Really?

From the looks of it, I think Christian himself had just about given up.

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I initially had the same reaction but I no longer agree. Three reasons:

1 - I think Christian had lost so much that he really needed to hold onto this friendship. Despite his bravado he was seriously insecure and isolated.

2 - I suspect they are meant to have been much better friends than is immediately obvious. At first it seems like Wyatt is just some old college buddy or something, long forgotten. But clearly these two have a connection that is stronger than the film successfully portrayed. It's a flaw, but not of the same nature as what you're complaining about.

3 - Christian is actually a very generous guy. He's trying to be mercenary and to 'dominate' at work in denial of how soft he really is. He's nothing but generous to an extreme toward Wyatt throughout.

His act of trust in the ending goes to show how deeply all three of these factors are at play in the story. Christian is actually willing to risk his life rather than lose the friendship if Wyatt, and he trusts in that friendship enough to believe he'll win that bet.

Yep, because forcing people to see a mental health professional always goes well.

Also, surely Mara would report Wyatt's actions in the basement to either the authorities or to Christian.

It's only unbelievable in that sense based on the fact that you are operating from your own perception of reality and what you would do in that situation (or imagine you would do).

SPOILERS AHEAD

Remember Christian refers to a suicide attempt he made a year earlier, so he's likely to feel more empathy towards Wyatt than someone who hadn't experience such mental suffering.

Also, Wyatt doesn't entrust Christian with this information until after they've already become quite close again. Had Wyatt immediately told Christian about his plans at their reunion, I'm sure his actions would have been rather different. However, you could argue that what Christian did at the end was both utterly brave but ridiculously stupid at the same time depending on how you frame it.

Before Christian is aware of Wyatt's plans, Christian is talking about joining the army so perhaps he was operating from the standpoint of if he's willing to potentially give his life for his country, why not do it for his friend?

It's not been that long since he tried killing himself, he still battles with his own self esteem, Mara appears to have gone and he's lost his job. He talks about maybe the army toughening him but, but then he essentially faces his own demon in that he has the courage to put himself in a very vulnerable position physically with an outcome that could potentially result in death. Two friends are struggling with their internal demons but from two different perceptions of reality, which they proceed to face together.