The unseen cards are shown below
At a glance we can tell that it is impossible to complete a suit of Diamonds or Clubs because there is no exposed Seven of Clubs, Nine of Diamonds or Ten of Diamonds. We can remove one Spade suit, but both Spade suits is clearly impossible. Hearts are impossible with both the only exposed Jack and Six underneath a King, and we only have one empty column. Clearly we need to turn over new cards and hope for the best.
The Danger of One-Hole-No-Card
Although most of the cards are good we have a new problem. There are only three “easy turnovers” in Columns 1 and 8 – and that is assuming we do get good cards. Once these easy turnovers run out, we may well be in serious trouble.
This phenomenon is not unusual. At the beginning of a game, our primary focus is getting an empty column so we usually have to put up with “junk piles” like columns 4,5,6. But during the endgame, we wish we didn’t have many face-down cards buried underneath these junk piles. So there is a trade-off between hunting for empty columns and avoiding awkward junk piles in the endgame. It is beyond the scope of this blog to discuss how to manage this trade-off in detail. I could spout horrible clichés like “you get better with experience” but I would rather lay down the following general principle:
- If you ever find yourself unable to expose a face-down card despite having one or more empty columns, then chances are you are not taking maximum advantage from a position of strength.
In our case, we desperately need very good cards, not just average cards. Fortunately any one of five unseen Tens would fit the bill. Any Ten can play onto the Jack in Column 3, and then we can start to work on Column 6. Alternatively if we expose a Seven of Clubs, then we have legitimate hopes of removing a complete suit of Clubs.
My first action is 5 of Clubs onto 6 of Clubs in Column 2, exposing the 3 of Spades.
Next action is 3 of Spades onto the 4 of Spades, exposing the 7 of Diamonds. This may be a problem since it is harder to expose cards in Column 6 (but there wasn’t much choice).
To simplify matters, I will tidy up the suits by making reversible moves only (even though it’s not an action reversible moves are always safe if we are not aiming to win in the fewest moves).
Note that it is not possible to swap the Kh-Qs in Column 3 with the Ks-Qh in Column 10, unless we remove the Spade suit first.
Despite having one suit removed and two empty columns (assuming we remove the Spades), our position is now very bad. We did not get any of the missing Tens or a Club Seven, and exposing the last Three counterfeited the Three in Column 6. This means it is impossible to turn over any cards in Columns 4 5 or 6, even if we were willing to give up both empty columns. This means we must expose a card in Column 1 or Column 2 (but not both) and hope for the best.
Our position is in fact Kadoban – one more bad card equals game over. There are two basic choices:
- Turn over a card in Column 1
- Turn over a card in Column 2
Note that both cards in Column 1 and 2 are not possible, even if we clear Spades since we need three empty columns.
Taking the dangers of One-Hole-No-Card into consideration it is quite possible that the latter option is better, despite losing both empty columns. What would you play here?