. Welcome to the rule of 15.. Simply this:  in the Fourth Seat if your High Card Points (HCP) and the number of spades added together is less than 15, then Pass.. Consider this hand I played recently vs BBO robots 

This hand is particularly interesting because in the third chair I would open 2♥ every time. In the fourth chair I can pass for a zero. It turns out it was the right thing to do.

To bid or not to bid that is often the question.. When you are in the fourth seat you are in a unique position.   You can Pass for a zero.. A zero i ..........

Bridge is a game of counting.  We count points; we count tricks; and we count individual cards. Of all of these, counting the cards played in each suit is probably the hardest. Personally, I probably lose more  tricks by being uncertain whether small  cards have "grown up" or not than any other way.  Rather than count individual cards or at least remember them I try to do two things: First, track sets of cards once for 4; twice around is 8; then, count again including the cards I can still see, hand and dummy.  Mentally I think it is eaeier to count  2X for 8 plus 3 is 11 than just remembering 11 and it has the added benefit of building a mental picture of the opponents' hands.. Do I still get it wrong? Sure I do.

Bridge is a game of counting.  We count points; we count tricks; and we count individual cards. Of all of these, counting the cards played in each suit is probably the hardest. Personally, I probably ..........

I came upon this recently and thought it was a good arrow to add to my arsenal. Suppose the auction has gone 1 ♥,  P,  1-NT,   P,   2  ♦  P,    ???,     Playing One No Trump Forcing the Opener responds with his best minor which denies  holing 6 hearts and it is up to Responder to advance the auction or place the contract. A bid of 3 ♦ by Responder  denies heart support and keeps the auction open but is undefined as to length and strength of the diamonds. The Impossible Spade treatment suggests Responder bid 2 ♠  to show good support in diamonds and to use the immediate bid of 3 ♦ as weak and preemptive. So, why is Two Spades “Impossible” and thus available for a conventional meaning?   Rewind the auction to the first two bids 1 ♥ followed by 1 NT (forcing). If Responder’s first obligation is to show a four card spade suit then holding four spades was denied by the 1-NT bid. Thus the spade bid can not be real. Use of the Impossible Spade does not eliminate a Non forcing Two Heart  call, nor the 3 card Limit Raise of Three Hearts in the auction 

Thus nothing seems lost by using the Impossible Spade in heart auctions.  Notably there is no "impossible heart."

I came upon this recently and thought it was a good arrow to add to my arsenal. Suppose the auction has gone 1 ♥,  P,  1-NT,   P,   2  ♦  P,    ???,     Playing One No Trump Forcing the Opener responds with his best minor which denies  holing 6 hearts and it is up to Responder to advance the auction or place the contract. A bid of 3 ♦ by Responder  denies heart support and keeps the auction open but is undefined as to length and strength of the diamonds. ..........

Sometimes I think my best friend is the MS AI, "Copilot."  I do a lot of fact checking and so on with Copilot.  I have also leaned I can discuss bridge bidding.  This is especially helpful when I am trying to determine what is "standard" and what is just my notion of "standard."  Here is a chart of Inverted minor bids with criss-cross after such a discussion. 

🧩 Inverted Minors Summary Sheet

(with criss-cross and passed-hand adjustments; OFF in competition)

➕ When Not a Passed Hand (No Interference)

🔹 Inverted minors are OFF after competition
→ Revert to standard raises, cue bids, or Jordan 2NT if applicable.

➕ When a Passed Hand

⚠️ Important Reminders

• All artificial raises are alertable, including criss-cross and inverted raises.
• Strong raise does not deny a 4-card major — show the major ASAP if holding one.
• If opponents interfere, do NOT use inverted minor structure — switch to standard competitive methods.
• Be cautious with passed-hand raises — no bid is ever game forcing.

Sometimes I think my best friend is the MS AI, "Copilot."  I do a lot of fact checking and so on with Copilot.  I have also leaned I can discuss bridge bidding. ..........