Furthermore, the chance of getting an initial combination of matching dice seems to improve drastically when opting for the smaller initial bet.

The remaining ten (where the initial bet was the smallest one), resulted in nine wins and only one loss. (This is as close to being confirmed as is possible without empirical evidence, having played twenty games of poker dice, ten where the initial bet was the largest possible one, and ten where it was the lowest, the statistics speak for themselves: Of the ten first games, eight were lost and only two won. This is unconfirmed mathematically, but has been anecdotally observed many times. A low first bet dramatically improving the chances that you will beat your opponent. The initial bet seems to determine the overall 'luck' of the game. There seems to be a possible way to game the system right back, though. So, basically, yeah, the computer is cheating. At higher levels this can be particularly frustrating, with Geralt's opponent easily cranking out great hands with each throw when he himself has trouble getting three-of-a-kind. What this means is that as Geralt moves on to progressively more advanced players, the system that calculates the dice values is modified to favour the NPC, with the NPC having a greater probability of getting a better hand than the player. This may be a 'game of chance' in theory, but in reality some players are inherently 'luckier' than others, including yourself. According to this wikia page on Dice Poker, higher level players do have better 'luck':

The witcher poker dice