This problem is very easy, so I may misread the problem. First player wins The first player's winning strategy Considering the central raw $1 \times 100$ which we call raw X.First player always put tiles $1 \times 2$ on X.Because second player always put tiles on $1$ cell of X, the number of remain cell of X change $100$→$98$→$97$→$95$→$94$→...→$4$→$2$→$1$.First player put $33$ tiles until the number of remain cell of X change $1$.Then first player put tiles on first raw(or third raw) corresponding the $33$ tiles.Next, second player put tiles and the number of remain cell of X change $0$.Then first player put tiles on first raw(or third raw) corresponding the $33$ tiles.Next, second player cannot put tiles.Therefore first player wins.$\blacksquare$