The mountains classification has been revamped in recent years, the win used to go to whomever got in the most breaks during the mountains stages. This resulted in the win often not going to the best climber, like in 2012 when Thomas Voeckler won the classification from Frederick Kessiakoff in a tough battle which was decided in the final stages. Since then, the points for the lesser climbs have been significantly reduced, and the doubling of the points on the summit finishes virtually assures that the GC contenders will be right up there in the polka dots standings.
The points are awarded (in order of passage past the King of the Mountains banner);
for HC climbs - 25, 20, 16, 14, 12, 10, 8, 6, 4, 2
Category 1 - 10, 8, 6, 4, 2, 1
Category 2 - 5, 3, 2, 1
Category 3 - 2, 1
Category 4 - 1
The stages with the most points on offer are stages 12 (Plateau de Beille) and 20 (Alpe D'Huez), both of which have 75 possible points on the line if a rider can crest every climb first. In both of these cases the stages finish on a HC climb, which normally offers 25 points, but are doubled to 50 in the rules, because it is a summit finish.
I must say, I preferred this jersey when it was more open to anyone who was willing to take on the effort of getting into breaks and putting in the huge amount of effort to do so then take the points on offer, and fight off all the other contenders who are trying to do the same thing. Under the current rules, the race for the polka dot jersey just gets wrapped up in the battle for the yellow, and it has less of the "race-within-a-race" feel.
As I said above the really key stages are the HC summit finishes, and whilst it is possible for a breakaway rider to take the win on one of those stages, it is much more likely to be a stage for one of the GC riders to win. There are 215 points available for a breakaway rider on the main mountains stages, but it would be unrealistic for a rider to make the breakaway in all of those stages, let alone win the maximum points available. (And this is including the Col du Glandon, Col du Tourmalet and La Toussuire, where the break could well be caught already).
The GC riders will be fighting it out for at least 185 points on summit finishes that look likely to end with the main contenders fighting it out. Of course, I wouldn't expect the same rider to win every stage or even finish in the top 3 on each stage, ala Nibali last year, so I would expect the GC riders to be in the low-mid 100s.
Maybe the happy medium is that an elite climber loses a lot of time early on, perhaps in the cobbled stage, and is given the freedom to join breaks for the occasional points grab, but saves enough energy to be good on the all-important HC double points finishes.
Generally, it is very hard to pick out who will be the main contender for the polka dot jersey at the Tour, as it used to be won by a rider who happened to get in the right breaks, and was also a decent climber. These days it is a lot easier, as it will most likely be taken by one of the riders who finishes top-5 (more likely top 2) on GC. And really the two exceptions I see to that scenario are an accomplished climber that targets the polka dot jersey from the start, or a GC rider that loses a lot of time early on, and has to refocus on stage wins and the mountains jersey.
Certainly, nobody has stated openly that they are looking at winning the mountains jersey, but it wouldn't really make sense to, as it would put a lot of pressure on the rider, as well as negate the element of surprise that might needed over another team that also has their eyes on the coveted polka dots.
The main contenders for this jersey are also going to be analysed in the yellow jersey post, so I won't pre-empt that here. Also the battle for the polka dots is really shaped on the road, and I doubt that any of my predictions at this stage will hold any weight come the end of the Tour.