# Win Frequency Overrated

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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.