Video Poker Wizard

The following article by the Video Poker Wizard, Cap Richards appeared in the April, 2003 issue of Video Poker Player, the monthly E-zine published by Skip Hughes.

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Maximizing your Expected Hourly Win Rate

"Winning isn't everything, it's the only thing" - Vince Lombardi

"I feel the need - the need for speed" - Maverick and Goose in Top Gun

Your goal as an advantage player is to win the most money possible consistent with the size of your bankroll and your risk tolerance. To accomplish this, you need to maximize your Expected Hourly Win Rate.

In spite of potential objections from IAAA (The International Association for the Abolition of Acronyms), we propose to add the acronym EHWR for Expected Hourly Win Rate to the Video Poker Player Glossary.

Your EHWR is determined by:

1) The Perfect-Play Expected Return for the game you are playing.
2) The comp rate for the game you are playing.
3) The reduction in Expected Return for the imperfections in the Strategy Table you use.
4) The reduction in Expected Return due to your playing errors.
5) The bet size for each hand you play.
6) Your playing speed - hands per hour.

For example, suppose you are playing Full Pay Deuces Wild for quarters at a casino where the comp rate is 0.2%, and your play rate is 500 hands per hour. Assume that the strategy table you are using costs you 0.1% relative to perfect play, and that your playing errors cost you an additional 0.1%. Then:

1) The Perfect Play Expected Return (ER) is 100.7%.
2) Adjusting for Comps yields 100.9%.
3) Adjusting for Strategy Table imperfections yields 100.8%.
4) Adjusting for playing errors yields 100.7%.
5) Multiplying bet size by hourly play rate yields $625 coin-in per hour.
6) EWHR is then $625 multiplied by 0.7% = $4.38.

So EHWR tells you how much (on the average, in the long run) you are being paid each hour for playing. One immediate conclusion is that you aren't going to want to quit your day job if you are playing for quarters.

Next let's examine how you might improve your EHWR for this game.

First, let's assume that we can use a perfect strategy, and play error free. Then adjusted Expected Return is 100.9%, so EHWR is $625 multiplied by 0.9%=$5.63, an increase of $1.35 per hour. Note that this is the absolute maximum we can achieve at 500 hands per hour by improving our accuracy. Further, it is a real challenge to maintain your playing speed while using a longer strategy table and trying to avoid any errors.

As an alternative, let's assume that we just work on playing speed, and don't try to increase our accuracy. Suppose that we can increase our playing speed to 650 hands per hour. Then our coin-in is $812.50 per hour, and our EHWR is $812.50 multiplied by 0.7%=$5.69, slightly more than the EHWR for perfect play. Further there is no reason to settle for 650 hands per hour. Practicing with your favorite Video Poker software, you should be able to reach 750 to 1,000 hands per hour (1000 hands per hour or more is an estimate for full-time professionals). At 750 hands per hour, your EHWR is $6.56. At 1000 hands per hour, it is $8.75. These are far higher than you can achieve with perfect play at 500 hands per hour.

From this and similar examples, we can deduce:

EHWR Principle 1: For full pay games with high expected returns, you will achieve a greater increase in your expected winnings by working on your speed instead of trying to improve your accuracy.

By "high expected returns" we mean games with perfect-play expected returns of at least 100.2%. Examples of games with high expected returns are Deuces Wild, Kings or Better Joker Poker, All American Poker, and any progressive game with a sufficiently large jackpot.

For an example using a game that does not have a high expected return, suppose you are playing Full Pay Double Bonus Poker for quarters at a casino where the comp rate is 0.2%, and your play rate is 500 hands per hour. As before, assume that the strategy table you are using costs you 0.1% relative to perfect play, and that your playing errors cost you an additional 0.1%. Then:

1) The Perfect Play Expected Return (ER) is 100.1%.
2) Adjusting for Comps yields 100.3%.
3) Adjusting for Strategy Table imperfections yields 100.2%.
4) Adjusting for playing errors yields 100.1%.
5) Multiplying bet size by hourly play rate yields $625 coin-in per hour.
6) EWHR is then $625 multiplied by 0.1% = $0.63

Clearly, this is playing for fun, not profit. If you attempt to improve our profits by just playing faster, even 1,000 hands per hour, you end up with an EHWR of only $1.25 per hour.

So instead assume you work on accuracy, use a strategy table with a 0.02% error relative to perfect play and reduce your playing errors to 0.02% as well. Then your adjusted expected return is 100.1% plus 0.2% minus 0.02% minus 0.02% = 100.26%, and your EHWR is $625 multiplied by 0.26% = $1.63, a much bigger improvement. This and similar examples illustrate:

EHWR Principle 2: For full-pay games with low expected returns, you must work on accuracy first, then speed.
Examples of such games are Double Bonus Poker, Flat-Top Jacks or Better, and many others.

There is happy news in this examination of Expected Hourly Win Rate. By playing games with high expected returns and by practicing with software to improve your speed, you can significantly improve your expected winnings. This is happy news because it is easier and more fun to try to play faster with a strategy that you already know than to try to memorize longer and more complicated strategies and to play error free. Finally, by playing faster you reduce the expected number of hours until your next Royal Flush.