UKC

GB lead US 5-4 in 6th end, and US have hammer. They have choice of win 1 stone or blank.

If they win 1 they are level with 2 hammers each (GB us gb us), barring further blanks).

If they blank they are 1 behind with 2 hammers each (us gb us gb), barring further blanks).

So why did they choose to blank?

Because the hammer doesn't get swapped after each end, the hammer goes to the losing team of the previous end. Tactically, it is better to not take any points (or in some cases even lose 1 point) and keep the hammer in the hope that it allows you to take more points in the next end

With the hammer they were in control; every end they can try to set up a score of two, and if they fail that they can (hopefully) blank and try again the next time. If they took a 1 (which their team members did suggest a couple of ends later) then GB would have control, with the option to blank an end and so make it asymmetrical.

The really shocking decision was in the ninth end when the skip decided he would rather try to win the last end by three with the hammer than take 1 in the ninth and steal in the tenth.

I'm not a curler (is that the right term?) but, as a mathematician, I'm still not entirely convinced. I know 2+ is the is the "par" score with the hammer, and the team with the hammer can sometimes (but not always) blank the next end, but I'd have thought being level with (probably) 2 hammers each to follow is better than being 1 down with (probably) 2 hammers each to follow?

Similarly I would have thought if you have the hammer in any odd numbered end (including the first) you're better off blanking as then you have a chance of 1 more hammer end than the opponents. 

Also, is it worth getting a steal of 1, instead of letting the other team win by 1?
You get a point, but they keep the hammer and "expect" to win that end by 2, in which you still end up losing 1 point overall, but it happens one end later. If that gives them the hammer on an even numbered end, again that means that they have 1 more hammer end than you do. From what little I've seen, this does seem to happen quite often on end 1, but not so much on later odd ends.

Taking it to the logical extreme, does the team with the first hammer ever try to blank the first 9 ends, to just win the on the 10th?

I know there are lots of hypotheticals, and this is a huge oversimplication, but I would have thought decisions should be made based on the most likely outcomes?

It was an interesting comparison between the calm, thoughtful approach of the Scottish team and the loud-mouthed, brash, over-confident Americans. I think the Swedes will be a bit calmer. Well done the Scots, and good luck in the final!

This desire to blank ends is partly why the rules were changed to prevent guard stones from being removed at the beginning of the end. This gives the opportunity for more guarded live stones in the house towards the end of the end, making a blank less likely (or less of a sure thing for the team with the hammer).

Yes there is an incentive for teams with the hammer on odd numbered ends to blank, you often see this on the first end for example. But a team with the hammer on an even number end knows this, and so that affects their decision making.

This is what the Americans did on the ninth end, but that was specific to the situation at that moment, and the commentators were shocked by the decision. It represents a swing of 2, which is pretty much the best you could expect to get on the next end with the hammer. Perhaps the reason it doesn't add up to allow the steal is that a score of 2 with the hammer is by no means a sure thing.

In some respects curling is a game of mistakes, a bit like tennis where having your serve broken puts you severely on the back foot. Having a steal against you, or being forced to a couple of 1 scores is pretty damaging.

Thanks for the explanations. It's a fascinating game.

I guess the thing that affects the pure maths and statistics of it is the human element. If it were two AI machines playing each other, I'm sure there would be an optimum solution - but a bit like poker, you're partly playing the odds but mainly playing the mind of the opponent.