Hand Evaluation

Basic System

We can’t have a system of bidding in bridge if we don’t have some way of measuring what a hand is worth. Alas, learning how to judge the playing strength of a hand (that is, how many tricks it will take in different circumstances) is the work of a lifetime. Further, this judgement must change with every step of the auction; our KJ75 of spades becomes decidedly less valuable when the opponent to our left bids spades, regardless of the way we calculated the value we gave to it before. The same holding decidedly more valuable when partner shows four spades.

Since we have to have some estimate of strength to even begin to play, we must adopt simple methods that beginners can learn and then refine our methods as we progress.

Most of the methods begin with the point method originally proposed by Work. Each Ace is 4, Kings are 3, Queens are 2, and Jacks are 1. This means a deck has 40 points, and an average hand is 10 points.

If this is all you do, it isn’t that bad. We will now describe a number of adjustments that you should make, but on a lot of hands they cancel each other out and the basic count is a pretty good evaluation of the hand. Use the “Rule of 20” that we will describe below and the basic count; if you bid correctly you’ll do fine.

The number of points in a hand owing to just to its high cards is called its high-card points, or HCP. The number of points in a hand with adjustments for suit lengths or other factors is called simply its points. Thus if we say a hand has 10 points, that may include some adjustments such as adding points for shortness in that situation; but if we say it has 10 HCP then we mean at least that many points attributable to honor cards.

Generally Aces are important cards. If you have a hand with an AK in one suit and another Ace somewhere, consider it an opening hand.

We need to correct for badly placed honors. One can subtract one point from stiff Kings or “bad doubletons” (a doubleton which has a Queen or Jack but not the Ace) such as Qx, KJ, and KQ. If partner bids the suit, remove this correction. Subtract one for each singleton K, Q, or J.

Alas, if the Work count is all we do, then we are claiming that these hands all have the same value, 13 HCP:

  • ♠AQ7 ♥K54 ♦K32 ♣J432
  • ♠AQT ♥KT9 ♦KT9 ♣JT98
  • ♠AKQJT987 ♥- ♦KT987 ♣-
  • ♠A32 ♥K54 ♦KQJ ♣5432
  • ♠QJ ♥QJ ♦QJ2 ♣KJ7654

Clearly we need to account for distribution, intermediate cards such as 10’s and 9’s, and the way our honors are grouped together or scattered. The third hand will take eight tricks in spades for sure; the last one might well take very few tricks.

The two most popular ways to do this are to add count for length, or to add count for shortness. These days, length is much more popular. There is some logic to this – a long suit is often a plus, but a short suit is only a plus as a ruffing value if our side has found a fit. Thus, to count shortness from the beginning is rather optimistic.

To account for length, add one point for every card in a suit in excess of four. Subtract one point for a flat (4-3-3-3) hand.

A “good” hand for a given point count is one with the honors concentrated and / or touching, and with more than its expected share of 9’s and 10’s, with Aces and Kings more than Queens and Jacks.

Open all hands with 13 or more points, or a good 12. (A flat hand with 13 HCP is “good” too.) Generally, 25-26 points between the two partners are sufficient for a game at 3 notrump or 4 of a major suit, and around 29 points for five of a minor.

Another guideline is the “Rule of 20”: Add your HCP and the lengths of your longest two suits. If the total is 20 or more, consider opening the hand if you have at least 10 HCP. There are always other considerations to ponder as well, such as seat and vulnerability.

If you get a very distributional hand, such as a 6-5-1-1, be very aggressive – such hands will take a lot of tricks. “Six-five, come alive” is wise advice.

Adjusting to the Auction

As the auction continues, revalue your hand. Discount the values in suits bid on your left, and discount bad holdings such as QJ doubleton in suits bid by the opponents. But don’t discount such things in suits your partner bids.

“When you and your partner find a fit of at least 8 cards, stop and smell the roses”, says my teacher, Mike Moss. It is crucial to take a moment to re-evaluate your hand. There are two parts to this process.

First, add points for shortness. Count 1 for a doubleton, 3 for a singleton, and 5 for a void. (If you are the original opener and have supported partner’s suit, you might want to only count a void as one point for each trump you have).

Losing Trick Count

Secondly, when a fit has been found, and only then, make a Losing Trick Count, or LTC. A full exposition of LTC is in “The Modern Losing Trick Count”, by Ron Klinger. Here is a simplified (albeit less accurate) version.

Warning

LTC is used only when you have found an 8-card or longer fit.

In each suit count a loser for each Ace, King, or Queen you do not have, up to the number of cards you hold in that suit. A stiff King is one loser and a doubleton Queen is two losers. The maximum number of losers per suit is the smaller of three and the suit’s length.

Add a loser if the hand has no aces.

Example: ♠AQ8 ♥Q8 ♦KJ32 ♣AQJ3 has 1 + 2 + 2 + 1 or six losers.

Take your number of losers, add those of your partner’s hand, and subtract from 24 to get an estimate of the number of tricks you should take with your agreed-upon trump suit.

