yeah,
the best way I have understood is that when Deshawn picked that box, a 1/3rd chance, there was still a 2/3rds chance (a 66% chance) the fire was in the other 2 boxes.

So when Jeff reveals one of those other boxes, then it is still that 2/3rds chance the fire is in that remaining box. The 2/3rds doesn't just disappear.

Best twist in years. It hasnt fouled up the game one bit

Yeah I was reading up on it to try and figure it out. One good explanation I saw was to imagine rather than 3 boxes, there was a million. Then Jeff reveals all but box number 768,932 or whatever. So now it's between the one you originally chose, and that one. Obviously you would choose that one, because you know Jeff is turning over only boxes with skulls, and he knows which box has the flame. The only way it's not #768,932, is if you originally chose correctly on a million-to-one shot.

I think the smaller number of 3 boxes makes it harder to see the advantage of switching, but the principle holds true either way and becomes more obvious the larger the number of choices becomes.

Conceptually, it's tough to understand. But that is a solid example.

Essentially, we are assuming that Jeff deliberately chose box 3 (in your example he deliberately chose all but 768,932) which adds value to box 2 while adding no value to box 1, which is Deshawn's original and re-chosen box. Thus, box 2 has a 2/3rds chance of being correct as, at a simple level, it assumes the probability of box 3 being correct from the original decision since it has been eliminated by Jeff. Box 1 still only has a 1/3rds chance of being correct, as it was Deshawn's initial box picked among 3 and he has no further information related to that box prior than he does after Jeff eliminates box 3.

Plenty of mathematicians and other very intelligent and math oriented people rejected the solution initially.

The math makes sense, but what makes it tough conceptually, imo, is that Jeff absolutely knows which 2 out of 3 boxes have a skull. Thus, regardless of what box Deshawn picks, Jeff will always play perfectly and pick the skull. However, mathematically, that conclusion does not change the odds of Jeff deliberately eliminating one of the boxes.

To be honest I don't actually 'hate' the twist per se.

Having an opt in / opt out system is essentially another prisoners dilemma which encourages people on the bottom to compete more and people in power to sit out, an example springing to mind being balancing pot on head challenge we saw in Guatamala where Jamie heckled Bobby Jon from the touchline.

I just really don't like being voted out not from a vote as it fundamentally breaks what Survivor is. Would much rather they had a less extreme 'punishment' attached to this.

I expect when the producers thought this up they were only expecting the 2 people on the bottom to compete. In this scenario Ricard, Erika and Xander all choose to compete which is baffling to me.

This. It basically changes the game into Big Brother briefly. There should not be anyone ever leaving without being voted out or a medical evac (or like a Brandon Hantz situation where he was legit dangerous, and even then they still kind of voted him out).

+Stephen (S18) would be a hilarious wrinkle

I guess I just don't see what Xander has done particularly better than Erika? The most influence they've had all game is with Xander as the swing vote and using his extra vote against Lianna and Erika making the split vote against Lianna-Shan.

Erika also is closer to Heather presumably if they got to the end together it would be Erika dragging Heather and not Heather coming by virtue of Xander, has at least been more aware of the votes going certain ways - so why do you think that Xander would necessarily deserve to win it more? What's his individual case that's better than hers. He won 1 individual immunity, she won 1 individual immunity. She's perceived rightly or wrongly as a big threat and has been targeted many times. If she won the game, why would it be woke culture and not that she's respected more as an individual? I think what you're saying here is like almost the opposite, you don't have to worry about this because Erika's clearly not got a winning edit but why in your opinion and how in your opinion has Xander played an actively better game than Erika?

I feel like the honest implication here from you is that Xander would deserve it more because he's a man, otherwise there's no point in bringing up the woke stuff. There's really no compelling case why either of them should really win over the other.

The idol gives him a decision at every tribal council and he’s 6 for 6 making the right one.

This is what people respect

I'm not sure why it's such a significant difference maker - if you wanted to make a case against that, you could say despite having the idol Xander has been less aware of the voting dynamics and has been less involved in guiding the strategy of the season. I actually think Xander has played quite well for his age, but I think more than "woke" culture the thing that will hurt Xander is his age. What reason is there for a 20 year old to get a million dollars? We see a lot of times younger people find it more difficult to gain the respect of older jurors.

Regardless, the point I'm making is there really isn't a significant case to be made for either over the other as far as I can see. I don't think Erika can win and I actually think Xander has a shot and played fairly well recently, but I think it would be utterly delusional to suggest that he's played a significantly stronger game than she has and there's literally no good argument. He has more confessionals because he's a more important character but when you look at how the votes line up, Erika is slightly more influential player than Xander and has also been flagged as a threat. She's had more working relationships.

I guess my point is, if Erika were to get to the end with Xander and win I would say it would be totally reasonable and not a bitter jury vote especially since in listening to the exits - they just have more respect for her and Xander's biggest move was apparently Evvie's idea.

I feel the twist makes it less likely someone who has the expectation of not going home tells the person who is likely to be going home that they are, in fact, going home. I think the producers like the secrecy and trickery, and the hail mary twist slightly reduces the chances someone spills the beans without good reason.

So not bitter jury, but ageism.

