# Strategy Games to Enhance Problem-Solving Ability in Mathematics

In the introduction the authors explain the goal of their book. When two opponents are playing a board game they need some strategy to win or at least maximize the chances not to loose the game. Mastering such strategies is a skill that can also be used in solving a (mathematical) problem. They even give a table drawing parallels between playing (and winning) the game versus the steps in solving a problem. I believe this is only superficial and much better and deeper analogies do exist. Winning a game is just another problem, where you have to first understand the goal, learn the rules, and develop some strategy. By repeated playing, one learns which strategies work and most of all which strategies work consistently and are not just a lucky hap. The meta question is then whether this strategy can be generalized, to other problems of larger dimension or when the rules are inverted or only slightly changed etc. This is a general approach to solve any problem, whether the problem is mathematical or not.

Once this has been made clear, the following chapters are basically an enumeration of games, stating the rules and the goal of the game. There is also what the authors call a "sample simulation" in which some moves or situations are simulated, pointing to some problems or possibilities, making suggestions, and sometimes asking questions to think about.

The different chapters group games that are similar or just form variations of the same game or at least they have similar goals and thus may require similar strategies. We have a chapter on tic-tac-toe-like games, one chapter is called "blocking games" which can come in many different forms (nim is and example), another chapter deals with games where the strategy has to be continuously updated while playing and finally a "miscellaneous" chapter where, among others, several classic western games are found like checkers, dominoes, battleship,...

So far, only the problems were formulated and the reader, or rather the players, are supposed to go through the steps that I sketched in the first paragraph: finding and analysing a winning strategy. The last chapter provides answers and hints to the problems in the previous chapters. What are possible strategies? For example what is the best first move to open the game? Sometimes a mathematical proof may exist for the claim that the one who starts (and makes no mistakes) will always win. However there are no mathematics involved here, although there could have been. And these mathematics need not always be connected with game theory.

In an appendix, illustrations of the (empty) game boards are given, although their geometry should be clear already from the previous chapters. Even if these pages are cut from the book, they may be too small to play on. I do not see the advantage of adding these pages to the printed book. Perhaps an electronic version could be printed with some magnification factor.

In conclusion, this is a nice collection of board games, and when pupils will play such games, they will develop some winning strategies for these games, and these skills will probably help in cultivating certain attitudes and perhaps working schemes to tackle mathematical problems. However it was certainly not the intention of the authors to involve mathematics in this book. I think however that it would not be very difficult to hook up several mathematical problems to these games, somewhat like what Matthew Lane did for video games in his book Power Up. But that would be a completely different book because here the focus is just the games and learning how to win them mostly by playing them, thereby avoiding all the mathematics and abstract game theory.

**Submitted by Adhemar Bultheel |

**23 / Jun / 2017