Win Frequency Overrated

            Why does a good blackjack Player stick on bustable hands aginst a Dealer 6?  The quick answer is that with a 6 upcard, the Dealer is likely to bust.  Of course, this is not completely accurate.  The Dealer's bust rate with a 6 is 'only' 42%, which means 58% of the time, he won't bust.  So, first he is not 'likely' to bust.  He is just more likely to bust with a 6 than with any other card.  58% of the time, he will wind up with a 17 through 21 and will beat your hand.  So, why stick?  Well, we need to take into account how often the Player will bust if he takes a hit.  If the Player busts, it doesn't matter what the Dealer does.  This is all a wordy way of saying that the Player is more likely to win if he sticks than if he hits.  Or, in other words, his expected value is higher if sticks than if he hits.  Depending on his specific hand, it might be a relatively small difference between these expected values or it might be a big difference.  But, the difference doesn't matter.  The correct play is the one that has the highest expected value.  This is the key thing to learn for EVERY casino game.

            Blackjack is essentially a binary game.  You either win or lose your base wager.  With the exception of blackjacks itself and Doubles and Splits, the wager is a single unit and the outcome is either even money or the Player loses.  Thus, the critical factor becomes win frequency because for the most part, one win is worth as much as any other win.  In video poker, the outcomes are a bit more varied and thus the analysis is actually a good deal more complex.  If we define 'winning' as any hand that is Jacks or Better, that leaves us with a win frequency of 45% (roughly), but not all wins are created equal.  There are essentially 9 different levels of winning, ranging from Royal Flush down to a High Pair.  The payouts range from 800 for 1 down to a push (which is all you get paid when you have a High Pair). 

            This explains why when playing video poker the win frequency is not very relevant.  Take the following hand as an example:

8♣       9♣       10♣     Q♣      Q♥

            There are two ways to play this hand.  A Player can keep the pair of Queens and have a sure winner.  He'll still have a chance to improve to Two Pair, Trips, Full House or Quads.  But, his win frequency will be 100%.  His other choice is to go for the 4-Card Inside Straight Flush.  If he chooses to go this route, his win frequency will be around 30%.  Of the 47 draws, 8 will result in a Flush, 3 in a Straight, 2 in a High Pair and 1 as a Straight Flush.  The other 34 will result in a loss.  If you're motivated by win percentage, then the right play is to stick with the pair of Queens.  If you're motivated to use the proper strategy, you use expected value to guide you.  When the math is all done, we find that the 4-Card Inside Straight Flush has an expected value of 2.39.  The Pair of Queens has an expected value of 1.54.  It's not really much of a choice.  The 4-Card Inside Straight Flush is by far the superior play.

            Decisions for casino games are made based on the criteria of expected value.  This is not a concept unique to any particular game.  The same methodology that developed blackjack strategy is essentially the same one used for video poker or Three Card Poker or Ultimate Texas Hold'em.  Some of the toughest decisions are of the type I just described where the Player might have to give up a sure winner to go for a hand that in the long run will pay more, but will have a significantly lower win frequency.  The example I gave here is probably not all that hard to follow.  Since the sure win is only a single unit, it won't feel like you are giving up much.  

            But, you may have to make a similar decision if you are dealt a Flush that is also a 4-Card Royal.  If you're playing max-coin quarters, you'll be giving up a sure $7.50 to go for that big payout of $1000.   IF you're a dollar player, you'll be risking $30 to win $4000.  Definitely worth it, but it might just be a little harder to walk away from that sure $30.

How do you say "Soft Hand" in Spanish?

            A couple of weeks ago, I discussed the strategy regarding Soft Hands in blackjack.  Soft Hands are those that contain an Ace which is counted as an 11.  Many of these hands should be played as a double down because of both the ability to significantly improve the hand (to a 17-21) AND due to the high probability that the Dealer will bust - as we mostly double down against Dealer Upcards of 2 through 6.

            As is the case with video poker, however, we must remember that the strategy changes with every paytable change or rule change.  We find slight changes to our strategy if we go from the Dealer hitting Soft 17 to the Dealer Sticking on all 17's.  However, if we go to the Blackjack variants of Blackjack Switch or Spanish 21, everything changes.

            In Spanish 21, the 10's have been removed from the decks, so that we are playing with a shoe of 48-card decks.  As may of us know, 10's and Face cards are our friends when playing blackjack.  They enable us to make good solid hands like 20's.  They help us Double Down on 10's and 11's and get strong hands.  Most importantly, they bust any Dealer hand above an 11.  When you hear about card counters, they are keeping track of the percent of 10's/Faces in the deck.  When there are more than 'normal', the game tips more into the Player's favor.  So, taking 4 of them out of each deck is NOT to the Player's advantage.

            Spanish 21 offsets this by giving the Player a host of other advantages.  The Player can double down on any number of cards.  So, if you start with a 5-3 and hit a 3 for 11, you can still double down.  Player 21's beat Dealer 21's.  Player Blackjacks beat Dealer Blackjacks.  There are also several 'bonus' 21 hands thrown in for free.  Get three 7's and win a small bonus.  The house advantage for Spanish 21 is about 0.8% which makes it a little greater than regular blackjack, but ONLY if you learn the proper strategy.

            Some of the biggest changes occur in the Soft Hands.  Not much changes in terms of how your hand will turn out.  The biggest impact is to the Soft 17's and 18's which have less of a chance to draw a 10, but a slightly greater chance to draw the little card you need to improve the hand.  The problem is that the Dealer will Bust less often.  The Bust rate for a Dealer 6 goes from 44.6% in regular blackjack to 40.6% in Spanish 21.  The changes to the Bust rate is enough to get us to make radical changes to our Soft Hand strategy. 

            To begin with, we NEVER Double down on a Soft 13 through 15 in Spanish 21.  We simply hit these hands.  We Double Down on a Soft 16 only against a 6.  However, if we have 4 cards or more, we hit these hands (remember that you can Double on 3 cards in Spanish 21).  Since there are special payouts for 5, 6 or 7+ card 21's, the lure of these payouts is stronger than the ability to Double Down. 

            Soft 17's are Doubled Down against a Dealer 4, 5 or 6.  BUT, only if the Player has 2 cards against the 4, 3 (or less) cards against the 5 and 4 (or less) cards against the 6.  If he has more cards than the minimum, he hits the hand in search of the 5+ card 21.

            Soft 18's bring us the most opportunities to Double Down.  We stick against a 7, but will Double Down even against an 8 as long as we have 3 cards or less.  We also Double Down against a 6 (5 cards or less), a 5 (4 cards or less) or a 2 through 4 (3 cards or less).

            Essentially we throw out everything we know about Soft Hands in Blackjack if we are planning on learning how to play Spanish 21.

            Next week, I'll discuss Soft Hands in Blackjack Switch and the impact of the Push on Dealer 22 rule on our strategy.  For those that want to get a jump on learning, I'm offering a 2 for 1 deal.  Order Expert Strategy for Blackjack Switch for $6.95 and get Expert Strategy for Spanish 21 for free.  Both books include a multi-color pocket-sized strategy card.  Send check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.

            

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.