To determine the number of deer in a game preserve, a conservationist catches 801 deer, tags them and lets them loose. Later, 729 deer are caught; 243 of them are tagged. How many deer are in the preserve?

Step 1 ：This problem is about estimating the population using the method of capture-recapture. The principle is that the proportion of tagged deer in the first sample should be approximately the same as the proportion of tagged deer in the second sample. Therefore, we can set up the following equation: \(\frac{{\text{{number of tagged deer in the first sample}}}}{{\text{{total number of deer}}}} = \frac{{\text{{number of tagged deer in the second sample}}}}{{\text{{number of deer in the second sample}}}}\)

Step 2 ：We know the number of tagged deer in the first sample (801), the number of tagged deer in the second sample (243), and the number of deer in the second sample (729). We can solve this equation for the total number of deer.

Step 3 ：Let's denote the total number of deer as X. Then the equation becomes: \(\frac{{801}}{{X}} = \frac{{243}}{{729}}\)

Step 4 ：Solving this equation, we find that X = 2403.0

Step 5 ：Final Answer: The total number of deer in the preserve is \(\boxed{2403}\)