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# Expecting Value

11 March 2004

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

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Elliot Frome

Elliot Frome is a 2nd generation gaming author and analyst. His father, Lenny Frome was considered one of the premier authors of Video Poker books. Titles include, Expert Video Poker for Las Vegas and Winning Strategies for Video Poker, which includes the strategy tables for 61 of the country’s most popular versions of Video Poker. Check out Compu-Flyers website at www.vpheaven.com, or drop Elliot an e-mail at compuflyers@prodigy.net.

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Elliot Frome
Elliot Frome is a 2nd generation gaming author and analyst. His father, Lenny Frome was considered one of the premier authors of Video Poker books. Titles include, Expert Video Poker for Las Vegas and Winning Strategies for Video Poker, which includes the strategy tables for 61 of the country’s most popular versions of Video Poker. Check out Compu-Flyers website at www.vpheaven.com, or drop Elliot an e-mail at compuflyers@prodigy.net.

www.vpheaven.com