In the English language, “Quantitative” means to measure something based on its quantity rather than the quality. However, for the Bridge world, the term has a little bit more importance. It actually becomes the very important part of a hand evaluation system, the bidding system and for “judging” the most common hands in Bridge: the balanced hands.

All starts with Milton

Milton C. Work popularised the High Card Point (HCP) system in early 1900 that make hand evaluation in Bridge easier. Because of him, we are now accustomed to giving an Ace a 4 points, King for 3 points, Queen for 2 points, and Jack for 1 point.  So, the HCP system becomes the corner-stone of most of the popular bidding system in the world today.

However, we know now that HCP is not really the only factor, especially for a suit contract. In a suit contract, for instances, one can have only 10 HCP but yet can have all 13 tricks (Imagine a hand of all 13 cards of S). Therefore, many have tried to modify and adjust the number to make it universal but without success.

Having said that, we also know that the simple HCP system still works to the most common hand in Bridge: the balance hand.

The Quantitative Simplicity

Let us start with the most obvious one. How many HCP required to win all 13 tricks? While there are 40-HCP in total, we only need a 37 HCP. Imagine one day you get the most balanced hand (4333 distribution) with all the 37 HCP as illustrated below:

 ♠ AKQ ♥ AKQ ♦ AKQJ ♣ AKQ A 4333 Hand with 37HCP

So, you can see from the hand above not only we do not need all 40HCP, we cannot really fit the 3 Jacks left into the hand. But not only that, 37HCP also represent that there is no possibility that the opponent have an Ace to defeat the contract immediately.

Then, how about if we split all those high cards into 2 hands: the declarer hands and the dummy hands. You can easily understand that we will still be able to win 13 tricks.  As a matter a fact, now with 2 hands are in play, you can choose any 3 points from the total of 40 (e.g.: a King, a Queen and a Jack) and the chance is we still can make 13 tricks.

The implication is this: when your partner opens with balance 20-22 HCP and you found your self with another balance of 17 HCP, you know straight away that you can safely bid 7NT. Do you need to ask for a key card? No. Do you need to know the distribution? No.

Thus, that’s a quantitative method. You just need to know the total HCP and you can set the final contract confidently

Quantitatively Bridge

With similar exercise as above, we can now “estimate” the number of tricks as a function of the total HCP.

For example, in order to have 12 tricks (small slam), we probably cannot afford to have an Ace and King in one suit that defeat the contract immediately upon the opening lead. So, we cannot have opponent have this precious 7 HCP, but 6HCP is still okay. Because of that, we know that for a small slam we need to have a 34-HCP total HCP in both hands.

And quantitatively it works too. Let’s work it out: we need 37HCP for 13 tricks, so on average we need 37/13 = 2.8 HCP per trick. Therefore, for 12 tricks, we can calculate 12 x 2.8 = 33.6 HCP ==> 34 HCP. All synced.

With that explanation, you now understand that the table of point requirement you probably familiar with below, are from “quantitative” framework:

No of Tricks Contract HCP Needed
13 7NT 37 HCP
12 6NT 34 HCP
9 3NT 25 HCP
7 1NT 20 HCP

And again, we do not need to know specifically what kind of point it is, but as long as we have that point, we can follow the guideline above.
Of course, in reality, there are many other matters that in play for you to be able or not be able to fulfil a contract despite having the required HCP. For example the opening lead, the stopper, the location of top honor, the length of the suit, etc.
However, for an NT contract with balanced hands, the HCP is pretty much the most significant factor.

The Quantitative Framework a.k.a Quantitative Bid

So, the practical implementation of the “Quantitative” concept we discussed above are the bids in the following table below. When your partner opens with a balanced hand and with certain point range, quantitatively you can just bid game, slam or grand slam just by sum up your HCP. As long as your hand is balanced. It might still work when you have an unbalanced hand, but there are other risks such as you can miss out a higher point contract (e.g: you only play 3NT while others play 6, or 4 is making while 3NT fails, etc)

Opener Responder Bid
12-14 Balanced 13-19 Bid 3NT
20-21 Bid 4NT: Opener bid 6NT if maximum, Pass if minimum
22 Bid Direct 6NT
23-24 Bid 5NT: Opener bid 7NT if maximum, bid 6NT if minimum
25+ Bid Direct 7NT
15-17 Balanced 9-16 Bid 3NT
17-18 Bid 4NT: Opener bid 6NT if maximum, Pass if minimum
19 Bid Direct 6NT
20-21 Bid 5NT: Opener bid 7NT if maximum, bid 6NT if minimum
22+ Bid Direct 7NT
18-19 Balanced 6-12 Bid 3NT
14-15 Bid 4NT: Opener bid 6NT if maximum, Pass if minimum
16 Bid Direct 6NT
17-18 Bid 5NT: Opener bid 7NT if maximum, bid 6NT if minimum
19+ Bid Direct 7NT
20-22 NT 5-11 Bid 3NT
12-13 Bid 4NT: Opener bid 6NT if maximum, Pass if minimum
14 Bid Direct 6NT
15-16 Bid 5NT: Opener bid 7NT if maximum, bid 6NT if minimum
17+ Bid Direct 7NT
23-25 Balanced 3-8 Bid 3NT
9-10 Bid 4NT: Opener bid 6NT if maximum, Pass if minimum
11 Bid Direct 6NT
12-13 Bid 5NT: Opener bid 7NT if maximum, bid 6NT if minimum
14+ Bid Direct 7NT

Summary

“Quantitative” is basically a principle that we can set the final contract based on the total High Card Point we have, no matter what kind of point it is (Ace, King, Queen or Jack). The only caveat is that both of the hand have to be a balanced hand.

So, what about another type of hand that is played in a notrump contract but not balanced? That’s what you need to read next: NTT (No Trump Trick) Hands in Bridge