Published on Tuesday, May 01, in featsgameslogic. Intro 1 board 2 boards Sacrificing 2X Trap Attacked!
Introduction Math professor and Backgammon expert Bob Koca was playing Notakto online dating with his 5-year-old nephew, when the nephew whimsically suggested that they should both play X. After mathematically analyzing such a game, Professor Koca realized that this was a deceptive new version of the classic game of Nim. Thane Plambeck later dubbed this game Notakto pronounced No-tac-toe.
In this tutorial, you'll learn how to play this game so that you can win every time! Notakto is played on a standard 3-by-3 tic-tac-toe board, and the rules are as follows: If you'd like to try out this game for yourself, you can play Notakto online dating first level online here click reset if you pass the first level to stay.
If you have an iPad, you can download and play the Notakto app here. When referring to general types of squares, I'll use the terms centercornerand edge to apply to the various squares as follows: When I need to refer to a square in more specific terms, I'll refer to the various squares with these terms: I'll also frequently use the terms rotations and reflections. These are important concepts, since patterns that are rotations Notakto online dating reflections will share the same strategy.
Notakto online dating you've got a basic understanding of the concepts involved, it's time to learn how to win 1-board Notakto! Winning 1-board Notakto Mathematician Timothy Chow originally likened the winning moves to that of a chess knight. If you're not Notakto online dating with chess, chess knights move either 1 square vertically and 2 squares horizontally or 1 square horizontally and 2 squares vertically, resulting in an unusual L-shaped move.
If we think of a chess knight on a Notakto board, you'll note that the knight in the corner square below on your left can only move into either of the edge squares marked with a dot. The knight located in the edge square on your right can only move into either of the corner squares marked with a dot.
Because of the unusual way the knight moves, a knight in the center doesn't have any possible moves.
Here's how to use the knowledge of a knight's move to win at Notakto. To guarantee yourself a win on 1-board Notakto, you must play first, and start by placing your X in the center. After each time the other player marks an X in a given square, you'll place your X a knight's move away from that square. As seen in the knight's move graphic above, there will often be two open squares that qualify. Before placing your X, make sure that you're not inadvertently making 3 in a horizontal, vertical, or diagonal line of 3 Xs, thus losing the game.
Played properly, the resulting game should look something like this: Why This Works By starting with your X in the center, that limits every following Notakto online dating to be played on centers and edges, which are squares where you can use the knight's move Notakto online dating. If the other player places an X in a corner at this point, the knight's move will place your X on an edge square.
Conversely, If the other player places an X in the edge at this point, the knight's move will place your X on a corner square. This results in a boot-shaped arrangement of Xs at this point: Notakto online dating refer to this arrangement and any rotations and reflections of this arrangement as the boot trap.
Take a close look at it. The other player in the boot trap above won't place their X in the lower edge or the upper right corner, because they would instantly lose the game. Notakto online dating leaves 4 remaining squares that seem harmless enough. However, when they place their X on any one of those squares, and you place your X a knight's move away again, making sure you don't accidentally complete a horizontal, vertical, or diagonal line of 3 Xsthe board then looks something like this: Notice that placing ANY X on this board must result in a losing play!
From the boot trap, you can always force this situation, which means you'll always be able to win the game. Practice 1-board Notakto online or with the iPad Notakto app until you can always win. Once you feel comfortable enough with the 1-board strategy, it's time to learn to win 2-board Notakto!
Playing 2-board Notakto For playing Notakto with 2 or more boards simultaneously, the rules are similar, but there are a few changes: While you'll still use the boot trap and the knight's move strategy, there are some new adjustments and new strategies to learn in order to win multi-board Notakto online dating every time.
To guarantee yourself a win in 2-board Notakto, the other player must go first. In fact, there is a simple pattern that will help guarantee you a win with any number of boards: When Notakto online dating on an odd number 1, 3, 5, etc.
When playing on an even number 2, 4, 6, etc. There's also a simple rule for remembering where to mark your first X: Your
Notakto online dating move will always be placing your X in the center square of any empty board empty board refers to any Notakto board with no Xs already on it.
When you go first, all the boards are empty, so of course you can make your first move this way. If you're Player 2, there will always be at least one other empty board after the other player's first move, so you can be assured of still having an empty board on which to mark the center square.
These are great strategies for knowing how to start the game in your favor, but as I mentioned earlier, you'll need to learn some more strategies to assure yourself a win. The first new strategy is learning how to sacrifice a board. Sacrificing Since only the person who makes a horizontal, vertical, or diagonal line of 3 Xs on the final available board loses, taking other boards out of play by purposely completing a line of 3 Xs can be very helpful.
Taking a board out of play in this way is called sacrificingjust like the same concept in chess. Let's start with the simplest possible example of sacrificing a board. In the example below, the other player is Player 1, and you are Player 2 "Notakto online dating" there's an even number of boards, remember? Their first Notakto online dating is the center square of one of the boards, and your reply is the center square of the remaining empty board.
From this arrangement, no matter where they put their next X, there will always be 2 Xs in Notakto online dating line. Your response is to complete that line with a 3rd X, and sacrifice that board: Once that sacrifice is made, the game effectively reduces to a 1-board Notakto in which the other person is the second player. As shown in the animation above, you set up your boot trap, and proceed to win the game just as before! While the above game can and does happen, not every game happens in such a simple and straightforward manner.
Our next example will still show the concept of sacrificing a board, but it will happen later, and after a more complex series of moves. This game starts, again, with the other player going first. This time, they're going to start in a corner though it could just as easily be an edgeand you respond just as you should, marking an X in the center square of the remaining board.
This time, however, the other player marks an X on the
Notakto online dating board on which you just played your center X. What do you do in this case? You respond just as you would in 1-board Notakto, and set up your boot trap.
From here, we'll assume the other player marks an Notakto online dating in line with the X they played first.
Naturally, you complete the row of 3 and sacrifice that board. The game then returns to the board on which you've set up your boot trap, and you win in the usual way: This latter, more complex game actually shows a number of concepts that will be important through the rest of this tutorial: When the "Notakto online dating" player marks their X on a board with pre-existing Xs, your next move will be made on that same board.
When the other player marks their X on a previously-empty board, your next X will be placed in the center of another empty board. In the previous tabwe discussed a similar rule that helps determine where you start. This rule, on the other hand, determines on which board you will continue play. Try practicing 2-board Notakto online or with the iPad Notakto app using this approach, but don't "Notakto online dating" discouraged if you don't win.
Playing this way will guarantee a win if the computer responds as we've assumed above, Notakto online dating you'll notice that there are some situations that haven't been covered yet.
The most common is when they start on a corner or an edge, and the next time they make a move on that board, there's no way to make 3 Xs and sacrifice the board!
In the next sectionyou'll learn how to use that kind of play to set up another trap for the other player! The 2X Trap When the other player marks their first X in a corner or an edge, it's quite possible that their next move could prevent you from sacrificing the board on your next move. It's not uncommon to see a situation such as this the X in the right board is yours, the 2 on the left belong to the other player: Another arrangement that could prevent an immediate sacrifice happens when two Xs are "Notakto online dating" on edges that aren't directly across from each other Again, the X in the right board is yours, the 2 on the left belong to the other player: In both of the above cases, the next move is yours.
What is the best move to make? With both arrangements, the answer is exactly the same! You should place an X to make the pattern shown on the left board: The next time your opponent places an X anywhere on a left board with that arrangement, they'll wind up with 2 Xs in a line. When they do, you can place the 3rd X and sacrifice that board! Yet Notakto online dating, you can prepare your boot trap on the right board, and win the game as usual.