Blackjack odds say hit 16 against a dealer showing 7
October 29, 2013 3:09 AM
by Elliot Frome
Last week, I described how all casino game strategy is based on expected values. You hit or stick in blackjack not because you hope the next card is of a certain value, but because there are certain probabilities as to what the next card will be and how it will affect your hand and your chances of winning or losing.
If dealt two face cards, you don’t give much thought to strategy. Hopefully, you’re not one of those players who even thinks about splitting 10’s!
But, if you are dealt a 16 and the dealer has a 7, you start giving thought to the strategy.
With a 16, you have five cards that will help you and eight that will bust. The odds don’t look too good and this is why a lot of people stick on this hand, albeit incorrectly. You can stay put, but with a 16, the only way you can win is if the dealer busts, which will happen only 26% of the time.
So, your choices are a 61% chance of busting right away or sticking and having a 74% chance of losing that way. Of course, by hitting you also have an opportunity to improve your hand. All of the five possibilities improve your hand.
If you pick up an Ace, you’ll be most likely to push. Pick up a 5 and you’ll win more than 92% of the time. Don’t get me wrong, it is not a strong hand and the decision to hit is not an overwhelming one, but it is still the right move.
In the simplest form, if facing this situation enough times – which you will if you play for a few hundred hours – you will do better by hitting than by sticking.
In blackjack, you don’t have to memorize all of the math behind the game. It’s not necessary to figure out how many cards will bust you or the dealer.To learn to play blackjack, many players use a simple strategy table. It is a simple little chart that shows every possible player hand and dealer upcard. It then shows what to do – hit, stick, double, split, surrender, etc. Guys like me have already done all the number crunching for you.
Video poker is no different than blackjack except the decision making process is far more complex. In blackjack, the result is essentially binary – you win or lose (okay, you can tie also, so it is not really binary).
In video poker, results can range from a Royal Flush down to a High Pair or you can lose. Since each of the winning hands pays a different amount, the specific result must be taken into account.
If someone invented a game of video poker in which all hands above a certain rank paid a fixed amount, then we’d be able to lump all the hands into win or lose. But, we need to know the probability of each final outcome with a different payout in order to appropriately determine the value of getting that hand.
Surely, it is more valuable to wind up with a Straight Flush than just a Straight. Video poker is also more complex than blackjack in that there is more than just a handful of different possibilities for each hand.
The player can hold or discard all five cards or anything in between for 32 different possible plays. Yes, most of these possibilities will be quickly discarded, but they still must be considered from a mathematical perspective. They are only discarded because the human mind can quickly recognize possible draws that would clearly not be the best strategy.
Despite the extra complexity of video poker, the similarities are still stronger than the differences. In the end the decision still comes down to the expected value. Like in blackjack, you don’t have to sit there trying to figure out how many cards are needed to complete a Straight or the like.
Again, guys like me have already done the job. We have looked at every possible deal and draw for all of the final hands. Using this distribution, each possible draw is assigned an expected value. Whichever draw has the highest expected value is deemed the right play.
The last step in the process is to try and categorize the way each hand is played into a format a human can use. We call this a strategy table.
Unlike blackjack where the strategy is a matrix that crosses player hands with a dealer’s and tells you what to do, a video poker strategy chart lists all the possible playable hands in order in a simple table.
This table usually contains the expected value of each hand too, but this is just for information. To use the strategy table, basically work from the top and find the first hand your dealt hand can make. That’s the way to play the hand.
So, if dealt a 4-card Straight and a Low Pair, you start at the top of the table and work downward. If a 4-card Straight appears first, you play that. If a Low Pair appears first, you play the hand that way.
If you can’t find any hand that matches the hand you were dealt, then you fall to the bottom of the table and find a RAZGU, which means throw all five cards.
Next week, we’ll begin breaking down a strategy table for full-pay Jacks or Better. You’ll be on your way to becoming an Expert Player.
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. Contact Elliot at ElliotFrome@GamingToday.com.