1. (40 points) There is a stack of cards numbered $1 \sim 15$. After arranging them in a certain order, the following two operations are performed: Place the top card on the table, then place the second card at the bottom of the stack. These two operations are repeated until all 15 cards are sequentially placed on the table. If the cards on the table are numbered from top to bottom as $1 \sim 15$ in order, what is the fourth card from the bottom of the original stack?
1. Assuming the cards are arranged in descending order from top to bottom as shown from left to right in Table 1. The first card originally becomes the bottom card, so it must be 15. The third card must be 14. And so on.
Table 1
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline 15 & $\alpha$ & 14 & $\beta$ & 13 & & 12 & & 11 & & 10 & & 9 & & 8 \\
\hline
\end{tabular}

Since the top 8 cards have been removed, the card marked “ $\alpha$ ” becomes the card after 8 and should be placed at the bottom. Therefore, the card marked “ $\beta$ ” is 7. And so on, we get Table 2.
Table 2
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline 15 & $\alpha$ & 14 & 7 & 13 & & 12 & 6 & 11 & & 10 & 5 & 9 & & 8 \\
\hline
\end{tabular}

Similarly, we can determine the original arrangement of the cards (see Table 3).
Table 3
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline 15 & 4 & 14 & 7 & 13 & 2 & 12 & 6 & 11 & 3 & 10 & 5 & 9 & 1 & 8 \\
\hline
\end{tabular}

Therefore, the fourth-to-last card is 5.