No, 263 is not a lot to get the gems you want. I have over 500,000 simulations for the 3800 gems. That brown bar is from the Achievements section in the game in the bottom right corner, the trophy when you are in the maps. With your 263 games, you should have about 185 gems. The formula is below.
20 * games^0.4 (^ = power), so games to the power of 0.4 multiplied by 20
Have you beaten all of the regular levels in the game? Another good way to get gems is maxing out the re-playable levels (flags with the mace on top). They may have a number in the flag telling you what level you are at on that specific level. Each time you win, it gets harder and more gems.