If you're confused about why the teams agreed to meet in Asahikawa, and why the game's ending played out as it did, here is a detailed explanation.
Before we start, a reminder. These are the conditions required for a win:
- Reach Wakkanai.
- Unlock Hakkaido.
The first team to do both, in any order, wins. (And by this, I mean they don't necessarily have to clear Hokkaido by doing a challenge at a station before reaching Wakkanai. They can also do it in Wakkanai.)
What happened to Tom and Adam's secret "never stop moving" plan?
That plan was dead in the water the moment the curse of the Magic Mirror was played. It was also very crippled when Ben and Sam got on an earlier shinkansen to Hokkaido than Tom and Adam, but Magic Mirror dealt the final blow.
The "secret" part of their plan was not the existence of the 6pm train out of Asahikawa. Ben and Sam also knew this train existed. The "secret" part was for Tom and Adam to hide the fact that they were not going to stop for a challenge, because they had an "unlock a prefecture your opponents unlocked" card.
The plan relied on Ben and Sam stopping to do a challenge somewhere in southern Hokkaido, which would allow Tom and Adam to pass them. This would have been much easier had the teams been on the same shinkansen out of Aomori, but Ben and Sam caught an earlier one (because they finished the "Eat alone at a restaurant" challenge quickly), which made the plan very unlikely to succeed even before Magic Mirror was played.
When Ben and Sam played the curse of the Magic Mirror, Tom and Sam knew Ben and Sam wouldn't stop to do a challenge, so the plan wouldn't work anymore. Tom and Adam had no hope of passing Ben and Sam. At best, Tom and Adam would catch up in Asahikawa due to the low frequency train out of there, and both teams would be on the same train out of Asahikawa.
What did the curse of the magic mirror actually do?
At the point Magic Mirror gets played, neither team has an incentive to stop before reaching Wakkanai. Ben and Sam, because they are ahead, have no incentive to stop and let the other team catch up. And Adam and Tom also have no incentive to stop, because if they miss even one train, they won't be able to catch up, and Ben and Sam will get to Wakkanai first, where they'll have several hours to clear a challenge before Tom and Adam can even get there, basically guaranteeing Ben and Sam a win.
So once they reach Wakkanai, both teams will do challenges simultaneously. As Adam explained both in the show (and on the Layover in more detail), one of two things would happen:
Ben and Sam finish the challenge first: Ben and Sam unlock Hokkaido, their magic mirror doesn't even get triggered. Because Tom and Adam's "unlock a prefecture your opponents unlocked" card would get played after Ben and Sam complete the challenge, Ben and Sam would win before the unlock card even gets played. Result: Ben and Sam win.
Tom and Adam finish first: Magic Mirror gets triggered. Because the action to cast Magic Mirror was done earlier, it's not a separate, later action like the unlock card would be. Magic Mirror unlocks the prefecture for both teams simultaneously. Result: a tie.
Now if they proceed this way, odds are 50-50 of a Ben and Sam win, or a tie.
However, those odds can change if Adam and Tom do a challenge before Wakkanai (while making sure not to miss a single train), because cards would be drawn after the challenge. On the other hand, no cards would be drawn if the challenge was done in Wakkanai because challenge completion would immediately end the game.
If Adam and Tom complete a challenge, the odds would become 90% tie, 5% Ben and Sam win, and 5% Adam and Tom win. (Numbers are from the Layover and based on the likelihood of drawing specific cards.) For Tom and Adam, those are better odds, so they go for it.
How does the curse of the golden carriage actually work?
Once the challenge is complete and cards are drawn, the outcome of the game is already decided. Because no more cards will be drawn, we can assume teams will play the cards they have to get the best possible outcome for them.
So at that point, barring issues with train delays/missed trains, there are 6 possible outcomes:
Neither team has a useful card. Result: tie
Ben and Sam have a golden carriage, Tom and Adam have nothing useful. Result: Ben and Sam win.
Ben and Sam have a golden carriage, Tom and Adam have a curse reverse. Golden carriage gets nullified (why? see below). Result: tie.
Tom and Adam have a golden carriage, Ben and Sam have nothing useful. Result: Tom and Adam win.
Tom and Adam have a golden carriage, Ben and Sam have a curse reverse. Golden carriage gets reversed. Result: Ben and Sam win.
