Animal Kingdom try demo is an old Chinese game. There are quite a few "animal chess" clones in the app store and this one has the best graphics. Objective is to get any one of your animals to the others Den. Bigger animals can eat smaller animals. All animals move orthogonally.

Chess 3 AI levels, options En Passant and Castling. Shows available moves. Tap and tap to move or drag. Criticisms: doesn't show last move, black player is on top hard to play if your the black player. Can flip board in two player wifi for chess and checkers. No 2D interface available.
Backgammon 3 AI levels, Points to win 1,3,5,10,15,25,50,75,100, option Doubling cube, Crawford Rule. Drag or tap to move. If you hold a piece it'll show possible move locations.
Checkers 3 AI levels, Huffing rule optional to force capture. Movement is by dragging pieces.

Ludo let met state I really hate this game, no strategy but kids like it uggh. 3 levels AI, 5 various options to toggle.
Nine Men's Morris 3 AI levels, Flying rule optional (which is 3 pieces or less can move anywhere on board). See Merelles below how to play.
Reversi 3 AI levels, option to animate pieces to show them flipping over.

Tic-tac-toe 3 AI levels fun for little kids.
Snakes and Ladders options include: Move again on 6 - Sticky final square, Wait for all players to finish. Also can slide the number of snakes and ladders to make it harder or easier.

Astraware Board Games has local LAN multiplayer for all 8 of its games. Chess, Backgammon, Checkers, Ludo, Nine Men's Morris, Revesi, Tic-tac-toe, and Snakes and Ladders. In games that roll a dice, a sceen with a cup holder slides out and you can shake your phone or tap to roll. Also it has an auto roll option. All games with an AI even on hard level it's still pretty easy. The value in Astraware Board Games is being able to play wirelessly with spouse, kids, friend on the same LAN. Also Easy levels are extremely easy so little kids can win

Ball Boom - Elements try demo is a strategic game played against the computer or you can play same device human vs. human. You start by placing a few balls of your color one turn at a time. Then you can start swiping in up, down, right, or left direction and it'll make babies of your balls. Object is to fill the board with more balls than your opponent. Also has a few more elements to keep the game interesting.

Glaurung Chess (free) has the strongest AI among the ones I've tried. It beats Cyber Chess. Plus it's free so if your looking for a good challenge this one is the one to get. Highlights last move and can undo by swiping left or can swipe forward to redo. You can tap to move or drag. Swipe left or right by 5 color schemes brown, blue, green, red, or gray. 2 different piece sets. Move options include: Take Back, Step Forward, Tack Back all, Step Foward all, Move now. Flip board if you wish. AI you can set with slider Stength from 1 to 100. Permanent Brain is an option to have it thinking while your thinking. Play style can choose Passive, Solid, Active, Aggressive, or Suicidal. Book variety opening moves can be set to Low, Medium, or High.

Chess Quest has 1,200 try demo has 120 solving chess problems.

Three best chess apps with the strongest A.I. are Fritz Chess, Shredder Chess and HIARCS Chess. I played Fritz vs. Shredder and Fritz won.

Five In A Row try demo those who like Sequence. Use cards to make five in a row. Can choose 1 player play against CPU or another on LAN wifi. Choose your chip color 4 choices. Have 5 or 7 cards to choose from at all times. Two-eyed Jacks are wild and one-eyed Jacks remove an opponent's chi.

Gipsy King aka Gypsy King is a strategic area conquest game like Through the Desert. You score based on the chain of your caravans.
Size 1 = 1 point, Size 2 = 3 points, Size 3 = 6 points, Size 4 = 10 points, Size 5 = 15 points, Size 6 = 21 points, Size 7 = 28 points.
Lake scoring is based on entire lakes connected. In screenshot above you see red has 4 cars connected so he'll score the 5 points.

Note in 2 player game person with majority will score all points if multiple lakes.

In a 3 player game lake scoring is doubled but just like in 4 and 5 player game those with 2nd majority will score second number of pips if a lake area has multiple pips.

