The bots problem can be solved in the following way:

Let the games be part of an online casino where the House has a small edge, just like a regular casino (~1%). The mined coins are created in the form of jackpots that are won simply by playing. The value of the mined coins (jackpots) that accrue to the player should be less than the house edge, on average. An owner of a bot farm will not want to apply his bots to the games because then, by the law of large numbers he will lose money. On the other hand humans will want to play because its fun. This is called Entertainment Value. Entertainment Value (EV) to a bot is zero because a bot derives no pleasure from playing the game. Here is the formula:

House Edge > Mined Coins
Mined Coins + Entertainment Value > House Edge

This would work best with a stablecoin lest the bot farm owner add an expected price rise to the formula:

House Edge < Mined Coins * (1 + Expected Price Rise)