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.
Everything below was measured by solving 26,000 positions exactly. No opinions.
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.
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.
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.
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.
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.
top trump keeps the contract alive 79% of the time (n=680), against 54% for a long side suit (n=1355).
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.
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.
| voids | nines | avg tricks | makes 6+ | bid |
|---|---|---|---|---|
| 0 | 0 | 5.56 | 53% | 5 |
| 0 | 1 | 6.35 | 71% | 6 |
| 0 | 2 | 7.11 | 89% | 7 |
| 0 | 3 | 7.76 | 100% | 7 |
| 1 | 0 | 6.22 | 68% | 6 |
| 1 | 1 | 6.98 | 91% | 7 |
| 1 | 2 | 7.72 | 99% | 7 |
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.
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.
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.
Generated from 500 deals · 26,000 exact solves · regenerate with bun src/distill.ts in apps/trainer.