A contract settles at the sum of three cards drawn without replacement from ten cards numbered 1 to 10, at Rs 100 a point. Quote a two-way market before any card, after the first card shows 9, and after the second shows 2, keeping pace with the dealer.

Fair value is 16.5 before any card, 19.22 after the 9 and back to 16.5 after the 2; quote about 15 / 18, then 18 / 20.5, then 15.5 / 17.5. The shortcut is cards shown plus cards to come times the average of the unseen pack: 3 x 5.5; 9 + 2 x 46/9; 9 + 2 + 44/8. The 9 and the 2 average 5.5 between them, so the fair value returns to its start, but the spread of outcomes has shrunk from 4.4 to 2.7, so each market is tighter than the last.

Three cards from a pack whose average is 5.5 are worth 3 x 5.5 = 16.5 on average. The spread is wide: the sum runs from 6 to 27, and its standard deviation is 4.39, a little less than three independent draws would give because drawing without replacementEach card drawn is removed from the pack, so the cards that remain are no longer an unbiased sample of the original ten. pulls the cards apart. A market of 15 bid, 18 offered puts fair value just inside the middle with 1.5 points of edge each side, about a third of a standard deviation, which is tight enough to attract trades and wide enough to survive the first card. Say it in one breath, because the dealer is already reaching for the pack.

Use one rule at every stage: fair value equals the cards already shown plus the number still to come times the average of the cards still in the pack. The pack summed to 55; take out the 9 and the nine cards left sum to 46, an average of 5.11. Fair value is 9 + 2 x 5.11 = 19.22, not 20: the high card lifted the sum but also removed itself from what is left, so the two cards to come are worth less than they were. The uncertainty has fallen as well, to a standard deviation of 3.66, so quote a little tighter: 18 bid, 20.5 offered, which keeps about a third of a standard deviation of edge each side. A candidate who quotes 19 / 21 has priced with replacement and will be sold to by anyone who did the subtraction.

After the 2, the cards shown sum to 11 and the eight left sum to 44, an average of exactly 5.5 again. Fair value is 11 + 5.5 = 16.5, the same as before any card, because the two cards drawn average 5.5 between them, so the pack that remains looks, on average, like the one you started with. That is the lesson of drawing without replacement: the fair value is not a running total that only climbs, it is a recomputation from the pack, and a high card followed by a low one leaves the pack unchanged. The outcomes are now eight equally likely sums, 12, 14, 15, 16, 17, 18, 19 and 21, with a standard deviation of 2.69, so quote 15.5 bid, 17.5 offered: a point of edge each side, 0.37 of a standard deviation, the same proportion as before.

Scale it with the uncertainty. The standard deviation goes 4.39, 3.66, 2.69, so a width of 3 points, then 2.5, then 2 keeps the edge at about a third of a standard deviation each time. Tightening as information arrives is how you keep the flow: a quote that stays 3 wide when only one card is left will be undercut, and one that was 2 wide before any card would have been run over by the first 9 or 10. Watch the other side too. If a candidate lifts your 17.5 offer the moment the 2 appears, they may simply have done the arithmetic faster; if the same candidate keeps lifting, start asking what they see that you do not. The limitation of the whole method is that it prices the mean and the spread and nothing else: in a live game your inventory matters as much, and after selling three lots at 17.5 you should move the market down to buy them back rather than keep selling.