Hot Streak or Cold Streak?

          I've written many columns in the past several years about how our minds can play tricks with us regarding odd results.  We have a tendency to remember what appears to be very rare events and all but forget the routine.  The end result is that we begin to think that all that occurs are those strange occurrences.  This eventually leads many to believe that a game is either broken (if we are winning) or rigged (if we are losing).  The most likely real answer is two-fold.  First, we're not correctly remembering what actually occurred and second, most people really aren't aware as to how rare or common some event actually is.

            How much does it matter if our memories are a little faulty?  In the grand scheme of things, perhaps not much.  But, from a math perspective, it can make a great deal of difference.  Several months ago, a friend of mine relayed to me his experiences while playing Let It Ride.  He claimed that in a five-hand span he was dealt a Four of a Kind, a Full House, a Straight and TWO Three of a Kinds.  He must have been able to read the expression on my face as he kept telling me that it "REALLY" happened.  I was a bit skeptical. 

            When I got to my computer I did some computations and discovered that the odds of being dealt those 5 hands in a row (in any order) was about 27 BILLION to 1.  Okay, I wouldn't call it impossible, but I wouldn't call it very likely.  But, what if his memory was a little flawed?  What if he was dealt those 5 hands in a block of 10 hands?  What if his memory just 'forgot' about the five losing hands?  In this case, the odds would drop to a 'mere' 492 MILLION to 1.  At least we're back down into Lotto territory.  So, did my friend get these 5 power hands in 5 deals?  10 deals?  20 deals?  I have no clue. 

            This past week, I had the opportunity to do my own research.  Family is visiting from out of town, which usually means I'm playing in the casino a bit more often.  On one evening, I sat down at a five-play machine.  In the first 31 hands, I was dealt 5 Three of a Kinds (on the first 5 cards).  I know these numbers to be true not because I sit there and count how many hands I've played, but rather I was able to see the point counter on the machine and specifically took notice of how many hands I had played after being dealt my 5th Trips. 

            This made me wonder about just how rare is it to be dealt 5 Three of a Kinds in 31 hands.  So, when I got home and went to work on the calculation.  Before you read any further, I'd like you think about this and come up with how often you think this happens?  1 in 100? 1 in 1000? 1 in a million?  This is one of the cases where I think many people would guess rather wrong if they don't know how to do the actual math.  Until I did the calculation, I didn't really know what to expect.  I knew it wasn't astronomical, but I figured it was a bit more rare than it turned out to be.  In the end, the number was 562.  The odds of having 5 Trips in 31 hands is in the same ballpark as the odds of being dealt a Flush on the deal.  It didn't seem like such an odd occurrence anymore, but at the time, I figured the machine was on fire.

            Of course, I didn't draw a single Four of a Kind out of any of these hands.  Five times I had five chances to get those Quads and I couldn't hit a single one.  So, maybe the machine was actually cold, not hot.  How cold was the machine that I couldn't hit a single Four of a Kind from my 5 Trips?  In reality, not at all.  I had an 80% chance of not hitting any Four of a Kinds from these trips.  So had I actually hit one (or more), it would've have been the more rare occurrence.

            There are many things to take away from this column.  One is that it is hard to rely on anecdotal stories.  If you didn't witness the event yourself, you don't even know if the story is true.  And, even if you did witness it yourself, we necessary learn a lot because once upon a time something rare happened.  We need to look at all the stories everywhere in order to learn what to expect.  This is best done by computer programs and computer simulations.  From this, we learn that virtually everything that happens when we play in a casino is just part of the normal ups and downs that happen 'randomly'.

Smackdown! Video Poker vs. Slot Machines

            

            This past week, I received an e-mail regarding last week's article about slots.  In that article I talk about how casinos can legally and do make sure that slot machines are created so that they produce a large number of near misses to make the Player feel like he almost won.   A reader wanted to know if the same is true of video poker.  He wrote:

             I'm always interested in the little things casinos do to try and influence how a player thinks.  Your article spells out an excellent example of how a slot machine display can create the illusion of coming close to a big win. I was wondering if the same thing applies to some extent to Video Poker.  If I'm holding 3 to a royal flush and my 2 new cards don't create a winning hand, but one of those 2 cards is one of the cards I need for the Royal, then I might be influenced to think that I was close to hitting a royal, even though the hand is as much of a winner as any losing hand.  Do you think that VP machines are set up this way as well?

            My answer depends on the definition of "set up".  Are video poker machines specifically programmed to have Player get more near misses than one would expect to occur randomly?  Absolutely not (in most jurisdictions).  In places like Nevada the law requires that any game that uses a real life object (like a deck of cards or die) in digital form must play as random as the real-life object.  In other words, if the game uses a deck of cards, every card must have exactly the same probability of being dealt as every other card. 

            Thus, the casino CANNOT program the video poker machine to have one of the two remaining cards for the Royal Flush be drawn just so it looks like the Player came close to winning - EVEN if it doesn't change the overall outcome of the hand.   So, if the Player is dealt a suited 10-J-Q and the two cards that are supposed to be dealt are the 8D and 5C, the machine cannot change the 8D to the suited King just so the Player comes closer, but still loses.

