# The Advantage of Expert Play

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This morning, I had a discussion with a friend of mine
about a game he is developing. I
explained that playing 'perfect' strategy would be nearly impossible due to
some subtle complexities of the way the game is played. As a result of this, the game would not
likely play anywhere near its 'theoretical' payback. Many games have this 'problem'. Blackjack pays 99.5%, but very few players
play anywhere near this. Ultimate Texas
Hold'em has a payback well into the 99% range too, but stats from the casinos
make it clear that very few Players, if any, can manage this high of a payback.

My friend stated that he thought that he would be able to
play the game close to the theoretical because he is an accomplished Poker
Player. I asked him if he was an
accomplished video poker Player and he said that he wasn't. I told him that any table game against a
Dealer was really nothing more than playing video poker and had no resemblance
to poker even if the game resembles poker. Poker is about reading Players, understanding
their betting patterns and their tells.
Video Poker is about one thing - math.
There is no one to bluff. All
that matters is what is the probability of all final hands given what I choose
to discard. Let's take a look at a
simple example:

5♠ 5♦ 6♣ 7♥ 8♦

In theory, there are 32 ways to play this hand, but I
think we can quickly rule out 29 of them.
I don't think anyone is seriously going to consider holding only the
off-suit 6-8 or holding all 5 cards (which would result in an immediate
loss). There are really on 3 possibilities, 2 of which are identical.
The Player can either hold the Pair of 5's or the 4-Card Straight
(hence, the 2 identical possibilities as it doesn't matter which 5 the Player
keeps.)

If the Player keeps the 4-Card Straight, 8 cards will
result in a Straight and the rest will result in a loss. So, if we add up the total payout, we'd have
8 Straights at 4 units each for a total of 32 units. There are 47 possible draws. We divide the 32 by 47 to get 0.68. This is called the Expected Value (or EV) of
this hand using this possible discard strategy.

Calculating the Expected Value of holding the Pair is a
bit more complex, but easy enough to calculate using a computer. There are 16,215 possible draws if the Player
holds 2 cards. We look at these possible
draws and look at the final hands. The
Player can wind up with a Four of a Kind, Full House, Three of a Kind or Two
Pair. We add up the total payout of all
of these winning hands and divide by 16,215.
The result is an EV of 0.82.

This Expected Value is greater than that of the 4-Card
Straight, so the proper play is to hold the Low Pair. When Playing video poker (and virtually every
other casino game), the proper play is to follow the one with the highest
EV. You don't go with a 'hunch' that a 5
is coming up or that you just feel a 4 or a 9 is going to fill out that
Straight. There is a distinct
probability of each of these events occurring and we use those probabilities to
our advantage. This is what allows a
Player go achieve the theoretical playback of a game.

It is an 'advantage' because most Players don't play this
way. Because of this, the casinos can
off the games with a relatively high payback, knowing that they can rely on
human error to pad their profits. For
the Players who play according to the math, they have the advantage of being
able to play to the theoretical payback over the long run.

Mastering video poker takes some significant effort. The strategy is a complex one and learning
whether to hold the Low Pair or the 4-Card Straight is merely one example of
where a strategy where you play by what you think is right may in fact be quite
wrong. The good news is that thanks to
guys like me, the toughest party of learning the strategy (creating it) has
already be done for you. The next step
is learning that strategy and putting it to practical use. We'll save more of that for next week.