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You can have three players, or you could have a whole circle of players. Everyone should stand in a circle and face toward the middle so that everyone's hands are visible. Take turns going clockwise or counterclockwise, and keep in mind that you aren't limited to only tapping the people directly next to you.  Adding people will make the game stretch on much longer. This method requires much more focus to win. With so many people playing, there may be a person with a hand about to reach five fingers who splits their fingers and it goes unnoticed by the group. Make sure that everyone is following the same set of rules before starting. There is no wrong way to play but make sure everyone is in agreement with rules before starting a round. Rather than having fully extended fingers for the whole game, you can used curled fingers or "nubs." Nubs are created by splitting an odd number of fingers on one of your turns.  Two nubs equal one finger so it takes longer to make a combination or nubs and full fingers equal enough for a dead hand. Decide if nubs are allowed at the beginning of the game. A desperate player will often add the nubs variant when they are about to lose. An example for splitting fingers into nubs can look like this: there are two fingers on your left hand and three on your right. If you split them, you can put 2.5 fingers or, two fingers and a nub, on either hand. Nubs are most beneficial for when you have a total uneven amount of fingers. You must complete someone's nub in order to make it a full finger. To make a dead hand you must have five full fingers, not four full fingers and one nub. A hand does not die but instead stays in the game or comes "back to life" when a tapped hand exceeds five fingers in a turn. When using leftovers, you can add three and four fingers together to get 7 fingers, which equals a dead hand plus two more.  Sometimes this variation is called "zombies." This rule could make the game could go on forever since you recycle fingers. The only option for a dead hand is that it equals exactly five fingers when tapped.
Play with more than one person. Increase the mathematical difficulty by adding nubs. Use leftovers to make the game last longer.