33 ms·

You can move to any unoccupied position in your half in (1). We didn't analyse it deeply tbh, mostly we'd just build an ultra-castle of some sort. And yes, you

by thom 7y ago

You can move to any unoccupied position in your half in (1). We didn't analyse it deeply tbh, mostly we'd just build an ultra-castle of some sort. And yes, you can put in a new piece to block check. We didn't initially realise this, but the king should be the first piece played, or obviously some smart alec will just leave it off the board. With the assassins, yes it's just a normal setup. But if your first move as white is to turn over the black d7 or f7 pawn, and one of those is the assassin, then you get to take the king. If they're normal pawns, you've spent the move, setting you back in development. Probability-wise I just mean there's a 2/8 chance that it's one of these pawns.

JadeNB 7y ago
> Probability-wise I just mean there's a 2/8 chance that it's one of these pawns. Right—there's a 2 in 8 chance that the assassin is one of those pawns, and a 1 in 2 conditional probability, given that one of them is the assassin, that the one you pick is the assassin; so, by 'deconditioning', a 1 in 8 chance overall. (I think it might make this more plausible—just in terms of probability, not a better rule—to imagine that the rule is changed so that the assassin has to be one of the pawns who can check the king. Then the probability of one of those pawns being the assassin is 100%, by fiat; but you've still only got a 50% chance of picking that one.)
- thom 7y ago
  Yup, this is correct. Apologies for the reckless use of numbers!
V-2 7y ago
"Probability-wise I just mean there's a 2/8 chance that it's one of these pawns" Unless I misunderstood the concept somehow, your calculation seems to be, as the great GM Finegold would put it, "incorrect!" How many ways are there to pick 2 pawns out of 8? (8x7)/2, or 28. How many ways are there to pick 2 pawns out of 6? (6x5)/2, or 15. In other words, there are 28 combinations in total, and only 15 combinations where NEITHER of the 2 crucial pawns is an assassin. This means the actual probability is (28-15)/28, or 13/28, or about 46% (rather than 25%). Let's do a sanity check. "Safe" combinations: ab ac ae ag ah bc be bg bh ce cg ch eg eh gh 15. "Unsafe" combinations: ad af bd bf cd cf de df dg dh ef fg fh 13. Yup, math works out.
- nwallin 7y ago
  That's not the setup. You don't have two assassins, you just have one assassin, so it's not 8 pick 2. But there are two squares the assassin can be on that give a move 1 mate. That gives the 2/8.
  - thom 7y ago
    Yeah this is what I’m picturing, although I’m all for creative misinterpretations!

by thom 7y ago

JadeNB 7y ago

> Probability-wise I just mean there's a 2/8 chance that it's one of these pawns. Right—there's a 2 in 8 chance that the assassin is one of those pawns, and a 1 in 2 conditional probability, given that one of them is the assassin, that the one you pick is the assassin; so, by 'deconditioning', a 1 in 8 chance overall. (I think it might make this more plausible—just in terms of probability, not a better rule—to imagine that the rule is changed so that the assassin has to be one of the pawns who can check the king. Then the probability of one of those pawns being the assassin is 100%, by fiat; but you've still only got a 50% chance of picking that one.)

thom 7y ago
Yup, this is correct. Apologies for the reckless use of numbers!

V-2 7y ago

"Probability-wise I just mean there's a 2/8 chance that it's one of these pawns" Unless I misunderstood the concept somehow, your calculation seems to be, as the great GM Finegold would put it, "incorrect!" How many ways are there to pick 2 pawns out of 8? (8x7)/2, or 28. How many ways are there to pick 2 pawns out of 6? (6x5)/2, or 15. In other words, there are 28 combinations in total, and only 15 combinations where NEITHER of the 2 crucial pawns is an assassin. This means the actual probability is (28-15)/28, or 13/28, or about 46% (rather than 25%). Let's do a sanity check. "Safe" combinations: ab ac ae ag ah bc be bg bh ce cg ch eg eh gh 15. "Unsafe" combinations: ad af bd bf cd cf de df dg dh ef fg fh 13. Yup, math works out.

nwallin 7y ago
That's not the setup. You don't have two assassins, you just have one assassin, so it's not 8 pick 2. But there are two squares the assassin can be on that give a move 1 mate. That gives the 2/8.
- thom 7y ago
  Yeah this is what I’m picturing, although I’m all for creative misinterpretations!