Game Review – Hidden Costs

Counting is important in Quoridor, especially midgame, after openings have been survived, players have moved some, and the shape of the final path is coming into definition. We have all had that close game.Walls are flying down, attacks, responses, and the two pawns quickly get locked into a shared path. You are ahead, just a matter of moving to the goal, and then, as the two pawns approach each other, you realize it: your opponent has got the jump. This changes everything. He win’s by 1.

2015-12-15 15_09_49-Presentation1 - Microsoft PowerPointI like to think of the board as a closed system: every move effects everything else. Let’s look at a game and watch how the numbers change over the course of a few moves. Here is the game code if you want to view the entire thing at the Quoridor Freeboard (ReBPNKwglK4p8Gkm5WkJ0CvCzSZGKEZmgmRkqm8QuSQCYmJiQkBAICZGQC2+IAhqBhRERiAgRkYgIE).

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Moves to goal: W-17, B-9

This game started with a sidewall from White. Black responded with a horizontal wall attack. At this point White is down moves, but up in walls. With Black in open territory, let’s see what White can do to lengthen Black’s path.

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Moves to goal: W-19, B-13

White plays the best kind of wall. Black wants to move once space down, but after White’s wall he has to walk 5 spaces around to get to the same place. Minus the cost of White’s turn, this wall can be thought of as a +4 wall. What’s not as immediately apparent is how many moves this wall will add to White’s total moves to the goal.

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Moves to goal: W-20, B-19

Over the next 3 turns White strikes twice more, winding Black around and forcing him to take more and more moves. From here we can look at a quick table of the moves to goal over the last six turns.

MovesTable

We can see that over the course of six turns White managed to add 6 more moves to Black’s path while only adding one to his own. With the wall count even, both players begin to march towards one another. Before we move, let’s look again at these numbers.

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Here we can see each player’s closest goal in red, and cutting the distance between player’s in half (24/2 = 12), the two spaces where they will meet (pink). Indeed, not to be lost is the fact that it is Black’s move, and the space between the player’s is even, so Black will arrive first and have the benefit of the jump. Could White have known this before his attack? It would have taken incredible foresight, but it is at least worth mentioning. Players of all skill levels can succumb to tunnel vision, only paying attention to the number of moves they are stacking against their opponent, while forgetting that some of these may stack against themselves as well.

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In this scenario, what does White do? He can’t delay moving and try to gain the jump by playing a wall, because Black has at least as many walls to respond with. White loses the waiting game. What would you do? This board is an excellent puzzle for newer players, as it is obvious that White, although down one move, has the advantage and can win this game (try it out at the Quoridor Freeboard with this code j51nX6rLuSxzYIRBJTwjZYQw)
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Unfortunately White makes a mistake a not only walls first, but blocks himself in at the same time.
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This gives Black the opportunity to close the path with one wall. Once the path is shared, the opponents trade the rest of their walls, White surrenders the jump, and Black’s victory is inevitable.

 

Screenshots from the Quoridor Freeboard, the most amazing thing to happen to Quoridor recently. Can you figure out how White should have won this game? Head over to the freeboard and record your solution. Post your answer in the comments below.

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