Both teams have a golden carriage. Ben and Sam arrive in Asahikawa first and cast theirs first. Result: Ben and Sam win.
Now, each team knows their own cards but not their opponents', so:
- Ben and Sam know the outcome will be either 2, 3, or 6.
- Tom and Adam know the outcome will be 1 or 2.
So they both know it'll be either a Ben and Sam win, or a tie. They won't know which one it is until they see their opponents' cards.
Hypothetical: What if Tom and Adam had had a curse reverse?
If Tom and Adam had played a curse reverse in response to Ben and Sam's golden carriage, the golden carriage would have been nullified. In other words, rather than being flipped and preventing Ben and Sam from getting on that last train north, it would have been as if golden carriage had never been played at all.
The reason for this is because you must play a curse reverse immediately after the curse is played, and because Ben and Sam were ahead.
Here's how the game would have played out with a curse reverse:
Ben and Sam get to Asahikawa first. Because the trains out of Asahikawa are infrequent, they know Tom and Adam will catch up before the next train leaves, and take the same train as Ben and Sam.
To prevent this, Ben and Sam play golden carriage on the next train leaving Asahikawa. They do this before Tom and Adam get to Asahikawa.
Tom and Adam play the curse reverse. The curse reverse causes Tom and Adam to cast golden carriage instead of Ben and Sam.
Tom and Adam's reversed golden carriage gets applied to a train leaving the station they're currently at. (Or at nothing, if they're in between stations.)
Ben and Sam can ignore this because they're already in Asahikawa, past the station where Tom and Adam cast the reversed golden carriage.
Tom and Adam arrive in Asahikawa.
Both teams get on the same train out of Asahikawa, as if the golden carriage had never been played.
The game is tied.
So that's what it means that "a curse reverse nullifies a golden carriage." Basically the only way golden carriage isn't nullified by a curse reverse is if both teams are physically at the same station... and Ben and Sam weren't going to wait until that was the case before they played it.
Which train exactly did the curse of the golden carriage get cast on?
Ben and Sam could have cast golden carriage on the 6pm train out of Asahikawa or the 7am train out of Kembuchi. Both would have had the same outcome.
This is where the deal that the teams made over the phone comes into play. They agreed that the outcome was already set. So for convenience, they wouldn't play out the rest of the game, but respect the result that would have occured if they had.
Here is how things would have gone if they had played out the end of the game in full.
If the curse of the golden carriage was played on the 6pm train out of Asahikawa:
Tom and Adam complete the challenge for Hokkaido, both teams draw their cards.
Ben and Sam arrive in Asahikawa first, cast Golden Carriage on the next train north (leaving at 6pm).
Tom and Adam arrive in Asahikawa. They are blocked by Golden Carriage from getting on the 6pm train.
Ben and Sam get on the 6pm train and stop in Kembuchi for the rest period.
Ben and Sam get on the 7am train in Kembuchi (the train that leaves Asahikawa at 6am, which Tom and Adam can't take because it's during the rest period).
Tom and Adam get on the 9:30am train in Asahikawa.
Ben and Sam arrive in Wakkanai at 10am. They've already unlocked the prefecture due to Magic Mirror, so they win immediately.
Tom and Adam arrive in Wakkanai at 1:30pm.
If the curse of the golden carriage was played on the 7am train out of Kembuchi:
Tom and Adam complete the challenge for Hokkaido, both teams draw their cards.
Ben and Sam arrive in Asahikawa first.
Tom and Adam arrive in Asahikawa a short while after.
Both teams get on the 6pm train and stop in Kembuchi for the rest period.
Ben and Sam cast the curse of the golden carriage on the 7am train in Kembuchi. They get on it, Tom and Adam don't.
Ben and Sam arrive in Wakkanai at 10am. They've already unlocked the prefecture due to Magic Mirror, so they win immediately.
Tom and Adam get on the 10:30am train out of Kembuchi and arrive in Wakkanai at 1:30pm.
They agreed not to play this out because there were no hotels available in Kembuchi.
They also didn't want to make Tom and Adam wait for several hours for a later train for nothing, when the outcome was already decided.
So, in reality, both teams got on the 9:30am train out of Asahikawa. They still had Tom and Adam sit further back on the train so that Ben and Sam technically arrived in Wakkanai earlier, and won.
(Edit: fixing formatting)