Wednesday, February 29, 2012

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'.

Tuesday, February 21, 2012

What to Do When Your Hand Goes Soft

            I'm going to continue talking about blackjack this week.  No, I'm certainly not giving up on video poker!  Blackjack is very similar to video poker in that they both require learning rather complex strategies in order to achieve a strong payback.  However, blackjack has the advantage, in my opinion, in that it is a bit easier to learn the strategy.  Recognizing hands in video poker can sometimes be tricky for the beginners.  But, with blackjack a 16 is a 16.  Well, sort of.

            You can actually have 3 different types of 16's.  The first is a Pair of 8's.  For this, we use Pair Strategy.  The second is a Hard 16, where there is no Ace counting as an 11 involved in the hand.  For this, we use our Hard hand strategy.  Lastly, there is a Soft 16, where the hand contains an Ace being used as an 11.  This hand cannot bust by hitting one additional card, so the strategy is quite different from a Hard 16.  For these, we use our Soft hand strategies.

            It is these Soft hands that I would like to focus on today.  Hard strategies are pretty well known.  Don't hit anything above a 16.  Don't hit most Hard hands between 12 and 16 unless the Dealer has a 7 through Ace showing.  There are a few exceptions with 12 and 13, but if you just followed what I wrote, you'll do okay.  But, when it comes to Soft hands, people do all sorts of things - many of them quite wrong.  We've all even seen a few people try to stop on a Soft low hand.  Which card could you draw that will make your Soft 16 more likely to lose as compared to staying put?

            The reason why learning Soft Hand strategy is so important is because these hands afford us the most opportunities to Double Down.  We Double Down for two reasons.  The first is that we have a strong hand (i.e. 10's and 11's) that is likely to get stronger with a single card.  The second is that we have a good hand and the likelihood is strong that the Dealer will bust.   

            When we have a Soft Hand, we have usually have at least 5 chances to make the hand better to the point where it matters - that is to say, wind up with a hand between 17 and 21.  If you can only hit one card and you hit a 13 and it becomes a 15, you really haven't done anything for your hand - positive or negative.  Quite frankly if you hit a Soft 16 and it become a Hard 12, you haven't done anything negative to your hand either.  So, when we Double Down on a Soft hand, we have a hand that MIGHT improve and we look to do this when the Dealer is likely to Bust.

            That last part tells us the first critical part of Soft Hand strategy - we NEVER Double Down when the Dealer has a 7 through Ace up with a Soft Hand.  The likelihood of the Dealer busting is not strong enough to make it worth Doubling Down.

            Next, you need to understand that when you Double Down, you are actually REDUCING your chances of winning the hand, while INCREASING how much you will win when you do.  So, imagine if an identical opportunity came up 100 times.  If you don't Double Down, you will win 75% of the time.  If you do Double Down you will win only 65% of the time.  Which would you want to do?  Well, if you don't Double Down, you will wager 100 and win back 150 for a net win of 50.  If you do Double Down, you will wager 200 and win 260 for a net win of 60.  If you want to win more, you Double Down even though you will win less often.

            As is the case with video poker, you don't have to do any amazing calculations on the fly to figure out what the right strategy is.  Someone like myself, with the help of some computer programs has already done all the hard work.  That is, unless you consider memorizing the strategy tables to be the hard work!

            There are some slight variations in strategy depending on whether the Dealer hits or sticks on a Soft 17.  What is presented here is for the cases where the Dealer does NOT hit a Soft 17.

  • ·         Double Down with a Soft 13 or Soft 14 against a Dealer 5 or 6 Upcard. 
  • ·         Double Down with a Soft 15 or Soft 16 against a Dealer 4, 5, or 6 Upcard. 
  • ·         Double Down with a Soft 17 or Soft 18 against a Dealer 3, 4, 5, or 6 Upcard.

            If you have a Soft Hand that is more than 2 cards so that you can no longer Double Down, you Hit ALL Soft 12 - Soft 17 and Hit a Soft 18 against a Dealer 9, 10 or Ace Upcard.

            Yes, there will be times you will turn a Soft 18 into a Hard 16 and begin to wonder if you made the right move.  But, in these cases, don't just look at YOUR hand, look at the Dealer's.  If he turns over a 10/Face to wind up with 19 or 20, staying put on your 18 would still result in losing.

            Next week, I'll explain a bit more why I like to use Blackjack as a sort of training tool as we see how the strategy I've covered today might change if you were playing a Blackjack variant, such as Spanish 21 or Blackjack Switch.

