Not all Button Men are evenly matched against one another. Though designers attempt to balance a Button Man’s strengths and weaknesses, necessarily it happens that some arrangements of die sizes and skills are more likely to win games than others. Buttons that are exceptionally powerful (or that have problematic special abilities) may be declared not to be “tournament legal” by Cheapass Games, meaning that tournament organizers should consider disallowing those buttons. Most illegal buttons are rare or promotional ones with unusual die skills or special rules. All buttons that have not been licensed from Cheapass (including all of those that exist only on the Button Men Online web site) are illegal by default.
Button Men Online maintains statistics on the hundreds of thousands of games that have been played on the site. Among tournament legal Button Men, win percentages range from the mid-teens to the high sixties.
Therefore, part of the strategy of the game is to begin by selecting a relatively powerful button. However, buttons may be stronger or weaker when playing against other buttons with certain characteristics. For example, a button with small Poison dice might be powerful in general because it has fewer dice worth positive points for its opponent to capture. However, a button with large Shadow dice might be powerful against that button specifically because it can allow the round to end with the Poison and Shadow dice unable to capture each other, and therefore still counted towards their owners’ scores.
Swing and Option dice help to offset buttons’ natural strengths and weaknesses by ensuring that a button’s number of sides need not be exactly the same from one round to the next. Tournament organizers may also choose to minimize the importance of the “meta-game” of button selection (usually with the idea of shifting importance to the players’ skill) by somehow penalizing stronger buttons, or by enforcing random button selection.
However, chance plays a large role in Button Men; it is always possible for a 20-sided die to roll a 1 at an inopportune time. Among tournament legal buttons, at least, no match-up is impossible for either side to win. Inevitably it happens that a weaker Button Man or a less skilled player will claim some improbable victories due to lucky die rolls. This effect is offset somewhat, however, by the rule that a player must win three rounds to win a game.
Articles on Cheapass’ “official fan site” discuss questions of strategy such as choosing the optimal size for Swing or Option dice (including a mathematical formula for how many sides the “larger” Button Man must keep in order to win), and determining which capture to make to have the best chance of protecting one’s remaining dice.