I know that playing multi-hand video poker doesn't improve your odds of winning, but I wondered how it is affects the likelihood of a royal appearing.
A royal appears about every 44,000 hands. That's a lot of hands if you're playing single-hand video poker. If you're playing 100-hand video poker, is that then 440 hands you'd play (44000/100) and then expect to see a royal?
Also, how does playing multi-hand video poker affect your comps? Would it only affect them due to the increased amount you're betting per hand? Or would the casino see that you're playing thousands of hands and thus you would be deemed a larger player?
Let's start with your second question. Casinos don't care how many hands you're playing, just how much action you're giving. If you're betting $5 per hand on dollar video poker or a nickel per hand on 100-play poker, you're giving $5 in action with each play. And that's all that matters.
Going back to your first question, you will see royals more frequently on multi-hand video poker, but not as frequently as you calculated. The 44,000 hand average is based on starting with each of the 2,598,960 possible starting hands. Many of these are low and high pairs, three-of-a-kinds, straights, etc., that have no chance of leading to a royal flush. Some of those hands will be your starting hands on the multi-play machine, so maybe you have a gut feeling that 440 hands is too low -- especially if you've played a lot of multi-hand video poker.
What you will see on the multi-hand game is that when you start with a partial royal, you will complete it much more frequently than on the single-hand game. Say you were dealt four cards to a royal. On average, you will complete it once every 47 hands (there is one card in the deck that will complete the royal and 47 cards total remaining). On a single-hand game, you'll draw to the royal once every 47 times you're dealt a 4-card royal.
Let's move to a 10-play machine. Each time we're dealt a 4-card royal, we have 10 tries at completing it. We have about a 20% chance of hitting at least one royal flush each time we're dealt a 4-card royal. One in 5 is much better than one in 47. (The Wizard of Odds was kind enough to do the math for this example on his website.)
Now let's play a 100-play machine and start with the same 4-card royal. We have about an 82% chance of getting at least one royal. Four in 5 is much better than 1 in 5, which is much better than 1 in 47.
We will complete partial royals more frequently, but we still have to be dealt a partial royal in the first place. And there are only 20 ways to be dealt a 4-card royal.
The main reason you won't see a royal every 440 hands is because the 100 hands you play each time are not independent. The 100 hands all begin from the same starting hand. If each hand in the 100-hand group were played independently, then you would see a royal every 440 plays.
But then, that would be no different from playing the hands one at a time, one after another, like on a single-hand machine. And the whole point of multi-hand video poker is playing one starting hand multiple times.
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