In this post I will discuss why Villain doubled after dealing the cards in round 1.
The position in round 1 is this:
There is only one way to get two turnovers. The best play is “fg,bf,bc,jc,jb” giving the following position (I used MS Paintbrush instead of explicitly undoing moves in the Spider Solitaire program).
Now let us compute the chances of improving our minimum guaranteed turnovers after turning the card in Column 10. For simplicity assume each of the 13 ranks are equally likely. Let us assume each rank is worth one happy star if it yields a turnover, 0.5 happy stars if you need the correct suit to get the extra turnover and 0 happy stars if no turnovers regardless of suit. Multiple turnovers are possible. For instance, 1.5 happy stars means you always get one extra turnover, with a chance of a second turnover if you were allowed to call the suit, etc.
Note that if the next card in Column 10 were an Ace or Four then we don’t get an extra turnover since we counterfeited the turnover in column 9. It turns out the only good ranks are Three, Nine, Jack and Queen. That’s only 4 happy stars out of a possible 13. Actually, we can increase that to 4 and a half, since a Jack of Spades gives us a double turnover in columns 8 and 10 to go with our turnover in column 9. Given that we only start with two turnovers, it’s about an even chance we get bad cards in both column 9 and column 10.
The other piece of bad news is there are no “atomic columns”. Note that we were forced to pollute column 6 to guarantee our two turnovers in the first place. If we assign the capital letters A and B to columns 9 and 10 respectively, then it’s hard to find decent plans corresponding to the rest of the alphabet. This also means that we need to turnover every card in column 9 or 10, not just the first to get a fighting chance.
In a nutshell, we have difficult short-term problems and long-term problems to deal with. This is why Villain doubled. If I were in Hero’s shoes, I would have passed the double.
One thought on “Villain’s Double in Round 1”
Very interesting! I have no reason to argue with any of your points. What I have very little experience with is this whole idea of asking, “How does this position compare with what we would be seeing now if we had a good chance of winning? After a deal, almost by definition you have no atomic columns, though you can hope to get some even in places where you can’t do turnovers. Idle question… If someone were giving you odds on your ability to win the game at that point, what would you require? Not 100:1, I suspect. 20:1? 6:1? You do keep reminding us that a deal of a full 10 cards can change the situation dramatically… however, if what they land on is lots of non-atomic columns, it admittedly is hard going. Next idle question… They say almost all Spider games can be won with “undo”. Have we had enough decisions that you can see us getting into a much better position if we had used “undo” up to this point and taken different paths? Or would the power of “undo” to create victories come into play in later stages of the game, after we’ve gotten through this position? All those questions posed, I do see all the downsides of the situation you point out and am entirely willing to believe that you were right to double and we should have passed.