Last week we probably saw in action how this voting system is one that ensures the judges predominantly construct most of the people in the final, possibly even removing public favourites along the way.

The public favourites that are at odds with the judges' opinions will have to overcome extraordinary odds to get to the final, while judges' favourites who are indifferent with the public can cruise to that final, getting almost no public votes whatsoever. In the rare case the latter do find themselves in the dance off, they will likely be saved by the judges anyway.

As we saw last week Ed Balls, someone who was likely to be getting significant public support, was eliminated from the show by the judges. Ed could have been 2nd with the public, still getting massive public support, but could have been pipped to first for a number of reasons. On these forums people have claimed they were wowed by Danny's dance and many were also wowed by Claudia and felt she was significantly under marked. Did one of these reasons drop Ed to a critically unsafe 2nd with the public?

The bias against public favourites who are at odds with the judges' opinions was bad last week, but this week (and next week) this bias becomes insane. Do not be surprised to see a very popular couple leave this week.

Anyway, here are this week's probabilities:

5 Couple Week
Judge Rank: A (first), B, C, D and E (last)
Percentage Chance in Dance Off (fair 40.0%): A = 10.8%, B = 25.0%, C = 40.0%, D = 55.0%, E = 69.1%.
Percentage Chance Eliminated (fair 20.0%): A = 0.0%, B = 0.8%, C = 5.8%, D = 24.1%, E = 69.1%.

Percentage chance of one of judges' bottom 2 eliminated: 93.2%

What is hidden in these probabilities is how those at the bottom of the leaderboard can do really well in the public vote, getting massively more public votes than other contestants, but still be chucked off the show.

This is the massive bias the judges' least favourite will have to face this week. Even being the public's number 1 does not guarantee safety.

Bottom of the Leaderboard:
Will be in dance off in 1 in 24 times when 1st with the public.
Will be in dance off in 12 in 24 times when 2nd with the public.
Will be in dance off in 22 in 24 times when 3rd with the public.
Will be in dance off in 24 in 24 times when 4th with the public.
Will be in dance off in 24 in 24 times when 5th with the public.

It is odds-on they will go if they are in the dance off since they are the judges' least favourite just a few hours earlier. The system makes it difficult for them to avoid the dance off in the first place even with high public support, then makes sure they get the boot if they ever do find themselves there.

They are almost certainly gone if 3rd or below with the public. Even if they are 2nd it is 50% likely they will be eliminated. Their only chance is being the public favourite and that is still not a certainty.

In contrast, look at the odds for the judges' favourite.

Top of the Leaderboard:
Will be in dance off in 0 in 24 times when 1st with the public.
Will be in dance off in 0 in 24 times when 2nd with the public.
Will be in dance off in 0 in 24 times when 3rd with the public.
Will be in dance off in 1 in 24 times when 4th with the public.
Will be in dance off in 12 in 24 times when 5th with the public.

They can be as low as 2nd from last and still be almost certain to avoid the dance off. Even if they are last with the public it is only a 50% chance they will be in the dance off. Even if they do find themselves in the dance off, then it is almost certain they will survive as the judges have already said they are their favourites.

What is worse the BBC mislead the public and tell them public votes run on the BBC will ensure every contestant has a fair chance of winning. This is the promise they make in their Editorial Guidelines. The maths shows this does not appear to be true. Read those crazy probabilities again. The vote is massively rigged in favour of the four judges' opinions, with the ability to override the public vote of thousands.

What does this all mean?

Others on this forum have speculated the judges occasionally sacrifice a higher ranking couple in the dance off to justify its existence. If this is true, we have not seen one yet this year so far. So be wary of that.

If there are any draws (and we have had a ridiculous number this year) then the middle and upper ranks will become vulnerable.

What should you do?

The simple answer at this stage is I do not really know. The probabilities are too crazy.

1. Do not split your votes for couples at opposite ends of the leaderboard. This is a really bad idea, more so than ever before. Your vote for the one near the top is even more likely to hamper the chances of your favourite at the bottom of the leaderboard, denying them the public rank they need to survive. In this case, just vote for your favourite at the bottom.

2. If you have a favourite in the bottom 2 (possibly 3) chuck ALL your votes for them. They are going to need it. The odds are massively stacked against them. It is 93% probable that one of the judges' bottom 2 will leave.

