The third card is the king of spades. Juno, who thus far has been simply bidding one higher than the rank of the prize, plays her own king. Either Sora bids his king too and they resolve the draw on the next round, or he doesn't and she wins the king. Either suits her fine – Sora has marginally better cards than her, but if he plays to win the draw using his other face cards he's more likely than not to waste them fighting for lower cards in the process. Her score lead is an advantage in this position.

Ace of diamonds.

It's moderately concerning that he's gotten rid of his ace on turn three, but the score is now 24–love and Juno has the king.

Sora flips over the next card, which happens to be the nine of spades. He considers his next play.

The Game of Pure Strategy is really a game of mixed strategy. Playing a pure strategy in the Game of Pure Strategy is a good way to lose. Consider the optimal play against an opponent using sealed bids selected at random: simply bid the same value as the prize each time, and your expected value is 59½ points to your opponent's 31½, for a win with a respectable margin of 28 points.

This strategy is utterly dominated by bidding exactly one rank higher than the value of the prize, and using the ace to bid on the king. This loses 13 points but wins the other 78 for an even more crushing victory. But consider also the pure strategy of bidding one higher than that, losing 25 points from the king and queen but winning the remaining 66. And so on…

There are two conclusions an alert player will immediately grasp:

1. Winning the ten through king nets you 46 points, enough to win outright. Any other victory requires more than four cards.
2. Unless your opponent is a moron, no pure strategy will allow you to do this.

Sora is therefore interested in playing like a moron. Not a complete moron, because Juno would see through an act like that, but up to this point he's played in a particular way. Making a calculated sacrifice in the form of the king, while shedding his weakest card in the process, is not prima facie a brilliant move.

The brilliant move is this one: Juno is going to make an overbid on the nine of spades, and he's going to let her get away with it.

So far Sora has played two equal-value bids followed by ditching his ace rather than fighting for the king. He still has the king of diamonds, giving him a suite of face cards that outranks hers, and he must be thinking of where to use it. Probably not on the nine. His king will be most valuable when the queen of spades arrives. She suspects he overbids in this spot, though. Juno plays the queen of clubs, hoping to nail Sora's jack or ten.

Two.

This is not ideal.

"You're going to lose at this rate," Juno remarks, sweeping the nine into her pile.

"Rates are subject to change," Sora replies, quoting the words and the cadence from a commercial for an insurance company.

The next card he turns over is the jack of spades.

She has the king and the nine already. Any two of the queen, jack or ten… won't quite clinch this for her, but if she can get there she'll be comfortably positioned for the win. She can't overbid on this card, but she still has a jack. If Sora overbids, so be it – he has to start playing his face cards eventually. She bids jack.

Sora is not going to overbid – in fact, he's going to bid jack too. He sweeps their bids to the side and reaches for the deck.

"In this round, we play for both the jack and the queen," he says, placing the queen of spades next to the jack.

The actual worst card. Juno flicks an ear irritably. She can't overbid, and she loses the jack and the queen in the process! Oh well, she can get rid of her ace here without too much risk of an underbid.

He could not look more chuffed if he tried. He plays the queen, just in case Juno uses her ten to call his bluff. That would be an awkward way to lose.

Then it's the three of spades in the prize pool. Sora bids five, his second-lowest remaining card. It's not much stronger than the two at this point, and it beats Juno if she bids three herself.

She doesn't need a three, and she suspects Sora is reasoning the same way. She bids three as well, just in case Sora decides to get rid of his own three.

Ace of spades. In most games this is a strong card to have in your hand – most games, but not here. He bids three, his lowest remaining option.

Juno is thinking along similar lines. She bids her lowest remaining card as well.

Next up: the six of spades.

What to bid? Juno has 33 points to his 27, so neither of them have the luxury of letting anything but the two of spades go without a fight. He has a small advantage in terms of high cards, so he can afford to overbid without it being obvious to Juno that she can afford to discard her four or her six. Ten of diamonds.

She anticipated that: goodbye, four of clubs.

Sora now has the queen, jack, six, three, and ace, tying it up at 33 to 33. She still has the ten, nine, six and seven of clubs in hand.

And Sora still has his king. He doesn't need to think about when to use it for long, because the next prize on the docket is the ten of spades. He can afford to whiff against Juno's low cards as long as he secures the ten, but if Juno plays her nine in hopes of a draw with his nine then so much the better.

Nice try, Sora, but it's not that hard to guess when you're planning to overbid. Your king sure outranks this six.

The three remaining prizes are the eight, five and two of spades. Sora has 43 points and wins if he takes the eight or the five. Juno, with 33 points, needs both the eight and the five. Sora has his nine, eight and six of diamonds remaining, while Juno strictly outranks him with the ten, nine and seven of clubs.

Next up: the eight of spades.

Juno has three options, as does her opponent. She wants to bid the card that's exactly one rank higher than Sora's, thereby securing victory if Sora bids nine or eight. Drawing her nine against his is also acceptable, since if the next street is the five she can automatically bid ten and win the game. The question is, what will Sora do?

She briefly considers using magic to try and guess Sora's strategy, but decides against it. His outward demeanor has been nothing but convivial since he sat down – not necessarily a hindrance if she had started earlier, but reading his microexpressions now without a baseline to compare against won't help her determine his strategy with any fidelity. They vary too much between individuals. Plus, this is a friendly game, and using magic goes against the 'pure strategy' ethos. It'll make winning less fun.

If she predictably bids ten in this position, Sora might well discard his lowest card again, giving him a clear shot at picking up the five. The safe strategy is bidding nine, which either wins the eight outright or draws and sends it to the next round. Then, if the next round is the five, she bids ten and wins. Sora knows that, but he can't do anything about it, so she may as well. Nine of clubs.

Juno is of course going to bid the nine. Bidding seven risks an immediate loss and bidding ten is a waste of a high card, which she has no reason to risk on this street. He can't let this one go, or else she'll have the highest card left to win the five with. He bids nine.

"Draw," he says, picking up the remaining two cards. He flicks the penultimate spade dramatically onto the table between them, next to the eight. "The second prize is the two."

He places his remaining diamonds flat on the table, one under each hand.

What does Sora do here? This is the last decision that matters. Juno considers the game as a whole, trying to get a feel for how this man thinks about strategy.