Ask the Slot Expert: How many cards I held when I hit my royals

A few weeks ago I addressed an incorrect statement I overheard about royal flush probabilities. This person said he had read an article that said that you're more likely to get a royal flush when you're dealt three cards to the royal than when you're dealt four cards to it.

Of course, that statement is wrong. You're more likely to complete the royal flush when you're four-fifths of the way there than when you're only three-fifths of the way. Your chances of completing the royal are 1 in 47 starting with a four-card royal and only 1 in 1,081 starting with a three-card royal.

The person making the statement missed an important point in the article. The article said that if you have a royal flush, you're more likely to have started with a three-card royal than a four-card royal. That's because there are so many more ways to be dealt a three-card royal than a four-card royal. Dan Paymar did the calculations for us in Video Poker Optimum Play. The chances of being dealt a three-card royal are 1 in 92 while the chances of being dealt a four-card royal are only 1 in 2,777.

I've been taking pictures of my royals for the past year or so, so I looked through my pictures to see how many of my royals started with one card, two cards, three, four, five and even zero cards. Well, the count for zero cards is zero. I never got a royal taking five cards on the draw.

Of my 13 royals last year (it was an unusually good year — especially compared with the way this year is going, so far), I was dealt two of them. I completed a royal twice holding just two cards. Of the remaining nine royals, four started with three-card royals and five started with four-card royals.

I'm surprised to see that I'm roughly 50/50 on royals starting with three and four cards. So far this year, the royals — well, royal (singular), it's been a bad year — have been few and far between. It started with three cards. As I hit more royals (fingers crossed), we'll see if the trend continues or I start having better luck completing more three-card royals.

Question: My wife and I were at Mohegan Sun last week. She hit a USPIN slot machine jackpot for $9,650. She took $4,000 in cash and the rest in a check. She gave the attendant $200 as a tip. Was that enough of a tip or should she have given that person more? What percentage of any jackpot is an appropriate tip?

One more quick question. What class of slot machines are at Mohegan, Class II or Class III?

I enjoy reading your answers to our questions and enjoy reading your articles in my Casino Player Magazines. They are always informative.

Answer: Mohegan Sun has Class III machines.

I think $200 was more than enough as a tip and I don't think tipping a percentage makes sense in the casino.

Compare hand pays with being waited on in a restaurant. I would certainly expect a higher level of service for a $50 entree than for a $15 entree. Using a percentage to figure out your tip in a restaurant makes sense because you usually get more service the more you pay.

Larger hand pays don't necessarily require more work. A $4,000 hand pay requires counting out 40 hundreds (or 39 hundreds and five twenties). Does a $10,000 hand pay require counting out 100 hundreds? Not necessarily. I've always seen handpays that are multiples of $10,000 paid with pre-counted, banded bundles of $10,000.

This is how a $20,000 hand pay was done. The attendant handed the player one bundle and said, "$10,000." Then she handed him another bundle and said, "$20,000." That was certainly not five times the work of a $4,000 hand pay. If anything, it was considerably less work.

Another argument against using a percentage is that the slot floorpeople don't have any skin in your game. They don't share in your losses.

I usually redeem large tickets at the cage. I always double-check the amount dispensed by the kiosk and I don't like counting large amounts standing at the kiosk. A few days ago, I redeemed a ticket at the cage. The cashier said, "You made some money today."

I said, "You don't know how much I put into the machine."

Actually, I did make some money that day, but that's not the point. You could be down when you hit that hand pay. In fact, if I hit another royal tomorrow, I'd still be down for the year. As I said above, it's been a bad year.

Assuming a two-person operation, I usually tip $10 each for jackpots under $4000 and $20 each for $4,000 and above. Because I mainly (99.999% of the time) play dollar video poker, the value of my hand pays is usually $4,000.

In my experience, and in those of players I've spoken with, slot floorpeople appreciate any tip you give them.

Finally, thanks for the kind words about the articles in Casino Player. I don't think I've ever had an article in Casino Player. Strictly Slots yes, but Casino Player no. In any case, I'm glad you find them informative.