is the probability of winning two 4 to 1 dog hands the same as winning eight 4 to 1 fav hands?

it makes sense to me that it is, yet i know it's highly likely that im completely off my rocker with my logic here since i have no clue how to figure probability.

just kinda wondering if i can expect to win sixteen 4 to 1 favs in a row as often as i lose four 4 to 1 favs in a row.