To play the game you take turns placing adjacent to lake #1, lake#2, lake#3, etc. up to 15. Then it's scored. Then 2nd stage begins in reverse order lake #15, lake #14, lake #13, etc. You may pass too and make subsequent move. During second stage you may place two double cars if you wish.

Hive is a very strategic game 2 player game. 2 humans on same idevice or against AI with five different levels of AI. Object is to completely surround opponents butterfly with pieces using your pieces or even some of your opponents. Each creature can only move certain ways like in chess. Are a few rules need to learn. Relatively easy game to learn but hard to master for sure. Try playing hive java game online if you wish. This includes Mosquito expansion. Mosquito clones creatures it's touching and can take on it's abilities.

iGoBang try demo is where you connect five to win. Supports Pente mode. Has Easy, Normal and Hard AI mode. Can play against another play on same device. Choose Black or White. Size of board 10 x 10, 11 x 11, or 12 x 12. Highlights last move with green dot in middle of stone.

Go weiqi can play on board sizes 9 x 9, 13 x 13 or 19 x 19. Komi set from 0 to 10 increments of 0.5. Handicap from 0 to 9. Have CPU play itself or play against AI or 2 humans on same device. No zooming is necessary movement is like on grid snapping system and stone is a few cm above your finger so it's easy to see placement. You can undo move, pass, resign or start new game during your turn.

Aya Go try demo has the best AI here I have it playing with highest AI strength 11 (1 to 11(against Go Weiqi (white). Only takes like 10 secs to move even after 145 moves which is rather impressive. Can save your games. Choose 9, 13, or 19 board size. To place you put your finger exactly where you want it and just above your finger is a small zoomed in window to help you precisely place it. Smart Go Touch is also nice to review 10,000 games with 2,000 problems to solve but has no A.I. Can record live games too.

Hexy is the game of Hex connection game. Has AI, 2 player local, 2 player wifi or internet. Object is to make a connection from your side to the other side while blocking your opponent from doing the same. Can play on 11 x 11, 15 x 15 or 19 x 19 board sizes. Larger the board the harder it is. Hex was invented by the Danish mathematician Piet Hein, who introduced the game in 1942 at the Niels Bohr Institute. It was independently invented by mathematician John Nash in 1947 at Princeton University. John Nash is profiled in the 2001 movie A Beautiful Mind.

Merelles Nine Men's Morris (also lets you play 4, 6 or 12). Play the game by putting all ones pieces on the spaces of board alternating turns. Once all pieces are placed move pieces to an adjacent area. Win by reducing opponents pieces to two or preventing opponent from moving. If you form 3 in a row (a mill) you can choose any opponent's piece to remove. Has Easy, Medium, Hard AI levels also can play against another human. Try online game other versions Merrills and Mills

Reversi which has 5 levels of AI (master level takes about 5 secs to think extremely quick), Hints, Undo/Redo. One or 2 player mode. For those who are serious about playing Reversi and want a serious AI challenge get this one. Play online against bots to test out game.
Morocco an ok AI for Othello (Reversi). Play 2 players mode is also available. My wife destroys Morocoo AI even on hard.
iReversi try demo to play over the internet or even better there is Reversi Online Tournament try demo.

Reiner Knizia's Robot Master is a game of strategy in solo play you maximize your points in all columns and all rows. Your lowest total is your final score. Game consists of 36 cards numbered 0 through 5 with 25 drawn for the game to be place in the 5 x 5 area. Pairs of numbers count as 10 times their face value so two 5's would be worth 50. Triples count as 100. So three 0's are 100. Also can play against an AI where you are columns for instance and AI is rows.

Strategery try demo doesn't have a ton of strategy at all but it's pretty fun like Risk. Can manually place armies if you wish or choose just borders or random. Decide which adjacent countries to attack. Others to check out in this genre include Lux try demo and Galcon Labs.

Zooloretto is a strategic board game. My long review is here.

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