BLANDCorporatio wrote:Fishy wrote:Plug that into your profit/loss/expected value calculation, and you get a divide-by-zero error. The value of 'the king survives the upcoming engagement' is infinite. If Cubbins' actions increased the odds of that happening from 98% to 99%, then the expected value he's added to the Jetstone Cause is 1% of infinity, which is infinity. From an optimizer's perspective, Cubbins is justified if the cost of his action- his life and everything he might hope to accomplish in it- is less than the expected value, which is zero from his perspective, and infinite from Jetstone's.
Min-max 4 life, yo.
Aaaarghhhh. Whatever the take everyone has on whether Cubbins did the tactical right thing, I cannot resist pointing out that the above is wrong.
IF we assign infinity to the value of the King's survival, then 98% odds of survival and 99% odds of survival both bring infinite expected value. So does 1% chance of survival, for that matter. So expected value is not enough.
First off... abstract all you like and this is (I agree) a silly argument, but if the question is how much better is 99% of infinity than 98% of infinity, then you would want the difference between the two. This would simplify to infinity*(0.99-0.98). This is infinitely better! Though I have to admit that I don't know my properties of infinity all that well... it might be that no two infinities are the same, in which case you couldn't simplify using the distributive identity. Either way, if the kings survival is the only outcome that is important to you, then you would want to do whatever you could to make sure the king survives.
Secondly... the least defensible portion of Fishy's argument IMO was the unquoted portion:
Fishy wrote:Coming at it from the other angle, remember the stakes. The king has no heir, and he's about to go into direct combat. If the king croaks in that engagement, the side ends.
That means Cubbins dies. The Prince dies. Cubbins' best friend Ace dies. The archers in the tower die. People Cubbins have never met die. People in cities Cubbins has never seen die. Everything that Jetstone was, and is, and could have been dies.
We don't know that JS has no heir (Ossomer may or may not be heir again) AND the kings death only causes the death of all field units. All units still in the city hex become neutral... it is arguable that this is tantamount to death... but that would be a difficult argument to make with Wanda out of the hex.