3. If the judges create any ties (with just 5 couples), then the middle and upper ranks become unsafe. If this happens, then the odds significantly change. How any typical person is meant to make head-nor-tail of the rapid change in odds with draws at this stage of the show is beyond my comprehension. For example, if all couples were tied, then spread your votes as you like.

Figures are often about interpretation. Is a cup half empty or a cup half full? If you want your favourite couple to avoid the dance off then vote for them, as the bottom couple of the public vote board is at risk even if they top of the leader board.

As always, our friend B_OR is assuming that all orderings of the public vote (each 'time') are equally likely when that is not the case. See previous threads.

This really is the week where public votes for those placed 3rd, 4th or 5th can make the difference between safety and being in the dance off. Yet also when tied scores can throw a spanner in the works.

I really hope the judges make a fool of themselves by having 2 way or even 3 way tie on the top.

So what are you suggesting? If Danny and Louise (for example) both do a dance that is equally good the judges should mark them differently just so they don't tie?

What I'm saying is... 3 way tie... public vote is very important for all of them.

There'll likely be at least one tie as I think Danny, Louise and Ore will all score very similarly this week if they live up to expectations. Wouldn't bet against all three of them scoring 39 or 40 each. It's going to be very tough for Judge Rinder and Claudia both doing Latin while the other three - who are already ahead in terms of the scores they've been getting - have ballroom.

With the way ties work in Strictly it benefits the lower places. 3 at the top of the leader-board on equal points gives 4th place 4 points and last place 3 points. Giving much less of a mountain for voters to keep them out of the dance off.

Well, have you read Len Goodman's interview today ? He makes it plain that he was so angry with the endless talk of fixing and of the judges being told what to do by the producers that it's one of the reasons he is leaving.

Interesting stats - for once I think I actually understood it all!

To be honest at times like this I really am torn between wanting to vote like crazy and just giving up, as the biased judges have far too much power. I really, really hope we can avoid the commonly predicted Judge V Claudia DO that is being predicted, if those two go this week and next then I feel like the judges will have created the final they wanted regardless of what the viewers think. I felt the same way in 2014 as well when Mark and Simon were dragged into the final and Jake Wood lost out at the final hurdle.

If all the moaning encouraged him to leave then that makes me all the more pleased that we moan so much!

I don't think they are being told by the producers... but you can sense if the judges got a favorite coz no matter what they do they always give a high mark.

Once again, daveGold who claims to be a mathematician, but clearly does not understand, is defending a system that is massively rigged against the public vote if their opinion is at odds with the judges.

You and I do not know how the public will vote. All we can say is even when public favourites do well, this is a system that can still give them the boot.

Please daveGold, if you truly are a mathematician, please start acting like one and finally admit the extent to which this vote is massively biased. You are presently undermining your alleged qualifications..

I think you are right. Even when there is a clear distinction between the dances, the judges mark the top ones the same a lot this year.

I also think you are right about Claudia and Judge Rinder. I think these two are quite popular with the public from what I have seen on these forum, but the system is likely to give them the chop this week. It is a shame.

This is right. The new tie system makes it a more even playing field. (The old system, eg when they had to cancel the vote in the Tom Chambers incident, made it impossible for the lower ranks.)

We have seen a lot of ties this year. Some people I know have questioned whether ties have even been manufactured to overcome the problems in the voting system.

That is why when there are ties you also need to start worrying about the safety of middle and upper ranks.

this seems very strange to me as a reason for going, I wonder if its true though, and that's why he's going

Oh dear ... poor Len ... might be a touch of guilty conscience and I dont think they are told what to do by producers

I know the BBC are fully aware for at least two seasons of the probabilities that show how biased the vote is towards the judges' opinions, but they still do not publicize these facts.

I also know up until early 2016 the BBC were incorrectly on written record as saying the public favourite could not be eliminated.

How do the odds work with the tied second place?

This is a test how much following Ore and Louise have.
So both of them is in danger to be in bottom 2 with Rinder.

Please, if we go back through the other threads we can find a number of people who make the same exact criticism of your mathematics - counting all outcomes as equally probable. Instead of listening to them you have repeated the same mistake for 6 weeks. By contrast, no mathematicians have confirmed that you have the right interpretation of your numbers. Posting repeatedly with long threads and insulting your critics does not make you correct!