            What makes Video Poker so superior, in my opinion, to slots is that there is no need for the casinos (or the manufacturers) to do this.  One of the beautiful things about almost any game being played with a deck of cards is that the suspense is built into the game by the very fact that a deck of cards is being used.  True, once in a while a hand is so bad, there is no suspense, but this is infrequent.  How many times have you played a hand of video poker where the first 2 cards are a Pair or 2 cards of a Royal Flush?  Your heart skips a beat as you begin to be believe you're about to be dealt Four of a Kind or maybe a Royal.  That suspense turns to much when the final 3 cards are a mess and help your hand not at all. 

            Conversely, how many times have you been dealt very little (a single High Card) and you wind up being dealt a Flush, a Straight or even a Four of a Kind?  Nobody is forcing these hands to come out of the machine.  They occur because of the nature of the random deck of cards which generates are near misses for us.

            When we look at my reader's question about a 3-Card Royal being dealt one of the necessary cards, we find that it is not such an unusual occurrence.  For a simplistic way to approximate the likelihood of this, we simply have to know that we are going to be dealt 2 cards and we are looking for one of 2 cards to appear.  So, this is roughly equivalent to giving us 4 chances to be dealt 1 card from 47 cards in the deck.  This works out to be about 8+% of the time, hardly making it a rare occurrence.

            I think this leads to an interesting question.  Does it really matter if near misses are occurring because of the nature of a random deck of cards or if it is purposefully being programmed in by the manufacturers.  Quite frankly, by itself, I don't think so.  However, I believe what this tells us about video poker machines and slot machines is the critical part. 

            Everything about a video poker machine is the result of using a random deck of 52 cards.  So, while it is random, we also know all of the probabilities with 100% certainty and thus we can calculate a payback, determine a strategy and know what to expect over the long run.  We can look at the paytable and know everything there is to know about the machine.  We KNOW that if we see 2 machines with identical paytables, they have identical paybacks.

            With slot machines, we know NOTHING.  We can look at 2 slot machines standing side by side with identical paytables and still know absolutely nothing about either of them.  We have no idea how often winning hands will occur.  We have no idea which losing hands are programmed into it and how often it will 'tease' us with near misses.  A moment ago I gave a rough estimate of how often we can expect to get a near miss when drawing on a 3-Card Royal.  This can be calculated with absolute precision too (8.3256%).  You can't do this with a slot machine just by looking at it.

            I guess in the end it comes down to the difference between NFL Football and WWE wrestling.  I don't know who will be the next Champion, but I prefer the NFL version where it comes down to the best team and not the WWE where someone decides who should win and then puts on a good show to make it happen!

Video Poker and Random Number Generators (RNG)

A reader sent me a question this week:

If video poker machines have a RNG in them, how does knowing how to play the game come into play since the results are already determined because of the RNG?

Here was my reply:

In the case of video poker (in most jurisdictions), the RNG serves to merely emulate a live deck, not to pre-determine the outcome.  Many years ago, video poker machines supposedly dealt 10 cards upon hitting the "Deal" button.  5 were face up (that the Player could see) and 5 more face down underneath each of the up cards.  When the Player decided which cards to hold and hit Draw, the cards he discarded would be replaced with the ones that were 'underneath' these discarded ones.

For some reason, this did not sit well with some people (and there was some concern that if someone had the RNG code, he could figure out what the 5 hidden cards were).  Over the years, from what I understand, the code for video poker has changed so that the machine deals 5 cards when the Deal button is hit and then when the Draw button is hit, it will deal the appropriate number of cards from the deck, replacing the discarded ones.

In the end, the exact method of replacement doesn't really matter.  The fact that the machine knows what cards were dealt face down or if it knows what the next 5 cards will be does not change anything for the Player.  You don't know what the hidden cards are, so you have to use the probability of each possible outcome combined with the payout of that outcome to figure out what is the best play.

Imagine if you were sitting at your dining room table and you deal 5 cards face up and then 5 cards face down as the 'replacements'.  AS you deal them face down, you show them to a friend (but not to yourself).  The fact that your friend knows these values does NOT change how you should play your hand.  The fact that your friend can know every possible outcome does not change what you should do.  Obviously for the ONE SINGLE hand, this knowledge might cause HIM to play the hand differently, but as the Player you have to assume that those 5 down cards are random - equally likely to be any of the remaining 47 cards.

This is the only purpose a RNG serves in video poker.  It does NOT determine what the final hand will be or what the 5 dealt cards will be in totality.  It only decides which of the 52 cards will be the next one dealt - just as if you were holding a real deck.  If a casino wanted to, they could turn video poker into a table game (not sure how they would handle multiple players, but imagine a live deck and a single player).

By contrast, slot machines do NOT work this same way.  The machine does NOT determine what symbol will show up on each real independently.  Rather, the RNG determines which of the specific final outcomes will be shown to the Player.  This would be like the RNG determining that the Player will be dealt a Pair of 10's and assuming you discard the other 3 cards that NOTHING will improve your hand.

In video poker only the cards are dealt randomly using the RNG.  In slots, the outcome is determined by the RNG.