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Last week, I introduced the concept of Expected Value as the driving force behind all decision making in the casino. It is the amount we can expect to receive back as a result of a specific hand/decision combination.

When we look at a game in its totality, we call this the game’s payback and express it as a percent. At the individual hand, we express it as a decimal. If the value is over one, it means that we expect to win money on average in this situation.

A value of one exactly would be a return of our original wager. A value of zero would mean we would lose our entire wager.

There are no negatives here as you can’t do any worse than losing your whole wager.

The example I used last week was as follows:






From a quick glance, the hand could be played as a Low Pair, a 3-Card Straight Flush or a 4-Card Straight.

Using a computer program, we were able to calculate the Expected Value of each potential choice by looking at every possible Draw and summing up the results.

This showed us that the proper play was the Low Pair, which had an expected value of 0.82.

This week, I’m going to tweak that hand ever so slightly, changing that 9H into a 3D.  So, we now have:






The choices have changed a bit.  We still have a Low Pair and a 3-Card Straight Flush.  But now we have a 4-Card Flush instead of a 4-Card Straight. So, from last week’s math work, we know that the 3-Card Straight Flush has an expected value of 0.63.

Nothing has changed here, so the Low Pair is still ahead.

But what does changing the hand to a 4-Card Flush do to our math?

There are eight ways to complete an open-ended Straight. There are nine ways to complete a Flush. But the real game-changer is because the Straight pays only four, while the Flush pays six.

So, our return for the Flush is 9 x 6 = 54, while for the Straight it was 8 x 4 = 32.  We divide this by 47 (the number of possible draws) to get an Expected Value of 1.15, which is far greater than the 0.82 of the Low Pair.

In fact, the 4-Card Flush is a net winner on average, with an Expected Value greater than one.

But this example shows the very nature of gambling. We will win just under 20 percent of the time in this situation, but when we do, we will win 6 units back.

So, expect to lose more often than you win, but expect to win more units than you will lose.

More importantly, this example shows how you have to learn to read the cards to play video poker the expert way.  You cannot decide that playing a Low Pair is always the right solution.

You also need to learn to pay attention to the pay table that the machine is using. In our original example, had a Straight paid five instead of four, then the 4-Card Straight would outrank the Low Pair.

Video Poker is a relatively unique game. There are literally hundreds of different varieties and pay tables.

The only other game that might be able to boast this is slots, but slots have no strategy associated with them.

Further, a machine with what appears to be a lesser pay table could actually be programmed to pay a higher payback than the one with the ‘better’ pay table.

With video poker, what you see is what you get. The machine must play the same as using a standard deck of cards (potentially with a Joker).  Thus, everything about the game is known once we know the pay table.

We know the payback of the game and we know the Expected Value of every possible playable hand – and in turn which ones are not playable.

For today, I’ll be happy if you learned that for most versions of Jacks or better video poker that a 4-Card Flush outranks a Low Pair, which outranks a 4-Card Straight.

If you just take that one strategy tip with you, you’ll probably notice a change in your bankroll.

These hands happen a lot and many players play it incorrectly.

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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