Unfortunately you can’t say, “Partner, how many losers?”, so you have to infer this from the bidding: an opening hand is about 7, a limit raise is 8, a simple raise is 9. A two-club opener is about 4. The hands in-between are 5 or 6.

Thus if you open one spade, and partner raises you to two spades, you want to be in game if you have five losers: 5 + 9 is 14, and 24-14 = 10. If you have six losers, you might want to seek more information with something like a help-suit game try, because you should be safe at the three level.

Use your adjusted point count together with your LTC to decide on game and slam tries. Often the LTC reveals that a hand is better or worse than it first appeared, such as an opening hand with an LTC of six or eight. When in doubt, go on with a known nine-card fit, but hold back with only eight.

Conversely, when you have a misfit, you usually want to stop as soon as you can. However, it is often true that 3N is the right place if you have the points for game. Most of the time you want to be in game if you have the points for it.

One final note: two hands of approximately equal value play better than two hands with much different strengths. In other words, 12 opposite 13 will usually play better than 20 opposite 5, because you will have less entry problems.

Bergen Method

Marty Bergen has invented a more elaborate method in his book, “Better Slam Bidding”.

The initial “starting points” for Bergen are determined by a five-step process:

  1. Calculate the Work Count
  2. Add 1 for every card over 4 in a suit
  3. Add 1 for each “good” suit, a 4-card suit containing three of the five honors.
  4. Subtract 1 for each “bad” doubleton – one that contains a Queen or Jack without the Ace.
  5. Calculate (number of Aces and Tens) - (number of Queens and Jacks). Divide this by 3, throwing away any fraction. Include that in the total. (if there are more Queens and Jacks than Aces and Tens, you’ll be subtracting).

As the auction proceeds, and a fit is found, adjust your hand as follows.

If you are going to be the dummy, add 1 for each doubleton, 2 for a singleton (but 3 if you have four or more trumps), and add up to five points for a void, but no more than you have trumps).

If you are going to be the declarer,

  • Add 2 for a singleton, 4 for a void, and exactly 1 point if you have two or more doubletons. Do not add anything for a single doubleton.
  • Add one point for each trump after five.
  • Add one point for a side suit with 4+ cards.

If you believe from your own count and that promised by partner that the partnership has 33 or more points, you should explore for slam; below 33, forget it.

Finally, when it becomes clear the hand is a misfit, count HCP only.

Examples

Let’s look at a comparison of the basic and Bergen models.

  • ♠AQ7 ♥K54 ♦K32 ♣J432

    This hand has 13HCP - 1 for a flat hand = 12 points, in either system.

  • ♠AK942 ♥KJ832 ♦ void ♣AKQ

    This hand has 22 points, 20 HCP plus 2 for length in the basic system. In the Bergen system we add two for length also. Clubs has three honors, but it doesn’t get the “good suit” bonus because it doesn’t have four cards.

  • ♠AT942 ♥KQJ4 ♦ void ♣AKT7

    This hand has 17 HCP, plus one for length in the basic system. In the Bergen system we add 2 for the 2 “good suits”, hearts and clubs, for a total of 20 points.

  • ♠QJ ♥QJ ♦QJ2 ♣KJ7654

    This hand has 13 HCP, minus two for bad doubletons, plus two for the six card suit, or 13 points. In the Bergen system we have seven Queens and Jacks, and no Aces or tens, so our adjustment is -7 / 3, so discarding the fraction we get -2. The Bergen method would not open this hand.

Assuming a fit has been found, the losing trick counts here are 8, 3, 2, and 8, respectively.

For another system, sort of between standard and Bergen in complexity, try Pavlicek Points. And to raise your consciousness, assume the lotus position and try Zar Points.

What Bid To Open

Assuming you have a good 12 point hand or more, what do you open?

First see if you qualify for a no-trump opening. You need 15 to 17 points and a balanced or semi-balanced hand. As we’ll see in the chapter on no-trump openings, with 18-19 you bid a suit and then 2N on the second round; with 20-21 you open 2N; with 22 or more, you bid 2♣ and then 2N on the second round.

If you do not qualify for a no-trump opening, you use this order of preference:

  1. Your longest suit five cards or longer, or the higher-ranking of two five-card suits.
  2. A four-card minor.
  3. If exactly 4=3=3=3 or 4=4=2=3, open 1♣.
  4. If exactly 4=4=3=2, open 1♦.

If you have two three-card minors you can also open the best one if one is really the suit you want lead, if you agree on this with your partner. If a partner tries to talk you into the ‘may be short’ club if 4=4=3=2, resist.

Sometimes one strays outside the rules: certain hands cry out to be opened 1N with 14 HCP, or 1♠ with four wonderful spades. Just remember, each such bid erodes your partner’s confidence in you and makes him pull in a little the next time. Use your freedom sparsely, a few times a year.

Sometimes there are strategic considerations to consider when choosing an opening bid. See Reverses.

Reverses

Reverses by Opener

Sometimes beginners will say they “don’t play reverses”. That is not an option.

A reverse by opener is a rebid that meets two tests:

  1. Opener’s rebid is in a suit higher than his original suit, AND
  2. Opener’s rebid is a level higher than responder’s bid.