Friday, February 17, 2012

Surrender and Insurance

            As I’ve described many times, the concepts of Expert Strategy apply to more than just video poker.  Essentially, they apply to every game in the casino (except slots of course).  You should always know which games to play, what strategy to play them with and what to expect.  Most games in the casino do not require learning very significant strategies to play them properly.  Two that do – video poker and blackjack (and its variants Blackjack Switch and Spanish 21 – require some serious effort to learn them correctly.  The reward for doing so is a payback that is above 99.5%.

            In order to achieve the theoretical payback, you have to learn ALL of the strategy including the less well-known parts and even the parts we might find ‘offensive.’  For blackjack this would be the concepts of insurance and surrender.  The idea of ‘surrender’ is the one that you may find to be ‘offensive’, but there are times it is the right play.

            First let’s begin with the definition of the Insurance bet.  When the Dealer has an Ace up, he will offer everyone at the table the option to make an Insurance wager (which must be ½ of your base blackjack wager).  In reality, it is nothing more than a proposition bet.  If the Dealer has a blackjack, then you win 2 to 1.  If he doesn’t you lose your Insurance wager.  Assuming you have not been counting cards, then the odds of the Dealer having Blackjack is roughly 4 out of 13 (I’m ignoring his upcard ‘Ace’ and any of the cards you can see).  Paying 2 to 1, gets us back 12 out of every 13 units wagered for a payback of about 92.31%.  Obviously, you can do some light card counting and only make this wager when it is more in your favor, but it will take a lot of non-10s/Faces to turn the deck in your favor.

            Sometimes you will hear a Player who has a Blackjack to ask for ‘even money’ when the Dealer has a Blackjack.  This is really the equivalent of the Player making the Insurance wager.  If he makes it and the Dealer does NOT have Blackjack he will win 3 for 2 on his base wager, but would have lost 1/2 unit on Insurance leaving him having won even money.  If the Dealer DOES have blackjack, he pushes his blackjack wager and wins his Insurance wager, which will pay 2 to 1 of the INSURANCE wager which is equal to his base wager – in other words, even money on the base wager.  To keep things moving along, most casinos will just allow the Player to call “even money” and get paid 1 to 1 on his blackjack wager. 

            In reality, this is no better a decision than making the Insurance wager under any other situation.  However, from an emotional standpoint, many Players hate the idea of a total push when getting a Blackjack.  This would be the outcome if you don’t take the Insurance Wager AND the Dealer has Blackjack.  The proper play is to stay unemotional and never take even money.  This situation should only occur about 1 in 275 hands (approximately) which would mean once every 9 hours of play.  For some strange reason, I seem to get it about 3 times an hour?!

            Next up is the Surrender rule.  Many of you may never have heard of it.  The casinos don’t really advertise it much.  You have the right to Surrender your hand before you take any other action by forfeiting half of your initial wager.  Once you hit, split, double down, etc… you can no longer Surrender your hand.  There are two different variations of Surrenders.  The first called Early Surrender is rarely offered.  It allows you to Surrender BEFORE the Dealer checks for a Blackjack when he has a 10/Face or an Ace up.  Thus, even if the Dealer has a Blackjack, you would have forfeited only half of your wager.  This is a big advantage to the Player which explains its rarity.  The other variation is called Late Surrender.  This version has the Dealer checking for Blackjack and only after it is confirmed that he does NOT have one can the Player opt to Surrender.

            Unlike the Insurance Wager, this is not a proposition wager better left ignored.  If that were the case, the casino would have it on the felt in big bold letters “PLEASE SURRENDER!”  Instead it is an option you need to take on occasion and you almost have to ask the casino permission to do so.  From a mathematical perspective, the decision is easy.  If you are going to win less than 25% of the time with your starting two cards, you Surrender.  At a 25%, you would win back exactly half of your initial wager which is what you’ll have left after Surrendering.  Hence, that is why this is the decision point.  There are slightly different strategies depending on whether the Dealer hits or sticks on  Soft 17. 

            You should always Surrender a Hard 16 to a Dealer 9, 10 or Ace.  You should also always Surrender a Hard 15 to a Dealer 10.  If the Dealer hits a Soft 17, you also Surrender a Hard 15 to a Dealer Ace and a Hard 17 (yes, I said 17) to a Dealer Ace.  If the Dealer has a 6 underneath, he gets to keep going and is that much more likely to wind up beating you.   These rules apply to larger shoes of 4-8 decks. 

            The impact of properly Surrendering is that the payback is increased by 0.07%.  This may not sound like a lot, but looked at differently, it can cut the house edge by about 15%.