# Evaluating Video Poker Hands and Draw Options

In regular poker, the only two things that make one poker hand rank higher than another are the assigned values of the thirteen denominations and the probability of occurrence of the various five card hands. In a deck of fifty-two cards, all of the thirteen different denominations are represented equally with four cards, one in each of the four suits.

The only reason Kings are worth more than Fives is not that they are harder to get, but because the designers of card games assigned a higher value to Kings than they did to the Fives. For the same reason of assigned values, Aces rank higher than Kings, Nines rank higher than Eights, and so on.

In Video Poker, we are concerned only with the types of hands that produce our payout objectives.

We know that all poker hands are combinations of cards that make up the different hands with their relative rankings. There are 2,598,960 combinations of five card hands in a 52 card deck. Aside from the assigned denomination rankings, there are only a certain number of combinations possible that make up each type of hand. The ones with the fewest possible combinations rank higher than other hands.

No hand is less likely to occur than a Royal Flush. Out of the about two and a half million possible poker hands, there are only four combinations of Royals, one in each of the four suits. Compare this to the next two highest ranking hands; Straight Flush and Four of a Kind.

There are thirty-six ways to make a non-royal Straight Flush. These are the nine denominations of King high through Five high Straight Flushes, times the four suits.

Four of a Kind can be made 624 different ways. There is one set of four like cards available in each of the thirteen denominations. The fifth card can be any one of the remaining forty-eight cards in the deck.

1 set of fours x 13 denominations x 48 cards left = 624.

All this goes down the hand ranking line in the same way. The more ways there are to make a certain hand, the lower it ranks in value.

This chart shows the number of combinations of all the pay hands in Jacks or Better.

Hand | No. of Combinations | Percent of Total |
---|---|---|

Royal Flush | 4 | 0.00015 |

Straight Flush | 36 | 0.0014 |

Four of a Kind | 624 | 0.024 |

Full House | 3,744 | 0.14 |

Flush | 5,108 | 0.2 |

Straight | 10,240 | 0.39 |

Three of a Kind | 54,912 | 2.11 |

Two Pair | 123,552 | 4.75 |

Pair, Jacks to Aces | 337,920 | 13.00 |

Other Than Above | 2,062,860 | 79.34 |

This Poker hand occurrence data is not something that you need to remember, but it does give you an idea of what to expect in the way of starting dealt hands. It also serves to show that only about 1% of all the hands you are dealt can probably not be improved by a draw. We draw new cards to just about every hand that the machine deals us. Our goal is to make all our draws exactly right, for the maximum long range return.

Draws to many dealt hands like these are very clear and just a matter of common sense.

Naturally, you hold the three aces and draw two in the first example, and hold the queens and draw three in the second.

On the other hand, many hold/draw decisions are not so easy.

Here's an example -

With this hand we have three reasonable choices:

- Hold the three card Straight Flush in hearts, draw two cards and hope to get either a Straight Flush, a Flush, a Straight, Three of a Kind, Two Pair, or a High Pair.
- Hold a 2 3 4 5 open end draw, draw one card and hope to get the Straight.
- Hold the Low Pair of threes draw three cards and hope to get either Four of a Kind, a Full House, Three of a Kind, Two Pair, or a High Pair.

The best choice here is to hold the Low Pair of threes and draw three cards. If the hearts were three High cards instead of three Low cards, we would hold those and draw two cards to a Royal Straight Flush. All this will be covered later in the book.

## Draw Hand Value Determinations

In video poker, as in Blackjack where highly skilled and successful players know exactly what to do in every situation, be it hit, stand, double down or split, an expert video poker player also knows exactly how to play every hand.

All of the possible draw hands have been given a power rating based on its long term expectation of either the highest amount of positive return or the least amount of loss. In other words, a draw option with the mathematical expectancy of a $1,200 return on 10,000 $1.25 plays will have a higher power rating than a draw with a $900 expectancy. Likewise, a draw that can be expected to lose $100 will have a higher power rating than another draw that has a $200 loss expectancy.

The power ratings of all the possible draw options are the basic information used to compile the "Best Shot" playing strategy at the end of the book.

## How the Power Ratings Are Compiled And Used

In my paperback book, "Beginners Best Shot at Video Poker", I devoted about twenty pages to this subject showing how the power ratings for all the different types of draw options were mathematically determined. I thought that most readers would be interested in this. In hindsight, I think I was wrong about that, so I will skip over it here.

I'll sum it up by saying that after countless hours of calculations, my conclusions about the relative strength of all the options were in complete agreement with other credible works already published on the subject. I guess I could have saved myself a lot of work.

## Card Order Display

Card order has nothing to do with any final hand values and all the hands are presented on the video poker screen in random order. Draw hands are also.

A four card Jack high open end Straight might show on the screen as:

But for illustration purposes, all the Hold cards are shown in an orderly way and in blocks like this:

When playing the machines, there is always some sorting out to do, but you are never rushed and will have plenty of time to do it.

## The Final Strategy Format

In the next chapter, all of your draw hand possibilities, with their abbreviations, are explained and shown in strategy order. This is the most important part of the book.

You will notice that several of the hand abbreviations are shown in red. These are all the hands that have either three or four cards of the same suit. This will speed up your play when you need to refer to your "Best Shot" Strategy.

The draw hands are divided into several groups. These groups serve only to make referencing a little easier and have been given names that are sort of consistent with the "Best Shot" theme. The groups as well as the hands within the groups are in strategy order with the strongest plays shown highest on the list and the weaker plays shown underneath.

eBook Pages

- video poker ebook
- Section I. video poker introduction
- Section II. five card draw poker - The Basic Poker Game
- Section III. jacks or better video poker
- Section IV. evaluating video poker hands and draw options
- Section V. jacks or better strategy - Draw Hands Defined