← Nines

What actually works

Everything below was measured by solving 26,000 positions exactly. No opinions.

A void is the single most valuable thing on your hand.

Hands with no void average 6.33 tricks (n=1630); with one void, 7.00 (n=363). Ruffing is compulsory, so a void does not merely let you trump in — it guarantees you will.

Nines are worth far more than their rank suggests.

No nines: 5.67 tricks (n=616). Two nines: 7.24 (n=460). Nothing beats a nine, and everyone who can beat the best card must try, so a nine drags out high cards and still wins.

Long suits are worth almost nothing — the opposite of ordinary card sense.

Longest suit of 3: 6.22 tricks (n=960). Longest suit of 5: 6.86 (n=194). Length is the first thing most card players count and it barely moves the number here.

Choosing trump well is worth about a trick and a half.

Best possible choice averages 6.459 tricks, worst 3.1, and simply naming your longest suit gets 5.795. You choose before seeing the dummy, so the gap between "longest" and "best" is the part skill can actually recover.

Do not name the suit holding your nine as trump.

Naming the suit with a nine in it averages 5.364 tricks, worse than simply naming your longest suit at 5.795. A nine in a side suit wins a trick outright; the same nine as trump is merely the top trump, which you were likely to control anyway.

Lead a top trump; a long side suit is the worst opening.

top trump keeps the contract alive 79% of the time (n=680), against 54% for a long side suit (n=1355).

After the opening lead there is usually nothing to decide.

The forcing rules mean most positions have exactly one legal card. Effort spent on the auction and the opening lead is worth far more than effort spent on the middle of the hand.

What to bid

Count your voids and your nines. Those two numbers predict more than anything else on your hand. The bid shown is the largest contract that hand class makes at least 60% of the time.

voidsninesavg tricksmakes 6+bid
005.5653%5
016.3571%6
027.1189%7
037.76100%7
106.2268%6
116.9891%7
127.7299%7

What to lead

How often the contract is still makeable after each kind of opening lead. The spread between the best and worst opening is larger than almost any decision later in the hand.

  • top trump
    79%n=680
  • side nine
    74%n=1320
  • low trump
    67%n=3769
  • high trump
    66%n=1365
  • side middle
    59%n=4576
  • side low
    58%n=2300
  • side high
    55%n=2635
  • long side suit
    54%n=1355

Which suit to name

Average tricks from each way of choosing trump, scored on the same deals. You choose before the dummy is exposed, so the gap between naming your longest suit and the genuinely best suit is what skill can recover.

  • best possible
    6.46
  • your longest suit
    5.79
  • your strongest suit
    5.49
  • the suit with your nine
    5.36
  • worst possible
    3.10

How often a contract is makeable

Share of hands where the declaring side can take at least this many tricks with the best trump choice. This is what a bid is up against.

  • 1
    100%
  • 2
    100%
  • 3
    99%
  • 4
    97%
  • 5
    89%
  • 6
    74%
  • 7
    52%
  • 8
    25%
  • 9
    10%

Generated from 500 deals · 26,000 exact solves · regenerate with bun src/distill.ts in apps/trainer.