I apologise if this has been explained before (I'm sure that it must), but can someone remind me how the voting works. I'm confused.

I thought that the judges scored the couples and put them in order:
eg Danny 5, Louise 4, Claudia 3, Ore 2, Judge 1 (or whatever)

And the same happens with the public vote. Just suppose that the public voted for the underdogs, we would then get:
eg Danny 1, Louise 2, Claudia 3, Ore 4, Judge 5.

I was under the impression that the judges' and public scores were then added together, which would give:
Danny 6, Louise 6, Claudia 6, Ore 6, Judge 6.

So how does anyone decide who should be in the dance off? What have I misunderstood?

The public vote placing breaks any ties - so in that scenario, then Danny and Louise would be in the dance off as their public vote placing was lower.

It works exactly as you have outlined.
The only difference can be if the Judges give a tied score to two or more couples.
EG
Danny gets 5
Claudia and Louise both get 4
Ore then would get 3
and JR 2

However, assuming they all get a score between 5 and 1, with no ties and using your example above, where the public vote exactly the opposite to the Judges, then the public vote takes precedence.

So in your example, Danny and Louise, with the lowest public vote scores, would be in the DO.

I think you have it right. The results normally give a bottom two but if I remember correctly from previous series that if three or more are tied after the votes are in its the two from that tie with the least public votes that are in the dance off. So in your example above it would be Danny and Louise.

All of the above is correct but....

If Louise and Danny is in the dance off... they will save Danny base on your example even if he is in the bottom of public vote.

I'm not sure if this happen before that the lower judges score defeated the higher scorer in the dance off... very rare anyway.

Phil Tuffnell and Katya went out despite scoring higher than whoever beat them in the dance off. Not that Katya bears any grudge at all and wasn't still going on about it in the show she did with Pasha

Thanks. I'm now reassured that the public vote takes precedence.

I had an horrendous vision of the producer making an executive decision.

Ricky and Erin very controversial week

Times The Lower Scorer Has Been Saved In The Dance-Off

Series 5

Letitia vs Stephanie
John vs Dominic

Series 6

Don vs Phil
Heather vs Don
Lisa vs Cherie

Series 7

Rav vs Martina
Ricky G vs Phil

Series 10

Richard vs Johnny
Richard vs Colin

Series 13

Kirsty vs Daniel
Peter vs Jamelia (*twitch*)
Katie vs Anita

This year week 8, they saved Grep over Daisy while she had be consistently better than Greg except for week 3 (32vs31) and that week (31vs31).

They are usually fair and judge on the DO only; for the last few years at least.

BIB - Still pissed off about that. I hope you're right that the celebs can choose the DO dance and not just dance their second dance.