Let other people present their views just as you like to present yours. If you really want to verify the maths then discuss it with other posters through forum mail. If you think your maths is beyond criticism then that may come across as being arrogant.

As I said in your very first thread, your broad message has some truth but the maths you back it up with has flaws. It is when you move onto talk of bias against the public vote that your case is weak since you only present selective statistics. The public vote has more weight than the judges vote in deciding who is in the dance off.

As I have explained before I am a PhD mathematician and I am the least qualified of all the people involved with this analysis. I have learnt over the many years that I do not trust or believe anything until it can be proven. For example most people think it is very unlikely for two kids to have exactly the same birthday in a class of 30 kids, but I do not hold any weight to that mass belief, because the mathematics proves them wrong. If everyone in the entire country, except skilled mathematicians, said the same thing, I would still not believe them because they are provably mathematically wrong. Reality always trumps mass belief of this kind. I can give you so many examples of quirky maths (one of my favourites is the Bill Gates, nontransitive dice story).

Sadly daveGold, you and the others who say the same are wrong. I am starting to believe you are not a mathematics graduate, because even someone with a 3rd would understand this.

I will explain again. Each public permutation has equal weight until the public cast their vote. Then and only then do we see the distribution and any possible skew. For example, being at the bottom of the leaderboard will not necessarily mean that the public are more likely to vote for them, because the public might not think they were any good either, or they might not find them entertaining.

You, me and the cat just do not know how the public will vote. That is what the vote is for; to find out.

All we can say is going into the public vote we can see the vote is massively biased against certain public voting possibilities.

For example, this week in unique judge ranking, if the judges' least favourite was 2nd with the public, then only half of all those possible conditional permutations would keep them out of the dance off. All public positions below that would almost certainly see them in the dance off. That is an unacceptable level of mathematical vote rigging.

You can use all the Mickey Mouse words and cornflake box mathematics in the world to try and say this vote is not massively rigged against the public vote that is at odds with the judges' opinion, but you are wrong. WRONG, WRONG, WRONG, WRONG. I cannot make it any simpler than that.

If you are a maths graduate, I respectfully suggest you go back to university and take a refresher course.

I would have to recalculate all the odds to find that out. It is quite a bit of work. However, the more ties, the more dangerous the middle and upper ranks become. However, the tie in second should still make one of (or both) of Judge Rinder and Ore vulnerable as they were at the bottom.

If Ore has the support, the tie actually makes him less vulnerable as if he polls higher than both Louise and Claudia, he can't be in the dance off. It makes Louise and Claudia more vulnerable as their scoring higher than Ore makes no difference if they don't get more votes as well.

If Judge Rinder has the highest public vote, he's safe as he gets a total score of seven and all options would have at least two of the rest scoring equal or lower than that. In fact, this is one week where the public's favourite actually cannot fall into the bottom two.

Let us consider a horse race at Newmarket instead of Strictly with 5 horses. It is complete fantasy to say that all outcomes of the horse race are equally likely because the race has not been won yet. Punters, bookies, and spectators all know that the the horses and jockeys are not all the same. In Strictly we know that the couples are not all the same as well. For you to say that it is just as likely for the horses to be any position, and for you to say that is just as likely for the couples to have any popularity, would not be a justified assumption.

Let us consider also the situation that everyone followed your advice. If they did then the number of votes going to the first two couples would drop to near zero. Those couples would certainly then be at risk of the dance off and the 'likelihoods' would not be applicable. This shows that voting patterns amongst the public stop are a good reason not to assume that each couple have the same chance of being in each position.

Let us consider also that if a couple are regularly in the bottom two but always avoid the dance off then we have extra information on them. We know that are not in the lower positions in the public vote, even after one couple has gone. This means they are not going to have the same likelihood of being bottom of the vote next week as someone who has survived the dance off - unless you are also assuming that the voting is independent from week to week (which you presumably are not).

The public will know all of the above as common sense, to some degree. The public know that the couples are likely to get more votes with certain types of performances than others. The public know that people do give votes to couples at the bottom of the leader board and ignore those in the middle. The public know that a lot of couples keep their popularity from week to week. All this information is discarded within your analysis (by assuming all outcomes are equally likely). The public are using information that your analysis does not, so please do not presume to tell them how to vote.

Others posters have told you this as well. Please listen to them even if you are determined to prove me wrong!