A reverse shows about 16/17+ points (including distribution) and an unbalanced hand with more cards in the first suit than in the second. A reverse is absolutely forcing for one round unless opponents interfere, but not forcing to game.

Example: 1♦ - 1♠ - 2♥. Hearts is higher than diamonds, and the 2♥ bid is up a level. Opener has more at least as many diamonds as hearts (typically 5-4).

How do we know that?

If opener’s shape were balanced, say 2=4=4=3, they would have opened 1N with 15-17 HCP; they would rebid 2N with 18-19 HCP. So while it is possible that opener has this shape when they open 1♦, when they bid 2♥ it rules out a 12-14 point balanced hand; hence my suggestion that they usually have five diamonds. A 1=4=4=4 is still a possibility.

Why does a reverse show a strong hand? Consider opening a 12 point hand that has five hearts and four clubs. We open it 1♥ and our partner replies 1♠. Our next bid is 2♣. Then,

  • Suppose partner has ♠J8642 ♥3 ♦Q86 ♣KT73. He can pass.
  • Suppose partner has ♠J8642 ♥KT ♦QT86 ♣86. He can bid 2♥. That shows a minimum with a preference for hearts over clubs.

But, if we had five clubs and four hearts, and bid 1♣ - 1♠ - 2♥, with the first hand partner would have to bid 3♣ to show that he preferred clubs to hearts. That would put us at the 3-level with a total of only 18 points between the two hands. We’d like around 23 points to be comfortable at that level. Subtracting six from 23, we see that we need opener to have around 17 to be safe.

In the auction 1♥ - 2♣ - 2♠, partner has shown at least 10 points, so if responder has to preference to 3♥, there is no problem – we’re already known to have around 23 points. Therefore, you need not consider this a reverse.

Note

There is no question about this if playing 2/1 game forcing, but this is a matter of agreement in SAYC. I follow Larry Cohen here in feeling this bid need not show extras, for the reason I gave.

Typically a hand that will reverse will have a five-card suit and a higher four-card suit. When you bid such a hand, you have to open the five-card suit, but on your rebid you cannot show your four-card suit unless you have the values.

For example, with five diamonds and four hearts, if the auction goes 1♦ - 1♠ - 2♥, opener has reversed. Lacking that many points, opener may have to bid an imperfect 1N or repeat diamonds.

With 4 diamonds and 5 clubs, such as ♠92 ♥Q9 ♦AQJ5 ♣KQT43, we have a similar dilemma but without the risk of hiding a major. If we open this hand 1♣, and partner answers with a major or notrump, we have a problem. So some people will open this 1♦ instead. Others will bite the bullet, open 1♣, and rebid 2♣ if they have to, even though that suggests you might have a six card suit. Expert fashion seems to go up and down with hemlines on this one.

Obviously the quality of the two suits will influence the decision, unless you just always open 1♣.

Note

When you make your opening bid, you’ll need to think about what you’ll do next depending on what your partner does.

When you open a suit and partner makes a negative double, can your response be a reverse? For example, 1♣ - (1♠) - X - 2♦. Cohen suggests no. Technically, your partner promised hearts and diamonds and you’re just choosing. Partner shouldn’t be wanting to preference back to clubs.

Note also that a jump rebid in a new suit like 1♦ - 1♠ - 3♥ is a jump shift, showing a huge (a good 18 to 21) hand.

Responding To Opener’s Reverse

If opener has reversed, as responder you must bid unless your RHO takes you off the hook by interfering. If you have already shown 10+ points of course the auction is now game forcing and you can just bid naturally. If you have a good 8 or more, you’ll want to get to game.

So the problem is what to do with a minimal hand. If you bid opener’s first suit, it is a simple preference with a minimal hand. If you repeat your own major suit, you’re showing five cards and a minimum.

2N!(relay) is a conventional bid telling your partner that you may have a minimal hand. It asks opener to rebid his first suit; then you will pass or correct to your suit. This convention is called Ingberman 2N or Lebensohl Over Reverses. Your partner should say “alert” (which is why I used the exclamation point).

Any bid other than a suit preference or 2N is game forcing.

Recommended reading: Downey and Pomer’s book “Standard Bidding With SAYC” has a long section on reverses with a lot of examples.

Reverses By Responder

When responder reverses, it is just a game-forcing natural bid. For example, 1♠ - 2♣ - 2♠ - 3♦ is a game-forcing reverse, since diamonds are a higher suit than clubs. Again, the same principal is at work; an opener who wanted to prefer clubs is now forced up a level compared to bidding diamonds first and clubs second.

Note that 1♣ - 1♦ - 1♥ - 1♠ does not count as a reverse; we’re not up a level. To show the bigger hand responder will have to bid 2♠, not 1♠.

Sometimes a responder reverse is the fourth suit bid and therefore unlikely to find a fit with partner, so most play it as a conventional bid that is one-round or game-forcing but not showing that suit, asking partner to bid notrump with a stopper in the fourth suit. See Fourth Suit Forcing.