Here are the 7 Couple Week probabilities.

7 Couple Week
Judge Rank: A (first), B, C, D, E, F and G (last)
Percentage Chance in Dance Off (fair 28.6%): A = 1.2%, B = 6.5%, C = 16.0%, D = 27.3%, E = 38.7%, F = 49.8%, G = 60.6%.
Percentage Chance Eliminated (fair 14.3%): A = 0.0%, B = 0.0%, C = 0.4%, D = 2.5%, E = 9.6%, F = 26.9%, G = 60.6%.

This is really the start of significant swings in the safety of middle ranks when judge-draws occur. Please make sure your family and friends all have their calculators at the ready and have swotted up on their probability theory before the voting starts. Some other shows truthfully boast, 'Your vote makes all the difference'. Due to the complicated maths in the Strictly vote that is not always the case for some or all of your three votes.

This is one of the weeks where we are more likely to start seeing couples being eliminated who are getting strong public support in terms of the number of public votes, but are at or near the bottom of the leaderboard. Being public favourite is still likely to save a couple at this stage (but not guaranteed for those at the bottom of the leaderboard), but being 2nd or 3rd with the public is going to dramatically increase their chances of being in the dance off.

To explain an extreme, they are suggesting it might be a 4 Couple Semi Final this year. In that case the couple at the bottom of the leaderboard can be voted 2nd with the public and will still end up in the dance off in 5 of the 6 possible cases where they are voted 2nd with the public, and in all cases where they are ranked lower than that with the public. Obviously, since the judges have already placed them last in the main show it will be odds-on they will be eliminated in the semis when being 2nd with the public, even when they are getting significant numbers of public votes.

If you think that is crazy and an unfairly biased voting system in favour of the judges, then join the club.

It is even possible for the public favourite to be eliminated if they are the judges' lowest rank. The most likely week for it to happen is the last public/judge combined vote of the season. Up until early 2016 the BBC were on written record incorrectly saying it was impossible.

Back to the 7 Couple Week.

Percentage chance of one of judges' bottom 3 eliminated: 97.1%.

Percentage chance of one of judges' bottom 2 eliminated: 87.5%.

As normal, ignore the angry people who are trying to convince you these probabilities are wrong or being misinterpreted. The naysayers are wrong.

There are 5,040 possible ways the public can uniquely rank the couples in the 7 Couple Week. Each one has been checked to see which couples would be placed in the dance off as a result, taking into account the public vote will break ties. The only assumption made for the dance off percentages is there is unique judge ranking. The additional assumption made for the elimination percentages is the judges' least favourite of the two will be eliminated. The latter is the overwhelming historical case.

There is a 97.1% chance one of the bottom three judges' ranks will be eliminated. Put another way, there is only a laughably small 2.9% chance one of the top 4 will be eliminated.

The judges' favourite will avoid the dance off in 99% of all public voting permutations.

The judges' favourite can get ZERO public votes and will still avoid the dance off in 92% of all the voting possibilities when they are getting zero public votes.

In short, contrary to the illusion that has built up over many years, some contestants are effectively already safe and do not need a single vote from the public.

It is becoming a little more likely the middle ranks might find themselves in the dance off, but if they do, then it is likely they will be paired with one of the bottom three from the leaderboard, in which case they are likely to be safe from elimination.

Even the public favourite can be eliminated, however it is still rare at this stage.

What does this all mean?

1. If you are voting for one person and do not care they may already be safe, then that is fine. Please do not reply to this thread with the very intimidating anger that occurred in my 8, 9 and 10 couple week threads.

2. However, if you vote for multiple couples, especially if they are at opposite ends of the leaderboard, be very careful.

Your bottom of the leaderboard favourite not only needs your vote, but also needs your help to ensure as few as possible do not rank above them. The latter is already difficult due to the judges' low rank. If you vote for the judges' favourite (who is already safe without your vote), that may be the vote that when combined with other people's votes denies your bottom leaderboard favourite the public rank they need to avoid the dance off.

3. If the judges create many ties, like they have been doing this entire series even though they have a full range of scores, then the middle or upper ranks become more vulnerable to appearing in the dance off with other middle or upper ranks. When they flash the leaderboard, quickly count up as many tied scores as you can. The more ties, the more help the middle ranks need. There are a few places on the web that show the leaderboard. If you know one, please reply below.

