Strategy 106: The End Game

So you’ve gone toe to toe with your opponent, thwarting each other’s roads at every turn, and now it’s beginning to look as though you are competing for a flat win. First of all, congratulations on making it this far. The ability to get this deep into a game of Tak without either of you getting tricked onto the road to Tinuë means that you have both played a beautiful game. However, the tools that have gotten you to this point will no longer be sufficient to carry you to victory. The board is likely polluted with enough walls that the initiative has little or no meaning. Instead, you should be concerning yourself with each player’s current flat count and remaining piece count, and focusing intently on the flat-count differential of possible moves.

flat_count_differentials

In this example, White currently has a flat count lead of 2 (6 – 4). Also of importance, white has 7 remaining pieces to black’s 10. White looks to be able to make an important tak threat by placing at D1 or E2, but Black is prepared to defend with the +2 flat-count differential move 3E< which will fight his flat count deficit back to 1. After that exchange, White will need to be careful not to feed pieces to black’s walls at A2/B3. Despite having a companion each, neither of them can currently make a +2 flat count move. White will likely have to respond to black’s road threat after he plays on A3, but she should be able to do so without hurting her flat advantage by sliding her cap to the center (2C4-). Moreover, she always has the the +2 flat move 2D2< in her back pocket if it becomes necessary.

When you have the flat count advantage and have fewer remaining pieces, you are firmly in the driver’s seat. Simply playing additional flats continues your inexorable march to victory. This is doubly powerful when it also places your opponent in tak since the forced responses likely don’t help them catch up in flat count; moves of this nature maintain your lead and effectively run out the clock  on your opponent. However, despite your distinct advantage, you also need to be wary of your opponent finding high flat-count differential moves. Make sure to guard your prisoners tightly, either under or near walls/caps to restrict your opponent’s ability to release them. Also pay extra close attention to your opponent’t ability to put you in tak. If your opponent forces you to capture, they may be able to leverage those new prisoners. Well-placed flatstones, or even a wall that doesn’t lose your flat count advantage, will limit their ability to find an edge this way.

fewer_pieces_and_flat_advantage

White has a pretty sturdy flat count lead of 4 (10 – 6), and has fewer remaining pieces (5 to Black’s 6). Black has a +3 flat count differential move in 4E5-22, but doesn’t hold up well against White’s ability to flat E5 in response. White does need to be worried about tak threats that try to reclaim the prisoner on A2, but should have adequate responses. It is probably in White’s interest to simply lay a flat somewhere and force Black into an inadequate capture (he won’t be able to flat without losing immediately because the board is nearly full).

Conversely, when you are behind in flat count and have more remaining pieces than your opponent, you are in a tight spot. Putting your opponent in tak can be useful, but only if it makes them capture in ways that you are prepared to directly exploit. You should shift your focus away from road building, and instead concentrate your efforts on controlling and then running stacks to achieve flat count parity.

more_pieces_and_flat_disadvantage

This game is very close, Black is down by a single flat (8 – 7) and has more pieces left than White (9 to 6). However, he’s managed to find some useful stacks that give him some +2 flat differential options (2B4>, 2B4-, and 1D5>). He could capturing B1 or E1 to create a road threat and force White to take on another prisoner. 1D5> is probably Black’s best option for gaining the flat count advantage since he has his captstone nearby for support. After this, he will need to be careful about White’s tak potential but can otherwise start laying flats to try and catch back up in “played piece count”. 

Things are less clear cut when you have the flat count advantage but have more remaining pieces. This advantage is precarious because you have more prisoners than your opponent and are further from ending the game via playing all your pieces. You are still interested in guarding prisoners and placing your opponent it tak, but the goal is no longer to run out the clock as quickly as possible. Instead, you should focus on placing more pieces than your opponent, and on how to weather the storm when they inevitably find ways to release prisoners.

more_pieces_and_flat_advantage

Black has a slim flat count lead of 1 (7 – 6), but has more remaining pieces than White (10 to 6). It is a tenuous lead because he has so many prisoners under B4 and C3. He especially needs to be concerned about White finding a way to flatten his wall and reclaim all its prisoners. He will need to try to keep his pieces well coordinated, eventually forcing White to capture in response to played flats, and play keep-away with the wall-prisoners as long as possible (and find a way to mitigate the damage if White does manage to release them).

Walls and captstones are pivotal pieces in the end game. Although you should avoid over-walling in the midgame, having some pre-existing walls can be quite valuable when you transition to the end game. Similarly, the more prisoners your cap accrues in the midgame, the less valuable it will be in the endgame, so be extra sure that the prisoners it does take are productive exchanges. Finally, although placing new walls during the end game may seem like a losing proposition, be on the lookout for sequences that build up a tall/zebra stack only to be immediately attacked by a new wall. These kinds of exchanges either concede the stack, force it to run, or force it to be claimed by a pre-existing wall/cap. Depending on its surroundings, these may be extremely uncomfortable options for the winner of the stack.

walls_may_be_necessary

This is an incredibly tense game that is very near a conclusion. Despite a flat count lead of 1 (9 – 8), White is nervous about her prisoners on E4 and B5, and sees that Black has a +4 flat count differential move in 4A4-112. Moreover, her capstone is nearly frozen with the weight of all those prisoners. In fact, it might be fair to say that Black’s position looks much stronger. She probably wants to start with 3A3-12 to force Black’s cap to run to A1 (where it will be frozen for the remainder of the game, but will then need to fight back for flat count (probably starting with tak on A4, and then even consider if a wall on C2 to try and liberate the D2 prisoner might be viable). Whatever she does, she’ll need to do it quick, because after 4A4-112 Black only needs to find time to play 4 flats to win the game. 

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