bending a rule

 

I usually don't post a picture from a current game, as I don't want to get advice on what to do or influence future rounds, but this is the final round and I've already committed myself to an answer --  though I'm not at all sure it's correct -- and I think I'd like to post while the situation is fresh in my mind [I have a surprising number of snapshots of game positions that I thought were interesting when I took them, but no longer remember quite what the point I was hoping to make might be.]

But here -- to win,  I need to either

• keep *more* than 10 sides uncaptured -- i.e the X=12, or any two of the other dice.
• allow randomlife to take all my dice but end the game with his poison as the sole uncaptured die.

Unfortunately, I probably have to decide now, still quite early in the round. Should I take the p(X=15)? and if so, with which die should I make the capture? I can see arguments for at least two of them. Or should I push the decision off a little by take non-poison? and which non-poison? and with which die should I make the capture? 

• 

is it obvious? are the choices close?

 

I have two options here:

• take the poison with my small dice and keep the X=20 safe for another turn
• avoid the poison by rerolling the X=20. If I do this, it certainly makes more sense to take the X=12 than the (6).

But which gives me a better chance of winning?

Two possible strategies

 I guess the natural thing to do here is take the shadow die worth 10 sides. But if you don't, and it rolls out of range, you could also win by capturing both 6-sided dice while losing at most 12 sides, and if  it doesn't roll out of range, you can take it on the next turn. 

Which plan makes more sense? Which is mathematically better?

puzzle

I think you could tweak the values on the dice to make this a still more interesting problem, but this is how it just presented itself:

I'm likely to win this round, but does randomlife have any moves with a chance of winning? and if there are, what's the best one?

 

counting exercise

Does devious have any chance of winning in this position? Or even coming out with a tie? What should he do?

what's the best move?

 I'm probably going to lose this round no matter what, but what is irilyth's best move to minimize my chances of survival?

You know, of course, that he has to take my poison to win, and so he can't afford to lose 18 sides. But should he capture my poison with his I(10), with a 40% chance of being captured -- and with the I(8) almost certain to be lost after that -- or is it better to capture with the X=20, with only a 25% chance of being captured (though if it is captured, he's lost for sure.)

It's the almost above that makes me pause. How likely would it be to escape if the I(10) rolled low enough to be captured? The die that rerolls when capturing the I(10) would have to roll a 1, which happens with probability 20% or 25%, AND the I(8) would have to roll higher than my only other remaining die, which would have value 2 or 4.  This doesn't sound like it's enough to trim that 40% chance of the I(10) being captured into a less than 25% chance of losing.