Every time I read your posts I say this person talks sense and I should listen then every week I get caught up in the excitement and vote without thinking. It looks like I really need to think before I vote this week, sounds like Rinder and Oksana will be in danger.

If I want to see the leaderboard again I go online to watch BBC1 live and then rewind back to the leaderboard. Or if you're watching online just pause it or print screen or take a pic.

Every time I open up these threads I feel a little fear because I'm not going to understand and yet I do want to do the best by my favourite.

Sorry Ore, you've got a mathematical dunce supporting you

Could you provide pictures, please OP!?

If you don't understand the maths then follow the much repeated rule: vote for your favourite couple. No regrets. Remember Pixiegate!

Do not for one second believe you are not clever for being unable to understand this. As I mentioned in my OP, the Strictly management incorrectly claimed in written form all the way up to early 2016 that public favourites could not be eliminated. That is not the only provable error they have made. The PhD mathematician that calculated all these probabilities realized something was wrong, but was amazed by the actual results. He only changed his voting patterns thereafter. He had been voting badly, wasting his paid-for votes for years.

Here are some tips if you are an Ore fan.


Summary:

1. If Ore is your only favourite. Throw all your votes at him.
2. If there are loads of leaderboard ties, especially at the bottom, again give all your votes to Ore.
3. If there are no tied scores on the leaderboard (or maybe just 2 couples) and Ore is 1st, 2nd (and almost certainly if 3rd with no ties) and you also like another couple such as Greg at the bottom of the leaderboard, then ignore Ore and give your votes to Greg instead. Ore is safe without your votes.

Explanation:

If Ore is your favourite, and your only favourite, then you can get away with putting all your three votes for Ore. He might not need those votes if he is the judges' favourite, but if he is your only favourite, then what does it matter? (If he is top of the leaderboard, or even second, do not purchase any additional votes like some people do, as that will almost certainly be wasted money on an already safe person.)

If you like multiple couples, then things get really complicated.

Say for the sake of argument, you also like Ed, Greg or JudgeR who are more likely to be at the bottom. Let us randomly choose Greg as your bottom of the leaderboard favourite, so the following is easier to write.

If Ore is top (or even second or third favourite), and there are no leaderboard ties, then your best bet is to put no votes for Ore, and instead put all your votes on Greg. The reason for this is Ore is almost certainly safe from elimination even without your support. BUT if you put a vote for Ore and also put a vote on Greg, then you might be shooting yourself in your own foot and be assisting in getting Greg eliminated.

The reason is Greg not only needs your vote to get a good rank, but also needs you and others not to vote for other couples that could rank higher than him. By also voting for Ore, you might give Ore a public rank that denies Greg the rank he needs to survive. Remember, if Ore is top or second, he is almost certainly safe without your support anyway.

This crazy Strictly vote means people like Greg could get loads of public votes and rank reasonable well with the public, but find themselves in the dance off with a judge favourite who they are very unlikely to win against. The craziest thing of all is the public favourite in a week can even be eliminated. The worst week for that possibility is the semi final.

All the above, however, must be completely ignored if there are a lot of ties on the leaderboard. If Ore found himself in the middle of the leaderboard, where he would normally be safe, but instead there were loads of ties, then you need to give Ore every single vote you can. Ignore your second favourites. When there are ties, especially at the bottom of the leaderboard, the middle and even upper-middle ranks become very vulnerable, especially at this stage in the competition.

I hope that helps. It is very complicated. I think it is crazy having this sort of vote mathematically biased vote. What pictures would you like me to post?

I've only read the bolded section... why would anyone vote for Ore!?

Tellymix show the leaderboard I just google strictly leaderboard and it's one of the top hits

Noted. Thank you.

Right. Skimmed the sums again. Sorry! My general voting intention tonight would be this: choose my favourite from the contestants ranked by the judges from 3rd to 7th and vote three times for that contestant (I only do the internet voting).

If my absolute favourite is ranked 1st or 2nd by the judges, I won't vote for them. Because a) they have less chance of being in the dance off, and b) even if they are in the dance off, the judges will most likely save them.

This basically fits with your sums, right, OP?

Thank you! That's really helpful and might save some money too!

Sorry for the late reply, but yes you are correct.