A computer game that programs peace instead of zap-thy-enemy.

If Tom Snyder's instincts prove right, he will be selling world peace to America's classrooms next year. His instincts haven't failed him yet. This young software designer seems to have made all the right moves. His first was to steer clear of blast-'em computer games - a market that looked great three years ago but has since fizzled. Instead, he zeroed in on educational software, which is beating even business software to the head of the class in market growth, according to Talmis , a Chicago research firm.

Smart move No. 2 was to avoid creating games that merely drill and test. As a result, Tom Snyder Productions Inc., housed in a cozy, homelike office just off Harvard Square, has gained a reputation as an innovative company whose games consistently make the top 10 best sellers on such industry charts as Softsel and Billboard. The Snooper Troops series, which turned detective novels into computer games, has been popular, as well as a game that sends children into the universe, In Search of the Most Amazing Thing.

The most amazing thing to Mr. Snyder would be if the market likes his next game, The Other Side, due out in March. The game vaguely represents United States-Soviet relations and was born after Snyder watched ''The Day After,'' the ABC-TV docudrama about the aftermath of a nuclear attack. The only way for players to keep the world from blowing up is to cooperate with one another.

Sounds heavy. The entrepreneur, a former teacher and rock musician, admits ''it's a tricky piece to market.'' That's why he wants his $1.2 million company to publish the game instead of going its usual route through companies like McGraw-Hill, Scholastic Inc., or Spinnaker Software. He wants to preserve the special ''Snyder'' touches, the ''how'd they do that?'' aspect to the game, he says.

The $80 game is for two players, either individuals or teams. The opposite sides can be in adjoining rooms, using the same computer, or in separate houses, using a telephone hookup to communicate between two computers.

It all starts with fuel - green, blue, and red. One fuel is found all over the world, the second is found only in one country and the third only in the other. The point is for each side to create enough wealth so the two can build a bridge together, linking their countries. The fuels, of course, play a major role in creating that wealth, and it takes constant back-and-forthing with the other side to try to secure some of its fuel and build the bridge - which gets more expensive as each brick is laid.

It seems simple, but it's not. No instructions will come with the game. ''There is no one in the world, I don't care how smart you are, who can build a bridge the first time,'' Snyder challenges, sitting in front of an IBM PC to demonstrate the game.

Each side has three minutes to make a move, using the keyboard to type decisions: Drill in this section, or send in a scouting patrol, for instance. Everything, of course, costs money, and if you are spending too much on cooperating with the other side, an internal defense system automatically kicks on, getting very aggressive with bombs and things. Then the decision is whether to placate this system and calm the domestic waters, or to keep working on foreign policy. Meanwhile, the people on the other side are messaging you, wondering what's going on, why the bombs, what happened to Mr. Nice Guy.

The game can go on for hours. Children and adults who have tested it ''get sucked into the environment'' it creates, Snyder says.

At first, he wanted The Other Side to be realistic, but the question came, how can you translate the impact of the end of the world to a computer game? He and his staff of 12 brainstormed some wild ideas: Make the program self-destruct if the players don't cooperate; even better, warn players that the program will ruin their disk drive, the expensive piece of computer equipment that runs the program, if they fail to make peace.

Making it truly realistic was impossible, so the game remains symbolic only, says Snyder, who believes its real merit is that it gets players to work together to resolve conflict. The ideal age group for the game is 12 to 14, and he hopes it will sell with schools, community groups, and teen-agers in upscale homes.

In a rough-and-tumble competitive world in which Snyder says he's seen many competitors fail this year, The Other Side is a gamble, costing $160,000 just to develop. But, he says, the project is ''energizing'' his company and has convinced him his firm must continue to innovate. ''Unless I've lost my touch, I don't believe we'll have any trouble overwhelming the world.''