Had decided on staying at the Paris hotel til I checked the rates & found it $100 per night higher than Caesars for the same dates. Is it that much better?

Caesars is much better, I can't believe Paris is more. Caesars rooms can be double the cost of Paris. Pay the extra $40 to get a Palace Tower room or tip the checkin clerk and ask to be upgraded.

How does one go about tipping the check in clerk to gain an upgrade? How much do I need to tip, say, for a 3 night stay?

Do I say "I appreciate your help gaining an upgrade" and hand the clerk $50? What happens if he/she says "we have no available upgrades" then keeps the cash?

Pat.

I'd say "Then give me back the money".

Walk up to check in with a $20 folded into quarters. Hold it in your hand behind your credit card with the top part sticking out so the "20" is visible to the clerk. Once the clerk has your reservation up, ask for a specific room upgrade, like, "is there any chance you could upgrade me into a palace room?" The clerk will notice that you have the tip there, they will most likely punch some keys on their computer. If they then say, "sorry, nothing is available" , simply say "thanks for trying" and pocket your 20. If they can upgrade you, leave the 20 under the credit card and slide it to them across the counter. I once had a clerk then say that the tip was not necessary (maybe she was worried about getting caught and wanted to keep it on the up and up) but I motioned for her to keep it. She had a nice gift delivered up to my room, on top of the upgrade. I always ask for something specific and never tip for a "strip view", only an actual upgraded room.

Loki- You're so slick! My DH has mastered the folded bribe, I mean tip, for a better table at a restaurant, too. We've even gotten into booked restaurants without a reservation. I haven't quite mastered the art of bribing while looking naturally, though.

I just had to respond because the visual you inspired was perfect!

Check the comments on tripadvisor.com. I've stayed at the Caesars in Tahoe and the room and bathroom were nice so I bet the LV property is even nicer. I don't think-from what I read-that Paris is better.

By the way, when does one offer $20 instead of $50 for upgrades; or is $20 enough for any room upgrade?

Not that simple.
Caesar's has some very old rooms which are not as nice as Paris' standard rooms, and rooms in the new tower which are nicer than Paris' standard rooms. So you need to try to compare apples to apples. When making reservations at CP, make sure you're not getting prices on the old rooms. You don't want those.

As for the upgrade question, no amount of money will work all the time. Depends on many factors whether or not you can get an upgrade, particularly occupancy rate and the specific hotel you're at. When the upgrade is obtainable, $50 is not necessary.

Thanks for the advice, Ted-good to know!