I'm don't understand Hilton's pricing. In this case, a five night reservation is more expensive than a three night reservation, followed by a two night reservation (for the same five nights)

I'm looking at the Tropicana Las Vegas, 8/2-8/7 in a 1 King/2 room suite using the California residents rate (code PL1), with a total of $1000.92. But if I break it up into a three night stay ($498.65), followed by a two night stay ($498.31), the total of $996.96 is a few dollars lower.

So why don't I just book 3 nights + 2 nights? Well, I'm paying with a Citi Prestige card, which offers the fourth night free. The Citi concierge can book the 5 nights at the higher rate with the fourth night free but is unable to book 3 nights + 2 nights and still get the fourth night free. The fourth night under the 3 nights + 2 nights scenario is about $50 ($199.20-155.20 = $44 + tax) more than the fourth night under the five night reservation, so my total would be lower by that amount.

Reservation 8/2-8/7 (total is $1000.92, including resort fee and taxes)
8/2 $135.80
8/3 135.80
8/4 155.20
8/5 155.20
8/6 135.80

Reservation 8/2-8/5 (total is $498.65, including resort fee and taxes)
8/2 $100.80
8/3 100.80
8/4 139.20

Reservation 8/5-8/7 (total is $498.31, including resort fee and taxes)
8/5 199.20
8/6 174.30

I'm perplexed why, with the five night reservation, the first three nights are more expensive and the last two nights are cheaper, relative to two reservations for the exact same nights. This plays havoc on my fourth night free.