Expecting Value

11 Mar 2004

By Elliot Frome

Last week's column showed possible outcomes from 2 pre-draw hands. Let's take a closer look at those tables.

Starting with: Low Pair (EV = .82)
Final Hand	Occurs	%
- Four of a Kind	45	.28
- Full House	165	1.02
- Three of a Kind	1854	11.43
- Two Pair	2592	15.99
- Losing Hand	11559	71.29
Total	16215	100.00

Starting with: 1 Jack (HON1) (EV = .47)
Final Hand	Occurs	%
- Royal Flush	1	.00056
- Straight Flush	3	.00168
- Four of a Kind	52	.03
- Full House	288	.16
- Flush	326	.18
- Straight	780	.44
- Three of a Kind	4102	2.30
- Two Pair	8874	4.98
- Jacks or Better	45456	25.48
- Losing Hand	118483	66.43
Total	178365	100.00

In the examples above, the Low Pair has a considerably higher EV than 1 High Card. From this we know that if we are dealt a hand that contains both, we hold the Low Pair and discard the 1 High Card. If we look closely, we'll notice, however that the Low Pair will actually result in a losing hand MORE OFTEN than the High Card. On the other hand, the High Card will offer a losing hand or return of your bet nearly 92% of the time. Only 8% of hands will result in a win. On the other hand, your ONLY hope for a Royal Flush is to hold the High Card. On the other hand, your odds of hitting that Royal are pretty poor. In fact, your odds of hitting much of anything beyond Three of a Kind is pretty poor, less than 1% in total.

On the other hand, we've run out of hands!

I don't think my Dad invented the words 'Expected Value' but he sure did make it a common term in gambling circles. It has become the standard, talking not only about video poker but almost every other game as well.

The goal of the term 'Expected Value' was to look at all 'the other hands' and come up with a common way to decide which 'other hand' was the one you wanted to follow. It looks at all those little differences between pre-draw hands, eliminates emotion and boils it down to a single number. The pre-draw hand with the highest Expected Value is the one to follow.

As the example above shows, Expected Value doesn't tell us which hand will win more often or lose less often. It calculates a weighted average of the likelihood of each post-draw hand using the payback of that hand. Again, it must be realized that these are all averages. Over relatively short intervals (dozens to hundreds), the actual numbers can vary greatly from those on the tables above.

When utilizing Expert Strategy, it's not important to memorize the Expected Value of any particular hand, but rather to memorize the order of the hands in the Strategy Table. While sometimes it comes in handy to have a rough idea of a hand's actual Expected Value this is more to level set our expectations of that hand. Our tables above, however, show that sometimes these numbers can be deceiving in terms of what to expect. A higher EV does not necessarily mean a more frequent winner. For this, we need to turn our attention to an outcomes table used in the calculation of the EV as shown above.

Becoming an Expert Player is a long process. Over the past few weeks, I have covered the basic principles of Expert Play as explained using our 'three-legged stool' model. Over the coming weeks I will continue to delve more deeply into each of the three legs. If there is any particular topic that interests you that you'd like me to cover, feel free to drop me a line at compuflyers@prodigy.net

Expecting Value is republished from CasinoCityTimes.com.