How do I prevent cheating on my token based card game?
You simply need a mechanic that makes it impossible for a player to see the other players' token counts until they are all simultaneously revealed.  There are quite a few ways to do this, so you have the freedom to choose something that fits with the theme of your game.


Many games (ex: Robo Rally, The Resistance) use cards for this mechanic.  It is one of the simpler methods.  Each player puts a card face down in front of them, and removes his or her hand from the card to show that the decision is final.  All players then reveal their cards simultaneously.  The cards can either be discarded or returned to hand based on the rules of your game.
A single token or tokens that can represent multiple values could be used.  For example, in Pizza Theory, each player has a 6-sided die that is use to signify their decision.  The players cup their hands over the dice until they are revealed.  This may not be practical for your game if each value from 0 to 15 must be possible; while you could use multiple or larger dice, it does increase the chance of a player accidentally bumping them on reveal and changing the values.
In games where multiple pieces of information are revealed simultaneously (rice counts in Shogun) or the pieces are impractical to hold in hand (Puzzle Strike), each player has a screen which can be used to hide their secret information until the reveal.