Before any rules, a simpler question: if you win the bid and name your suit, how many points does your team take? To answer it, 800,000 hands were dealt; each seat in turn was made the bidder at 4, named its best suit, and the hand was played out with basic card play. The declaring team's points were then sorted by what the bidder could see before bidding.
A hand takes 0 to 10 points. "Declaring at 4" is the average result of winning the bid at 4 with such a hand: your team's score minus theirs, where a failed bid costs the bid and gives the other side its points.
Top cards decide it
Counting the ace, king, queen, jack, off-jack and jokers in your suit:
| Top cards | Share of hands | Points taken | Makes 4 | Declaring at 4 | Declaring at 5 | Declaring at 6 | Declaring at 7 | Declaring at 8 |
|---|---|---|---|---|---|---|---|---|
| 0 | 10% | 4.3 | 56% | −3.9 | −5.2 | −6.9 | −8.8 | −11.0 |
| 1 | 35% | 5.2 | 69% | −1.5 | −2.7 | −4.3 | −6.3 | −8.8 |
| 2 | 36% | 6.0 | 80% | +0.8 | −0.2 | −1.7 | −3.7 | −6.3 |
| 3 | 16% | 6.8 | 89% | +2.8 | +2.0 | +0.8 | −1.1 | −3.8 |
| 4 | 3% | 7.4 | 95% | +4.5 | +4.0 | +3.1 | +1.5 | −1.1 |
| 5 | 0% | 8.1 | 98% | +6.0 | +5.7 | +4.9 | +4.0 | +1.9 |
Each top card is worth about three quarters of a point and ten percentage points on making the bid. Each level you bid higher costs another point or two. That is the arithmetic behind every rule on the ladder.
Trump count barely matters
The usual advice is to count your trump. The declaring team's points hardly move with it, because the bidder collects every trump left in the deck anyway:
| Trump in your suit | Share of hands | Points taken | Makes 4 |
|---|---|---|---|
| 3 | 24% | 5.5 | 73% |
| 4 | 47% | 5.7 | 75% |
| 5 | 23% | 5.9 | 77% |
| 6 | 5% | 6.1 | 79% |
| 7 | 1% | 6.4 | 82% |
Trump count includes the off-jack and the jokers; the suit is the one the bidder would name, so three is the fewest it can hold.
One card at a time
Points taken with and without each card in your suit, over all hands:
| Card | Without | With | Difference | Makes 4, with |
|---|---|---|---|---|
| the ace | 5.31 | 6.61 | +1.30 | 88% |
| the king | 5.58 | 6.20 | +0.62 | 82% |
| the queen | 5.58 | 6.22 | +0.64 | 81% |
| the jack | 5.61 | 6.19 | +0.58 | 81% |
| the off-jack | 5.67 | 6.00 | +0.34 | 79% |
| a joker | 5.69 | 5.87 | +0.18 | 77% |
| the 10 | 5.79 | 5.63 | −0.16 | 74% |
| the 3 | 6.00 | 5.18 | −0.82 | 65% |
| the 2 | 5.65 | 6.02 | +0.37 | 78% |
- The ace is worth about two other top cards.
- The 3 in your own hand is a liability with basic card play. It is worth three points to whoever captures it, and a bidder who cannot protect it hands those points over. The ladder's rule 4 comes from this, and expert players can ignore it.
- The 2 is a quiet point: it scores for whoever was dealt it, so it is one point you cannot lose.
Basic card play only. The table is for finding rules; the ladder is what proves them, with both kinds of card play.