Bidding strategy, measured

How many tricks should you bid? Every other guide says it depends on your high cards. We counted — and we publish the one place our own arithmetic falls over too.

Every other guide to this game answers that question with an adjective. We can answer it with a number, because we built the engine: 240,000 hands, dealt and played out by strong bots at every seat, with the tricks each hand actually won recorded against the cards it was dealt.

What comes out is a value in tricks for each kind of card. Add them up and you have your bid. The method is at the bottom of the page, along with the things these numbers do not tell you — of which there are several.

The ten-point count

The short version, usable at a table with no paper. Score your hand:

• 9 — A Wizard
• 7 — Trump, Jack or higher (trump 10–13)
• 7 — Off-suit Ace or King (12–13)
• 4 — Any other trump (trump 1–9)
• 2 — Off-suit Eight to Queen (7–11)
• 0 — Off-suit Seven or lower (1–6)
• 0 — A Jester

Add it up and drop the last digit — that is roughly how many tricks the hand wins. Nineteen points is 1.9 tricks, so you bid 2.

A worked hand, round six, trump is hearts: the Wizard (9), the heart King (7), the spade Ace (7), the club Nine (2), and two low diamonds (0). That is 25 points → 2.5 tricks — a genuine coin-flip between bidding 2 and 3. Take the lower one unless you are chasing, because the scoring punishes overshooting and undershooting identically.

What one card is actually worth

The measured values, pooled across three to six players. Our deck numbers each colour 1–13 with no face cards; if you are holding a standard deck, 13 is the Ace, 12 the King, 11 the Queen and 10 the Jack.

Pooled across 240,000 dealt hands. R² = 0.674 — see the limits.

Four things the numbers say that players do not

1. An off-suit Ace is worth as much as a high trump. 0.65 against 0.66 — the same card, for bidding purposes. Players systematically hoard trump and undercount the top cards of their side suits, and the measurement says that is simply wrong.

2. A low trump is not junk. 0.43 tricks — more than double a middling off-suit card at 0.19. A trump Three wins a trick surprisingly often, because it only has to outlast the trumps, not the whole deck.

3. Low cards are worth nothing at all. Not "not much" — 0.00. A hand of one Wizard and six low cards bids one. The temptation is to round up to two because six cards feels like a lot of hand. It is not; it is six cards that lose.

4. A Wizard is not quite a trick. 0.94, not 1.00, because Wizards collide: play two into one trick and the second one wins nothing. With four in a 60-card deck that happens often enough to shave the value.

The Jester scores 0.06, which is zero with noise on it. Count it as zero — though note it is not negative, because a Jester is a guaranteed safe discard, and that is worth a shade more than a low card you may be forced to lead.

Which rounds are hardest

How often our own bots hit their bid, by round, at a four-player table — the most common size. Read this as a difficulty curve, not as a target to beat.

Round one is a coin-flip you can usually win: one card, and 71% of bids land. From there it falls away steadily as the hands get longer and there is more to go wrong.

Then the last round goes the other way. In a four-player game the fifteenth round deals all 60 cards, so no card is left to turn over and there is no trump — and the hit rate jumps back up to 48%. No trump sounds chaotic and is the opposite: with nothing wild in the deck but the eight special cards, high cards in long suits simply win, and a hand becomes much easier to read. The average bid drops from 3.97 to 3.09 and more of those bids come in. Bid the no-trump finale with confidence.

One exception, and it is ours rather than the game's: in a three-player game the final round deals twenty cards each, and there our bots are at their worst — they miss by 2.53 tricks on average, against 1.06 the round before. A twenty-card no-trump hand is the one shape the counting above handles badly. We would rather publish that than hide it.

Your hand tells you less at a big table

The same model fitted per table size, with R² — the share of the variation in tricks won that the dealt hand explains:

At three players your cards explain 73% of what you win; at six players, 57%. More players means more hands interfering with yours, so the same cards tell you less. Practical consequence: bid more cautiously at a big table, and pay more attention to what has been bid ahead of you, because your own hand is a weaker signal there.

How this was measured

The harness is packages/server/hand-stats.mjs in our own repository. It plays 1,000 complete games at each of three, four, five and six players — 240,000 dealt hands in total — choosing every seat's trump call, bid and card with the engine's strongest bot setting. The moment a round's bidding ends and before a card is played, it snapshots each hand, sorts its cards into the seven kinds in the table above, and pairs that with the tricks the hand went on to win.

Those pairs are fitted by least squares with no intercept, so each weight reads directly as "a card of this kind wins this many tricks on average". No intercept because a hand of no cards wins no tricks. The counts sum to the round number by construction, which is what makes the weights add up to a usable bid.

The simulation runs with screw the dealer on — the dealer may not make the bids total the round number — because that is the default at our tables and in the engine. It also checks, every round, that the tricks awarded total the number of cards dealt; if that ever failed the numbers would be meaningless, so it throws instead of reporting.

What these numbers do not tell you

A third of it is not your hand. R² is 0.674, so roughly 33% of the variation in tricks won is something other than the cards you were dealt: how you play them, what everyone else bid, who sits where, and luck. The count gives you a starting number. It cannot give you a safe one.

It measures bots, not people. Every seat is played by our engine's strongest setting, which is a good player and not a great one. Against humans who signal, revenge-bid and remember what you did last round, the card values will shift — the top cards least, the marginal ones most.

It ignores position. Bidding last is worth real information, and the model has no term for it. That is the next thing we would measure.

Trump length is folded in, not broken out. Six low trumps are stronger than six low trumps spread across six rounds would suggest, because they run the suit. The partition counts cards, not shapes.

Everything above is reproducible: run the harness and you will get these numbers, because the bots are seeded. The tables on this page are generated from its output at build time rather than typed in, so the page and the measurement cannot drift apart.

Test it on a real hand

The counting method takes about three hands to become automatic, and you do not need to assemble a group to practise it: play against the computer seats two bots and deals immediately. Count your hand, bid the number, and see what the round does with it. Free, no sign-up, no ads — and it keeps score, so you can watch whether the count is working.