The strategy of Strike-A-Light is a combination of Chess and Othello (or Reversi). You need to protect your own Discs whilst at the same time devising a form of attack on your opponent's Discs.
The Lasers in Strike-A-Light provide the means to protect your Discs and attack your opponent. A simple rule of thumb is to cover as many Discs as possible (yours and your opponents) with your Lasers - but be careful of other Lasers on the board. You may inadvertently set up a chain reaction that could let your opponent win in the next move!
Since you can place Discs and Lasers on the board in any order, this creates many different Strike-A-Light playing styles. Some people like to get all their Lasers down on the board straight away, capturing as many of the opponents Discs as possible early on in the game - this is known as the Strike Aggressive or SA style of play.
Other people like to be more cautious and wait for the layout of the board to reveal itself in order to optimise the placement of their Lasers - this is known as the Strike Strategic or SS style of play.
Both SA and SS styles have their advantages and disadvantages:
SA can give you a slight advantage by taking optimal Laser positions on the board, but also reveals your 'hand' and strategy to your opponent, who can now avoid placing their Discs in the path of your Lasers.
SS has the advantage of keeping Lasers in reserve while you analyse the layout of the game, thus allowing you to capture as many Discs as possible later on. The disadvantage is that you will probably miss some good opportunities to cover a lot of Discs - especially if your opponent is an SA.
The best Strike-A-Light player is usually somewhere in between an SA and an SS - varying their style to match the situation and their opponent.
Placing your Lasers is only just the start of your strategy - remember you can strike (activate) a Laser at any time during a game. Usually the 'shooting match' won't happen until the very end, but sometimes a Laser chain reaction may reveal itself. This may allow 'permanent capture' of a Disc or Discs, in which case you need to make the decision on what is best - lose the coverage of an active Laser for a certain gain, or hope you will still be able to capture more Discs later on. Of course if the number of permanently captured Discs is more than half, then the decision is simple - you can win the game in one turn!
Also remember that an active Laser propagates your opponents Laser beams whilst an inactive Laser does not. An inactive Laser can provide a great deal of protection. Sometimes it is wise to sacrifice the coverage of an active Laser for the protection of an inactive one.
The strategy for three and four player games is similar to a two player game - except it now gets political! It is not uncommon for teams to form during a game, with the inevitable 'stab in the back' move played at the end.
Finally, remember that the placing of your Lasers is only part of the strategy, the placing of your Discs is also just as critical, and must be considered throughout the entire game!
...and don't forget the Strike-A-Light motto: "Who strikes last, strikes best."
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