:❤️:

Sora's game with Stephanie is just one of the many simplified versions of poker used to explore the underlying game theory. Like stripping the parts from an engine to see how it works, these shadows of the true game can illuminate the best way to play for real.

Another such game is poker without forced betting. Suppose you're playing a game of no-limit Texas hold 'em, identical in every respect to the game as it is commonly played but without blinds or antes. What is the Nash equilibrium strategy?

Without involuntary betting, there's no incentive for any voluntary betting under conditions of uncertainty. The Nash equilibrium is to only ever play with the best possible hand – that being pocket aces, at least before the flop – and to immediately fold to any aggression. This sets the opponents' expected reward for showing aggression to zero regardless of what cards they have, which is the same reward they get for checking behind on every street until showdown (at which point the best hand either wins nothing or splits the pot with an equally strong hand).

The only winning move is to leave and do something more worthwhile with your time.

This has two implications for real poker. The first is that, should you find yourself not winning, you should leave and do something more worthwhile with your time. The second is that poker is a game where the blind structure is paramount. As tournaments drag on and players hemorrhage chips into the pot for someone else to win, the blinds are the slowly advancing wall of death that eliminate the weakest players first.

After the first blind increase to 50/100, Shiro goes from a good position to a great position. After the second blind increase to 75/150, Shiro goes from a great position to a dominant one. Her massive pool of resources gives her a comfortable buffer to make raises when her range has even a microscopic edge. This strategy has a lot of variance, but by the 200^th hand the tight player has busted out and the loose aggressive player is faring poorly. The other players at the table have their own quirks and foibles, giving Shiro ample opportunity to drain their chips into her own stack.

The tournament must be getting to the point where the organizers start breaking up and consolidating tables. Six players is on the low end for a poker game; five is pushing it.

Sora ought to be paying attention to this as well, since he'll be directing her to a new table once she's finished butchering this one, but Shiro is also on the hunt for signs of players who don't know how to react when they're losing at tournaments.

Early tournament play is only analogous to cash games for players with an M-ratio of around 20 or higher (the current blinds sum to 225, meaning that anyone who is not down more than 500 chips is still in this position). Below that, the conventional wisdom is that players descend through varying stages of needing to play looser and more aggressive in order to avoid ignominious defeat. This is fundamentally why the tighter player is gone: having failed to adjust his preferred playstyle, he was simply not going to be dealt enough strong hands to afford to continue playing. Beating down people like him is the cornerstone of their plan.

Shiro would ideally start making completely outlandish preflop raises with objectively bad cards to bully the rest of her table around with her winnings, but by sheer happenstance the loose aggressive player's unaltered strategy is a good counter – she's toning that down whenever she acts before him.

(Having a reliable signal that your cards are marginal is to be avoided in most games, but Shiro still doesn't believe anyone here is reading her in enough detail to set up a counter-exploit.)

There remains value to be extracted from this table, since she's got a decent understanding of all of the players after playing with them for hundreds of hands, but『____』can win so much more by working together. Hopefully Sora's half of the plan is going apace.

The floor is in the process of getting the people who were up and about to sit down and go back to playing poker, along with encouraging tables to break for lunch in unison. Anyone who wants to play short-handed at the beginning of the tournament is welcome to it – there's a table of heads-up hold 'em on one side of the room right now – but six seems to be just right for letting skill shine through the noise of luck.

One such table is Chloe Zell's, where the action is coming to a close earlier than expected.

"What? No!"

"She still has sixteen hundred chips. Why is she leaving?"

"She's been drinking all morning," Sora points out laconically. A few people titter in response.

She was the ideal candidate: a woman playing against Zell, plausible for an outsider betting on the local action to pick as the weakest link, but virtually guaranteed to visit the little girl's room before anyone else busted out. She was the first to leave the table, which were his exact words when specifying the wager, but any reasonable interpretation would suggest that the wager is still unresolved. Two thousands chips is too many to let indeterminate phrasing pass by, which means the man he's gambling with will accuse him of cheating. He'll deny the accusation, and Disboard's response—

"Of all the crummy luck," he says, sounding resigned.

What? No, he's supposed to—

The hijack was the weakest player at the table, sure, but it's clear that Petra is getting worse over time. If she doesn't sharpen up (she won't) he's going to lose fair and square. Might as well get it over with before—

:Go.:

She smiles, laying her cards down

"Lunch time already, Petra? I suppose time slips past when you're having fun."

She leaves the table as well.

The rest of the players are quickly directed to new seats. The hijack, who really wasn't doing well either, breaks to follow Zell towards the food.

Both of you seem to think this is a draw, so you're splitting nothing.

"I ought to get playing," says the gambler. He takes his intact starting stack and leaves for the nearest open position.

Inconvenient. Sora will have to launder a few of Stephanie's chips back into the tournament through some other player. Maybe he'll strike up a conversation with the approaching hijack, see if he can induce some more side action.

Under the gun, Shiro raises by 450 chips.

The loose player has 1,090 chips remaining in the small blind. It's a tough spot, but it's only 375 to call and he has ace-two suited.

He makes the call, and the flop comes with an inside straight draw and a backdoor hearts flush.

The pot is now 1,050. Shiro raises by 525.

"You're making it too expensive to play this game," he mutters.

His inside straight draw, ace through five, is missing the three. Exactly four cards can give it to him – call it 1:4 odds, assuming Shiro doesn't have pocket threes – which is not great, but if you add the possibility of hitting two more hearts on the turn and river, the possibility of pairing his hole cards, or the possibility that Shiro has nothing and his ace wins, this is starting to look like a playable hand.

The problem is that raise. He only has 715 chips left – if he calls and loses, he's done for. Either he folds now and tries his luck later or he risks it all to get back to a safer position.

He tanks, drumming his fingers on the table while he debates the decision. The kid's weirdly intense stare isn't helping.

In the end, it's the size of his stack that makes the decision for him. These are the best odds he's going to get.

"All in."