Probability

I have to give my dog medicine twice a day. She is a small dog so the dosage is 1/2 a pill AM and 1/2 PM. If I open a new bottle of 100 pills and break one, put the 1/2 back in the bottle, when does it change to be more likely to get a 1/2 pill than a whole pill. I think it is random whether I get a whole or half as I don't consciencly take a whole or a half each time, although I guess the half pills are closer to the top of the bottle. In other words I just shake a few pills into my hand grab one, put the others back. If the one I kept is 1/2 I put it in her food, if it is whole, I break it in half, give half and put the other half back in the bottle. I may not be smart enough to ask this question let alone read the answer. This is just what I thought would be a fun question, not homework, not important, just asking for the sake of asking. -- JHF