The turn in question is

I thought you were going to G1->F1->E1, protecting D3, E3, and hence your +2 production. Instead you did




Even if you miss the 3v1 but hit the 2v1, I'm still in all kinds of trouble. Definitely caught me off guard.

Umm that didn't work.

I think we have a genuine bug to report. I too tracked down tom's post and tried this command:

(gamethumb=16718 turnid=156)

only with brackets instead of parens as suggested. It did not give the game image corresponding to that turn in the preview, but the endgame position as your post gave. Any thoughts from the forum experts?

testes...

 

Yeah, actual bug.  Image links to:

"http://www.wargear.net/rest/GetBoardImage?gameid=16718?turnid=156"

 

Should link to:

"http://www.wargear.net/rest/GetBoardImage?gameid=16718&turnid=156"

 

^^^ and from here, I lost.

Damn. Just realized that the board has the reverse labeling (numbers for columns, letters for rows). Too late to go back now.

The move I made in the pictured position might be the best move available, but I'm unconvinced (in spite of the fun I had) that it is good to allow that position to occur.  Here is why:

61% of the time I break through and your best move is to take the >40% shot at the home base (since my shot is going to be really awesome on a 3v1 or a 2v1 breakthrough).

As an upper bound (for me), within the 61%, I have 36.6% equity, you have 24.4%.   What about the remaining 39%?  If I miss both shots, you are way ahead.   It appears difficult to analyze estimate precisely what your edge would be, but I'm putting it above 80% for sure, and 90% (or more) doesn't seem unreasonable (black is producing +2, white only +1 and black may be able to keep it that way).   So, even in the 80% case, I only win an additional 7.8% for a total of winning 44.4% of the games in this position.  This number is an upper bound, which is why I think I should have made different moves earlier in the game.

wow Hugh, said like a true mathematician, but where did those numbers come from.

I got the 61% (3v1 followed by 2v1) is 61% chance to win one.
On a 2v1 breakthrough, the move to take as black is fortify back and take the 4v1 attack on white to eliminate their forward position (otherwise, you get a 7v4 shot at the home base.) This resets the positions and brings the game back to even.
On a 3v1 breakthrough, as you got, you get a forward position with 2 units next to the base and can follow with a 8v4 attack which is great (quote "really awesome"), so as you said, black must take the 5v5 attack on your base.

I am missing the equity discussion and still think that you played correctly. I wanted to revisit the game, but when I tried to watch the game a second ago, I couldn't find it (error - game deleted or missing).

An important detail is that I used my transfer to get 3 units on the spot to swing at his 1 unit. So, I have 5 units defending no matter what, and 2 or 3 units on the kill spot upon breakthrough. There could be a 4v2 to eliminate the forward position, but no 4v1.

http://www.wargear.net/games/view/16718 still works for me. Two points about numbers - when possible I use exact, but I can't do a continuous 5 armies against 5 with 5v5 die by hand in a short amount of time, so I use my trusty simulator (which does change from 3v2 dice to 3v1 and 2v1 when the simulated situation arises). I kept getting 41,41,42,41 etc for percentages for black's attack on white after a breakthrough, so I use 40% as a worst-case number. The 80/90% number if I lose both attacks isn't at all precise and therefore refutable, but I think most of us would guess that it's better than 80% black at that point.

Equity isn't a great word to use there, but I've been reading a lot of poker books lately. The method of analysis I'm using is forming a tree of possibilities, labeling the edges of the tree with probabilities (estimated, simulated, or exact) and then calculating. The conclusion is that white is doing worse than 45% with his decision to breakthrough, and while the move is the right one for that position, white should play differently _on an earlier move_.

Said another way, black's probability of winning is (.61 * probability of winning after white breaks through) + (.39 * probability of winning if white fails to break through). This much is irrefutable, even if my 80-90% estimate is wrong :)

Thanks for the correction, I don't know what I was thinking, clearly I cannot keep track of small numbers (ex. 1,2,3).

I think 70-80%(essentially the same, very likely but not guaranteed) is correct, if you fail on both attacks, black had a +2 bonus and should be able to maintain a blockade of white while getting a bomb in front of white's base, (if white attacks forwards, it will take two turns to get to black's base, at which time black takes the same move Mongrel did, all out attack on white's base. Every turn white waits, the outlook for black gets better.

I can do better.

At this moment, parity.

http://www.wargear.net/boards/view/Spy%20vs%20Spy/Charts

Lies, player 3 hasn't won a single game.

Seat 2 has 1 more game won than Seat 1.

It's hard to have an even split with an odd number of games.

There could have been a stalemate in there somewhere! :P

A stalemate is certainly possible on this map.

In the standard map, place 3 each turn, end turn. That's a stalemate too.