Why have the sacrifice chosen at (seemingly, see below) random? First, the card game fits into the families gaming empire, and into the idea of the devil making bets with people. Second, it, and other games of chance like dice, are great for the strategy used by lots of demons in stories; make you think you have the advantage so you don't realize how much they're screwing you over. A player thinks the dice are likely to role in their favor, but if the dice are loaded then victory is impossible. The Le Domas' think the odds of having to do the ritual are low, but in reality Le Bail can have them whenever he wants.
As he was sent to fetch Alex, Daniel tells Grace that it wasn't too late to flee from the wedding, and that she doesn't belong in this family. He adds that he meant that as a compliment. A lot of his actions and conversations are in support of Grace, which hints at how Daniel genuinely cares for her. As the movie progresses, he is the most active in trying to help Grace escape.
Grace promised Becky that she would bring Alex back into the family fold shortly before drawing her card. By the end of the film she had: at the start of the game Alex was doing everything he could to protect Grace and help her escape regardless of what the family tradition dictated, by the end he showed he was just as willing to sacrifice her if it meant saving his skin as the rest of his family (with the obvious exception of Daniel) and ended up experiencing the same fate as the rest of his relatives as a result.
Grace surviving the family and the Le Domas' incompetence makes a lot more sense when you consider her life compared to the Le Domas. Grace is a former foster kid, and, as many can tell you, likely had to fend for herself against a manner of threats, or at the very least, was raised without a silver spoon. On the other hand, the Le Domas are not only incompetent, but are all clearly pampered, and have difficulty doing things by themselves or without some type of advantage (they can't find Grace without using any of the cameras, Fitch needs to use his phone to use a crossbow, etc.). That combined with the fact that the "hide and seek" card isn't called often means that they are woefully out of practice, so when they need to kill Grace, they are horribly underprepared.
There’s also the fact that amongst them, the individuals of the family are all incompetent due to specific factors. Not only are all of them inexperienced with the weapons, but the oldest ones who know what they’re doing are all older and slower (Tony, Becky, and Helene), and the ones who are most able-bodied are either impaired with drugs or alcohol (Emilie), don’t give a shit (Fitch), or both (Daniel). Charity and Alex are the only remotely competent people in the family, and Alex is working against them most of the movie. The only real advantage they have over Grace is that they outnumber her, and they only gang up on her near the end.
The attitude is also important. The Le Domas are sure of their victory in the beginning (having stacked the odds in their favor), and when they don't win easily they get frustrated. Grace, on the other hand, is focused on the task since she finds out what is going on.
Fitch and Charity had to go through the same "welcome to the family" ritual, and lucked out by drawing harmless games to play. While we don't know how Fitch reacted when he was told, Charity reportedly "didn't even blink". They both participate in hunting Grace, who Daniel repeatedly states is nothing like them. This coupled with the nature of how one is selected as a sacrifice, suggests that Le Bail is careful in how he selects his tributes. Charity and Fitch were evil people, or at least "bad", and were allowed to join the Le Domas because they would participate in the rituals. Grace was chosen as a sacrifice, because she is a good person who never would have gone along with this. The same is probably true for Helene's husband, and the other victims.
Alex said that the Hide and Seek card is hardly ever drawn, but how true is that really? Unless the extended family is much larger than what we see in the movie, the fact that he had already participated in Hide and Seek once in his life so far shows that there is probably about a 1 in 3 chance of it being drawn at any given time.
As an add-on, there's also speculation that Le Bail is fixing the draw- if you're willing to participate in the ritual, you get a safe game, if you're not, you're the hide-and-seek victim. If this is the case, it doesn't matter how rare the hide-and-seek card is. Would you call the police if told about the animal abuse, Hollywood Satanism, and occasional murder the Le Domases commit? If so, then you're always going to be the next victim. Hope you're really good at hiding...
The surviving Le Domas do not begin exploding until after Helene declares she will kill Grace even though the game has technically ended. Is this Le Bail just screwing with them by giving them a Hope Spot - or was he waiting to see if they would be willing to break the rules, thus giving him the excuse he needed to kill them all?
On a meta level, James Vanderbilt as Le Bail is fitting. Who better to play an overseer of inherited wealth than someone who is themselves from a family with inherited wealth?
Grace surviving the night is a definite win, and, as has been stated elsewhere, she stands to inherit the Le Domas estate as the only living member of the family. However, consider the situation from the police's point of view: they arrive to the home of an extremely wealthy and well-respected family, to find it burning to the ground. The family are all missing (as there won't be enough of them left to even identify as bodies after the fire) with their blood splattered all over Grace, and it would only be a matter of time before they discover the bodies of the maids in the stables, and the crashed car with Stevens nearby. What are the odds that Grace would likely be considered the prime suspect in the case? Even worse, she may actually end up institutionalized if she tries to tell them the full story of what happened, as there's no way that anyone would believe that she was the victim of an attempted Satanic ritual, the failure of which led to thespontaneous deaths of the entire clan. What's more, if the discussion about what happened to the Van Horne family was true, then there are likely other powerful, wealthy families out there who made the same deal, and who would likely be looking to scapegoat Grace as a crazy, gold-digging killer in order to protect their secret.
On the other hand, Grace could always point them to the corpse filled Goat Pit to prove to the police that the family were bonkers and then spin a story about self defense.
Given the ages of the corpses in the goat pit, including a 30 years dead man with arrows still in his gut who could be dentally identified as Helene’s missing husband, it’s really her best security.
Also, the crashed car, damaged fence and gunshot to the hand would probably indicate a two-sided struggle. Not to mention the (relatively) intact corpses of Daniel, Becky, and Stevens the butler.
Fitch's search history and texts might also be a factor, if his account can be accessed.
What if Grace didn't pull the Hide and Seek card? Sooner or later, she would've found out about the family's Deal with the Devil and/or had to participate in the game as a "seeker" when another initiate into the family drew the card eventually.
It's speculated that Le Bail rigs the draw so that only people who wouldn't approve of the ritual would be sacrificed, which was why Finch and Charity were spared. Either because he wants the sacrifices to continue and wouldn't want a 'good egg' convincing the family otherwise, or he just wants innocent people to suffer (he is the Devil after all). So there would be no way for Grace to not draw the fatal card,
It's entirely possible that Grace (having married Alex) now qualifies as part of the family. If so, she may be unable to marry again, lest she either die horribly or risk her spouse also drawing the Hide and Seek card.
That's actually fridge brilliance: Alex tells her in the beginning that the game tradition is more important than the actual marriage, and she isn't part of the family until after the game. Which lead her to cut all possible ties with the family. Also, Le Bail wanted a fair game and shows respect to Grace for winning it, he would want the victim to have a honest chance to make it out.
Grace slipped the ring off her finger when Alex was begging her to stay, spiritually severing her from being married in.
Rewatch the part of the ending when Emilie tries to rush her kids out of the room. We're shown two small geysers of blood followed by one big one. Le Bail made Emilie watch her kids explode before he killed her.
