All this info is based on past seasons of Big Brother from trends that I've picked up from competitions and whatnot. Feel free to add and share as you see fit.
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1. First HoH Competition will involve endurance.
This was the case, to some extent, in BB4, 5, 6, 8, 9 (Power Couple), and 11. BB 2 and 3 involved the HG's narrowing down each other until 2 were left and then it went to popular vote, which hasn't been used since. BB7 (All-Stars) let HG's basically eliminate each other until we had our first co-HoH. BB10 had the HG's vote for an HoH before they even went into the house. The winner of the first HoH competition has only won Big Brother once (Lisa in BB3).
Might not be the best idea to win this if it is endurance since you'll likely be seen as a threat.
2. An evicted houseguest has been voted back into the game once every 3 seasons.
This was the case in BB's 3, 6, and 9, so 12 will likely be the next Big Brother that we see this twist. It will usually happen RIGHT BEFORE or RIGHT AT the Sequester point. The method of voting the HG back in has varied in each season. In BB3 2 of the 4 HG's were finalists based on how long they'd go on PB&J and how much prize money they'd give up. Of the 2 that remained, the remaining HG's still in the game voted on who to come back. In BB6 it was an America's Choice between previously evicted HG's. In BB9, it was an America's Choice, but then the HG's remaining in the game got to choose between the Mystery Houseguest that America voted for, or the person they had just evicted (James).
If you get the boot early, at least establish good relationships with the other Houseguests and play in a way that America will like you. This will better your odds on being voted back in.
3. If someone is voted back into the game, the next HoH competition will be endurance.
The returning Houseguest won this competition 2 out of 3 times. The only one who didn't win, Kaysar, was evicted this week after only 1 week back.
It would probably be a good thing to win this one, or at least let someone in your alliance win it.
4. If it's Eviction Night and there are between 8 and 6 total houseguests left, prepare for a possible Big Brother Fast Forward (double eviction).
The double eviction was introduced in BB5 when there were 7 people left. It was used twice in BB6 (9 and 6 HG's remaining) and once in BB7 (8 HG's remaining) but never since. The Big Brother Fast Forward was introduced in BB7 (6 HG's left at the start of eviction night) and used again in BB8 (6 HG's left) and BB10 (7 HG's left). It was planned for BB11 with 8 HG's left but canceled when Chima was expelled. It's a good bet that if you started with 13 or more total HG's you'll have a Big Brother Fast Forward. BB9 is an exception, they started with 16 HG's but because of the Couples at the beginning, the first 3 evictions saw 2 HG's leave at a time. Also, the HoH competition will likely be Before / After (BB8, 11's PoV comp). The PoV competition will likely involve speed and dexterity (BB7, BB8, BB10).
Come up with your Alliance at least the day before so you're on the same page and not scrambling when Julie Chen drops the Fast Forward bomb.
5. If there are 5 or 6 HG's left, prepare for a Morph-O-Matic PoV Competition.
Morph-O-Matic was introduced in BB5 and has been used every season since. BB5 used it when there were 8 HG's left. BB6, 9, 10, and 11 used it with 5 HG's left. BB7 and 8 used it with 6 HG's left.
If you want to win, study the memory wall intently starting at least a few days before the competition
6. When there are 7 or less HG's left, one HoH or PoV Competition will involve past events in the BB house.
This is usually in the form of an Otev PoV competition or a "What day did such and such event happen on?" HoH / PoV competition. It helps to know not only what happened on what date, but also to whom. Helps to know details of evictions and competition winners. There has been a competition like this in BB6, 7, 8, 9, 10, and 11.
Memorize dates, eviction vote tallies, and such
7. The first time the HoH faces powerless-ness is when there are 5 HG's left
It's happened in BB5 and 10 - the HoH has to put up 2 people and leave 2 people safe. One of the safe people wins the PoV and uses it. The HoH has no choice but to nominate the only eligible person. It's only gone down like this twice in BB history, but both times (Karen and Renny) the replacement nominee went home.
If you're the HoH, nominate the strongest competitors NOT in your alliance. This increases the chance that they won't win the PoV and you can keep some power if the PoV is won and used.
8. Final 4 HoH comp will likely be Fact / Fiction, True / False, or Before / After.
This can sometimes be a crapshoot with questions of things outside the BB house (BB9, 11), but can also be about past events in the Big Brother House.
If you're playing there's no reason to throw this one
9. Final 4 PoV comp will involve evicted HG's and their competition history / eviction. Speed helps a lot too
This has been the case going back to the first Final 4 PoV in BB4. Usually having to match an evicted Houseguest's Face / Name to something that describes them, often times you hafta match 2 clues per HG and clues can apply to more than 1 evicted HG. It's important to know how many times each HG was on slop, number of comps they played in, how many HoH's and PoV's they won, how many times they were on the block, and the vote tally when they were evicted.
Don't wait for the last week to prepare for this - keep mental notes as the game goes on. Also, be quick!
Also: No HG has EVER won the Final 4 PoV and gone on to win Big Brother! Since it was introduced in BB4 - Alison, Cowboy, Ivette, Janelle, Daniele, Ryan, Memphis, and Kevin won the PoV, was safe that week, but was either evicted next or lost at the end. This is probably just a bad coincidence.
10. The Final 3-part HoH competition will be Endurance, something involving HoH's / Veto Winners / Nominees, and Jury Fill-In-The-Blanks
It's been like this since BB8, and BB4, 5, and 6 wasn't much different. Winner of Round 1 moves on to Round 3. Winner of Round 2 moves on to Round 3, Round 2 loser is eliminated. Winner of Round 3 is the new HoH.
The First tie-breaker for part 3 of the Final HoH comp is "How many total eviction votes have been cast (including tie-breakers)?"
We saw this in BB6 and BB11. BB4's tiebreaker was different since the answer was different for each Houseguests and involved that season's X-Factor twist. The 2nd Tie-Breaker, which has only been come to in Season 6, was "How many total hours have you been in the Big Brother House?"
It helps to be good at endurance (particularly cold water, since we know BB loves cold water), to be able to identify the order of HoH's and nominees quickly, as well as have good relationships with the jury members to guess how they answered. Know the total eviction vote count and hours in the house in case of tie-breaker