Erika has been flagged as a threat a few times. Is she really a threat? I'm guessing there's snippets of basically everyone saying at some point on the island, player x is a threat. Why are they showing the Erika ones? Maybe trying to piece together as much as they can to justify a win by her? As you said, Xander is more of a character, so more confessionals. Sadly Erika just doesn't have many confessionals, probably not due in any part to her gameplay, just that she's not as interesting to the viewer or a character.

But I agree gameplay wise they've been relatively equal in my mind and would have no issue with one of them chosen by the jury over the other.

The concept of a threat is barely even real.
People just call someone a “threat” when they want them out of the game

I usually like to use an example with a larger number than 3 as well when explaining Monty Hall, but I usually use a deck of cards. If you pick the ace of spades you win.

Pick 1 card. Now after you pick, I'm going to reveal 50 of the remaining 51 cards that are not the ace of spades. Now, do you want to stick with your original pick or switch to the one card I didn't turn over? Most people can look at that and grasp that it isn't a 50/50. The key is in explaining that no matter what, I'm going to be revealing 50 non-As cards, so you're not gaining any new info about your original pick. It's still just a 1/52 shot that you actually picked the As.

Ye'p. The old adage that every strength is a weakness and every weakness is a strength in Survivor.

Xander was deemed a 'threat' early merge because he is athletic, fairly likeable and had a public idol.

Last two episodes he has barely been mentioned as an option to go, possibly because everyone has decided he's not that much of a 'threat' after all and his jury equity has taken a plummet from being left out of the vote so often.

Always reminds me of the Varys quote from Game of Thrones

'Power is a curious thing, my lord… Power resides where men believe it resides. It's a trick, a shadow on the wall. And, a very small man can cast a very large shadow”

Chaos is a ladder

if they bring it back, they need to give better odds ... maybe 1 in 3 (if they are using dice)

...but the odds were 1 in 3. Technically 2 in 3 for those in the know.

He is talking about the Save Your Life Dice.

Also, he is wrong

I'm open to the frozen envelope theory but I was shocked that it ended up being 2/3* he goes home - that seemed incredibly punitive and makes opting out of the challenge +EV for almost everyone**. I thought it would be 1/2 or 1/3 - especially after the discussion at tribal.

That's something they easily could have adjusted on the fly - which is something I am sure they do all the time. (Which is why I am more of a traditionalist since the twists allow production to manipulate the game for their preferred players.)

I enjoyed Lianna confidently saying 33% chance as if she cracked some unsolvable mathematical problem. And Xander saying Monty Hall problem and nobody knew what he was talking about. Was disappointed that Deshawn didn't switch because I think he's played a (mostly) strong game.


* Yeah, I think Survivor's RNG might have some issues.
**

Assuming every one had an equal challenge ability, every one had an equal chance of being eliminated at tribal, and the first player out of the challenge has a 2/3 chance of going home:

Players In Challenge/1st Out %/Not 1st & No Immunity %/Eliminated% (Opt In)/Eliminated %(Opt Out)

7,...................................14%,......... ........71%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,14%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,N/A
6,...................................17%,......... ........67%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,16%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,7%
5,...................................20%,......... ........60%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,17%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,7%
4,...................................25%,......... ........50%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,20%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,7%
3,...................................33%,......... ........33%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,24%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,7%
2,...................................50%,......... ........0%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,33%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,7%
1,...................................0%,.......... .......,,,0%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ,,,,,,,0%,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,20%

Yeah, have no idea what people are saying. Xander has played really well given the hand he was dealt. The guy was cursed with the worst idol of all time (-EV for sure), with a huge alliance disadvantage, while being the obvious post-merge physical threat, yet he is still in the F6 with an idol.

edit:

Re: The post above. The analysis is obviously wrong if it is actually a true Monty Hall dynamic where you are allowed to change and the 1st box opened is always a skull, meaning only a 1/3 chance of being eliminated.

This is correct and makes for a reasonably interesting and fair dynamic:

Players Competing/ First Out/ Not 1st or No Immunity /Eliminated (Opt In) /Eliminated (Opt Out)
7............................. 14%..................... 71% ..................................14% ....................................... N/A
6............................. 17%..................... 67% ..................................14% ....................................... 13%
5............................. 20% ..................... 60% ..................................15%............. .......................... 13%
4............................. 25% ..................... 50% ..................................15%............. .......................... 13%
3............................. 33% ..................... 33% ..................................16%............. .......................... 13%
2............................. 50%..................... 0% ..................................17%............. .......................... 13%
1............................. 0%..................... 0% ......................................0%.......... .............................. 20%


Of course, I am guessing < 50% of players make the correct decision and change boxes.

The question is whether it was always a Monty Hall problem or if production did that on the fly. I am guessing they had it as a contingency in case they had a player they liked.

Jeff intentionally removing a skull means you now have two safe boxes (the fire box and the skull box Jeff intentionally selected) and one unsafe box. Assuming you correctly switch.

Not switching means you aren't using the new information to your advantage. It's basically like saying I don't want to convert one of the two skull boxes into a fire box.

Re Xander realistically we only can have a solid read on his game if he gets to the final three.

Similar to Spencer in Cambodia.

Wonder what happens if everyone but one person opts out of the challenge. Do they automatically win immunity or (as the only participant) are they also last place and must do or die?

Right. That’s pretty much what I said lol.