The inspiration for this week’s column comes from a friend of a friend. A friend of mine has a friend who is an avid fan and frequent player of video poker. His question was one I’ve heard many times throughout the years. It deals with the method the video poker machine uses to deal cards – specifically the potential draw cards.
The question was whether or not the machine has pre-determined the draw cards as soon as the deal is made or if it only determines them after the player hits the Draw button. Clearly, this makes a huge difference in how each hand will turn out. Let’s take a look at a simple example. If the initial deal is as follows: 5-diamonds, 7-clubs, Q-hearts, 5-spades, K-hearts.
The proper play is to hold the Pair of 5’s. Now, if the machine has pre-dealt the next five cards and placed them “under” the initial five, the cards that will be “drawn” are the specific three that are under the 7/Q/K, which would really be the second, third and fifth card from the remainder of the deck. But, if it deals three off the top of the remainder of the deck then you get the first, second and third cards from the remainder of the deck. So, the method the machine uses to draw the cards will have a material impact on our final hand!
If the machine dealt five cards face down under each of these cards and they were (in order): 5-clubs, 4-hearts, 8-diamonds, 2-clubs, J-hearts, when we hold the Pair of 5’s, the three cards that will be drawn are the 4/8/J and we have a losing hand.
But, if the machine were to give us the top three cards we would get the 5/4/8 and wind up with Three of a Kind. So, knowing the method of drawing cards is very important to us.
In similar fashion, if the machine “knows” what the next (up to) five cards will be is the game still really random? Maybe the machines should be built so it doesn’t even determine what the next cards are until just before it actually displays them!
Okay, I have to admit, I’ve been tongue in cheek this entire column. Absolutely none of this matters at all to the player (other than maybe psychologically). To the best of my knowledge, there are no regulations dictating how cards should be dealt in a video poker game other than stating they must be random. This means the probability of any card being dealt at any point in time is the same as any other card (assuming a card hasn’t already been dealt from that deck).
In the example I gave earlier, it is exactly as likely the five cards dealt under the initial 5 looked like this: 4-hearts, 8-diamonds, 2-clubs, J-hearts, 5-clubs.
In this situation, it would draw the 8/2/5 and give the player Trip 5’s. If it dealt the top three cards it would give the player a 4/8/2 and the player would lose. Knowing the method of drawing provides us with no useful information.
The second concern – the machine “knows” the cards – is also a meaningless concern. Imagine if video poker was being dealt as a live table game. I’m the dealer. I deal you the five cards as shown earlier. I now look at the next five cards. I know them as much as the machine knows them. How does this change what you’re going to do? How does this change the strategy? How does this change the probability of any outcome?
It doesn’t. You are not playing against the machine and the machine in an inanimate object.
To better understand all this, you also need to have some idea of how a computer uses a Random Number Generator. In its simplest form, it “randomly” generates a number between 0 and 1 (with 15 or more decimal places). With some simple manipulation this can be converted to a number between 1 and 52, which will represent one of our 52 cards.
The Random Number Generator essentially uses a really large stack of these numbers between 0 and 1 and starts at a “random” point and goes thru them one by one.
Now, some of the RNGs used in gaming devices are a bit more complex than this, but the basics are the same. Whether the machine converts the random number into a card or simply knows what the next random number will be doesn’t change anything.
The notion that the machine will “choose” the card only when hitting the deal button can be a bit misleading. There isn’t some endless spinner inside the machine that “stops” when you hit the Deal button. Under normal circumstances, the machine will simply take the next random number and convert it to a card. There are methods that can allow a computer to simulate this type of “spinning,” but in all honesty, I don’t know if it is used in video poker machines. I do not do anything like this in any of my simulations.
The biggest fear of going thru the list of random numbers is that at some point a player may figure out exactly where in the list the machine is and from this predict (know?) the next random number and thus the next card. This is extremely unlikely given how long the list is.
The bottom line is what is important is that the machine randomly chooses the cards. This means each time a card is dealt, the probability of it being dealt is the same as the probability of every other (not previously dealt) card. This is what all the math relies on and what the regulations require. Worrying about the exact workings of how cards are dealt and drawn is nothing more than a distraction.
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Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Email: [email protected].