I am confused about how production in cities work. Looking at the little Civ style map, but it's grain and hammer symbols don't line up. For instance, I start a new game, my home city square shows 5 hammers, but the breakdown is 4 grain, and 13 hammers (3 from production, +10 for being a city). I don't have buildings built yet. Why do I have a city square showing 5 production hammers, but the game is only giving me 3? Where did the 4 grain come from if my only city square don't grow grain?

Then my city expands. I pick a tile with 1 hammer and 1 magic. I gain 1 magic production, but 1.5 hammers production. Is this a bug? Do I not understand the way the system works?

I know it really doesn't matter, I just like to understand how the game works. Thanks...