Boop. Two theories, both of which are possible, the second of which is easier than the first and more likely, but the first makes for better Nao. Second makes for better Akiyama. We'll see how it works.
1) Group of the Three Profiteers refrains from bidding. Their group of three ends up losing, and everyone else moves on. This would be reason why the three of them teamed up and why Nao's strategy seems to have failed horribly. If this happens, it will be Akiyama orchestrating it through whats-her-face.
2) This one is easier to have happen. Akiyama bids on one of the next two lots. Yep, that's pretty much checkmate. Everything becomes chaotic as people frantically discuss whether to bid or not. If Akiyama wins a lot, gg, need to redo everything, since we can't have more than 2 4-player lots. Even better, if Akiyama wins both lots, G! G!, we're at five 3-player lots and one 4-player one. What to do
now, LGT?
Even if someone wants to win the lot, that means they've given up on Akiyama, but... does anyone
really want that? Essentially, everyone has two choices: outbid Akiyama to get someone they don't want on their team, or let Akiyama take it, and you can't join with him, as a 2-group can't pair up with a 3-group.
My guess would be that he'd bid last-second on the next lot and win it. Together, the two of them would bid on the last and final lot while everyone is confused. Now, the only four-player group is Yokoya, Nao, and co., and the LGT can't have a game with just them. Well, they could. But would they be happy with this, considering they set this up to end up with more players than just four (a team game, played by 4-player teams)? Also, Nao can't really hold her own against Yokoya, I think we can agree. So this will let the board reset and throw a wrench in everything. It's also
extremely easy for Akiyama to do, since no one wants the lots.
The more difficult situation is my first situation, but I can definitely see it happen, if Akiyama can convince the three of them to drop out. Then we get the Akiyama vs. Nao/Yokoya situation we've been gearing up to see, and Nao gets a small victory over Yokoya.
Rereading the rules explanation, they do not explain what happens if not enough teams are formed. This leads me to believe it less likely that the second option is the case, even if it's MUCH easier and more reasonable. In addition, Yokoya seems partly confident that Akiyama isn't
skilled enough to pull whatever it is off. This hints at the solution being something more complex and difficult to convince people to do. Of the two, only the first requires real skill to pull off and requires convincing someone of something they're not likely to do.
Of course, if I were Akiyama, I'd take the second option every time (but that's because I'm a rebellious
idiot brat). I'd form the two-man team and after doing that calmly ask the dealer what happens if not enough four-man teams can be formed, pointing out that at the moment, at most 2 instead of 4 teams can be formed. I'd ask what would happen if, say, just suppose, we were to end up with five 3-man teams and a single 4-man team. You can't rule any team weaker than another and thus split it up (while you could argue that if it's one 2-man team, three 3-man teams, and two 4-man teams). Thus, either everyone has to move on, or the auction has to be redone, as it's not possible to count one group as weaker than the rest. Each team is made up of three players and their money. In total, it will be the exact same. You could argue that the team whose largest player's sum is highest is strongest. However, you could also argue that the team whose smallest player's sum is smallest is weakest. Due to the nature of the bidding, this is likely to result in opposite situations. Debt from previous games is ignored in individual games, so taking that into account would be unfair. Essentially, getting five 3-man teams and a single 4-man team results in LGT standstill, and they never addressed that initially. They could try and split up the Akiyama-whoever group to "solve" that (they were the last group to form), but then I'd mention how that's "unfair" (what if I really want to be on a group with them, and no one else does!).
So, reasonably, they have to either accept the 3-man teams or restart the auction. They could keep the Yokoya team formed. However, Akiyama could also work with everyone to force only 3-man groups. This is basically a rebellion until things change, and either LGT can change, or they can force a penalty to speed things up. Still, I doubt that's happening, since it would take too long, and the manga's not going in that direction. But it's fun to think about?
Most likely is scenario #1. Easiest to pull off irl but much more risky is scenario #2.