Score
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Best
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Bid on a lot you can only half see. Winning is usually bad news about your cards.
Every lot is eight face-down cards and is worth the sum of all eight. A few of them are shown to you and a few different ones are shown to your rival. You each write a single sealed bid, and the higher bid takes the lot and pays exactly what it wrote; profit is the lot's true value minus what you paid. The catch is that you tend to outbid the rival precisely when the cards you happened to see were the high ones, so the lot is usually worth less than your sample suggested — bid your estimate and you bleed money, bid far below it and you never win anything. A fee is charged every round and it grows without limit, so hanging back forever is not an option either. Your score is the largest amount you ever held above your starting bank.
Start with the arithmetic. The eight cards run from one to nine, so an unseen card is worth five on average and the whole lot averages forty. Add up what you can see and add five for each card you cannot, and you have the honest estimate the game hands you. That number is not your bid. It is the number you shade down from.
Why shade at all, when the estimate is unbiased? Because it is only unbiased across every lot, including all the ones you lose. Filter down to the lots you actually win and the picture changes: you win when your sample ran high, which is exactly when your estimate overshoots. That selection is the whole trap, and it is why a bidder who writes down their honest estimate ends up losing money in a game where every estimate was fair.
In practice, take something like fifteen percent off. Too little and you buy lots that were never worth it; too much and you sit out round after round while the fee eats you alive. The shading also should not be a fixed habit — when you can see four cards your estimate is sturdier and deserves less discount than when you can see only two, and the game shows you fewer cards as you climb.
Finally, keep an eye on the fee line rather than the cards. Early on the fee is small change and almost any sensible bid turns a profit. Later it grows past what a typical lot can return, and at that point every round is a slow loss no matter how well you bid — the run is ending and your score is already set. What you are really playing for is the height of the pile you build in the middle rounds, before the fee catches up with the lots.