Two players are playing a game on a tape divided into cells that is infinite to the right. The cells are numbered with $1, 2, 3, \ldots$ from left to right. Each cell $x$ is adjacent to cells $x - 1$ and $x + 1$, except for cell $1$, which is only adjacent to cell $2$.

There is a finite number of red chips (the first player's chips) and blue chips (the second player's chips) on the tape. Each cell contains either several red chips, or several blue chips, or no chips at all.

The players take turns. On their turn, a player can either skip the turn or take one of their chips and move it to an adjacent cell. If there are no opponent's chips in the adjacent cell, the turn ends; if there is at least one opponent's chip there, one chip from each player is removed from that cell~--- thus, at the end of the turn, there will still be no two chips of different colors in the same cell.

\newcommand\gameSingle{} % (x,y,color)
\def\gameSingle(#1,#2,#3){\draw[fill=#3] ({#1 + 0.5}, {#2 * 3 + 0.5}) circle (0.2);}
\newcommand\gameDouble{} % (x,y,color)
\def\gameDouble(#1,#2,#3){
    \draw[fill=#3] ({#1 + 0.27}, {#2 * 3 + 0.5}) circle (0.2);
    \draw[fill=#3] ({#1 + 0.73}, {#2 * 3 + 0.5}) circle (0.2);
}
\newcommand\gameMove{} % (label)
\def\gameMove(#1){\draw node at (4, 1.75) {#1};}
\newcommand\gameMoveArr{}
\def\gameMoveArr(#1,#2){\draw[->, thick] ({#1 + 0.5}, 4.1) to[bend right={75 * (#1 - #2)}] ({#2 + 0.5}, 4.1);}

\newcommand\gameBoard{} % (y)
\def\gameBoard(#1){
    \pgfmathsetmacro{\w}{5}
    \foreach \x in {1,2,...,\w} {
         \draw ({\x}, #1) rectangle ({\x + 1}, {#1 + 1});
         \draw node at ({\x + 0.5}, {#1 - 0.3}) {\x};
    }
    \draw ({\w + 1}, #1) -- ({\w + 1.75}, {#1});
    \draw ({\w + 1}, {#1 + 1}) -- ({\w + 1.75}, {#1 + 1});
    \draw node at ({\w + 1.75}, {#1 + 0.5}) {\ldots};
}

\newcommand\gameState{}
\def\gameState{
    \gameBoard(0)
    \gameBoard(3)
    \gameSingle(2,1,black)
    \gameDouble(3,1,black)
    \gameDouble(4,1,white)
    \draw[->, thick] (3.5, 2.3) to (3.5, 1.2);
}

\newcommand\gameImage[2]{ % {caption}{image}
    \begin{minipage}[b]{5cm}\begin{center}
         \begin{tikzpicture}[scale=0.8]#2\end{tikzpicture}

         #1
    \end{center}\end{minipage}
}

\begin{center}\begin{tabular}{c c c}
    \gameImage{Moving to an empty cell\\~}{
        \gameState
        \gameMove(\texttt{2 -})
        \gameMoveArr(2, 1)
        \gameSingle(1,0,black)
        \gameDouble(3,0,black)
        \gameDouble(4,0,white)
    } &
    \gameImage{Moving to a cell\\with your own chips}{
         \gameState
         \gameMove(\texttt{3 -})
         \gameMoveArr(3, 2)
         \gameDouble(2,0,black)
         \gameSingle(3,0,black)
         \gameDouble(4,0,white)
    } &
    \gameImage{Moving to a cell\\with your opponent's chips}{
         \gameState
         \gameMove(\texttt{3 +})
         \gameMoveArr(3, 4)
         \gameSingle(2,0,black)
         \gameSingle(3,0,black)
         \gameSingle(4,0,white)
    } \\
\end{tabular}\end{center}

If both players run out of chips, the game ends in a draw. If only one player runs out of chips, they are declared the loser, and their opponent is declared the winner. Finally, if after $10^{100}$ turns the game has not ended, it is forcibly concluded and declared a draw.

You are given the initial setup of the tape. Determine who will win with perfect play from both players, and find any optimal first move for the first player.