As @Stucon says, hitting a pair with only 2 choices would be 5 out of 23, roughly 22%
Assuming you miss first time you would then have a (5+5)/22 chance that your third guess matches either guess 1 or 2, and that's better odds of 45.45%
Instead of increasing the stats, how about reducing the production time by 1 hour per additional artifact? This would help to offset the natural slippage between collections on 24hr cycles