Draw Poker with Dream Card

Introduction

 

 

Draw Poker with Dream Card (not to be confused with Dream Card Poker) is a video poker variant I encountered at the Red Rock casino on December 15, 2009. It is an optional feature that is added to some multi-play and Spin Poker video poker machines. If the player bets ten coins per hand, as opposed to five, then sometimes the player will get four regular cards on the deal plus a "dream card." Any of the other 48 cards can be used in lieu of the dream card to complete the hand on the deal. The game will select what it thinks is the best one to choose, although sometimes the game gives incorrect advice. If you don't like the card offered, you can click "Dream Card Enabled" to toggle through the other cards until you find one you like better.

The following picture shows an example. On the deal, I received four cards of different ranks, including the queen and the dream card. The game replaced the dream card with the queen of hearts. After the draw, I didn't improve the high pair on the top two hands, but the bottom hand improved to a four of a kind.

 

 

In the screenshot below, from VideoPoker.com, the player got four to a royal in the first four cards, and was lucky to have the Dream Card activated, because it filled in the royal flush.

 

Upon reading the rules for the first time, I was confused if the Dream Card is guaranteed if the player gets a three of a kind or four to a royal in the first four cards. The rule in question states:

If after 4 cards you have a three-of-a-kind, the dream card feature will give you that 4th card for a quad. Four to a royal, the suspense is over — you will get that 5th card.

 

However, as the screenshot below shows, it is possible to get three of a kind in the first four cards and not get the Dream Card. The Dream Card probability is always the same for any given game, for example 50.5% for jacks or better.

 

 

There has been some debate about whether the best card is offered to the player when he gets the Dream Card. In his article A Look at DreamCard — Part II of II , Bob Dancer says, "I've played the game for many hours and I've never seen a case where the DC isn't perfect — or at least tied for being the best. " However, at VideoPoker.com, sometimes the advice is incorrect. As an example, the following is a screenshot from the 9/6 jacks game at videopoker.com.

 

 

In the game above I was offered the Q♣, giving me three to a royal. It would have been better to pick any jack or king for a high pair. Here is the expected value of the suggested play and a correct play:

9♥ J♣ K♣ 4♥ Q♣: expected value = 7.5902 coins
9♥ J♣ K♣ 4♥ J♠: expected value = 7.6827 coins

I have more examples of bad Dream Card advice at VideoPoker.com at the end of this page.

The game usually does give correct advice, however. Bob Dancer's article A Look at DreamCard — Part I of II says that when two more or cards are tied, the game will sometimes tease the player with a card that might lead the player to play incorrectly. Take the following two screenshots of VideoPoker.com as examples. In the one on the left, the game correctly gave me a card to complete the straight. However, any six or jack would do. I don't think it was random that it gave me a heart, tempting me to go for the straight flush. In the hand on the right, the game was correct to complete the flush with any spade. However, it gave me the jack of spades, as a temptation to go for the royal.

 

The following table summarizes both the regular 5-coin return and Dream Card return for all pay tables available from Action Gaming, the manufacturer. Note that the Dream Card return is always higher, although the degree of improvement ranges significantly from 0.02% to 1.55%.

 

 

 

The games at the Red Rock are as follows, with the Dream Card return in parenthesis.

• 8/5 Bonus Poker (99.27%)
• 20/12/10 Deuces Wild (98.10%)
• 9/6 Double Double Bonus (99.04%)
• 9/6 Triple Double Bonus (98.21%)

Next, let's take an in-depth look at the math for 9-6 jacks or better. The following is the pay table for the regular game, which the player will play against 49.5% of the time.

 

This table shows the return table when the player does get the Dream Card. So the player will go against this return table 50.5% of the time. The lower right cell shows the expected return with the Dream Card is 2.98 times a 5-coin bet.

 

 

The next table summarizes the two tables above. The second column shows the probability of each Dream Card state. The third column shows the expected return of each state, relative to a five coins bet. The fourth column is the product of columns 2, 3, 4, and 1/2. The reason for dividing by 2 is that the player must double his bet to enable the Dream Card possibility. The lower right cell shows an overall return of 99.56%.

 

 

The following table takes everything into consideration and reflects the overall return of each hand on the draw. The return column is the product of the probability, win, and 1/2. Again, we divide by 2 because the player must double his bet.

 

 

What follows are overall return tables for all the other games and pay tables.

 

 

More Bad Suggested Dream Card Examples at VideoPoker.com

 

In the game above I was offered the Q♥, giving me a high pair. It would have been much better to pick either the 5♠ or 6♠ for four to a straight flush.

8♠ 4♠ Q♣ 7♠ Q♥: expected value = 7.6827 coins
8♠ 4♠ Q♣ 7♠ 5♠: expected value = 11.7021 coins

 

 

In the game above I was offered the Q♥ again, giving me a high pair. It would have been much better to pick any spade, for a pat flush.

Q♠ 7♠ 3♠ 2♠ Q♥: expected value = 7.6827 coins
Q♠ 7♠ 3♠ 2♠ A♠: expected value = 30.0000 coins

 

 

In the game above the card offered was the 2♠ for a pat straight or four to a straight flush draw. The better card would be the ten of clubs, for four to a natural royal.

J♣ K♣ Q♣ A♠ 2♠: expected value = 18.8298 coins
J♣ K♣ Q♣ A♠ 10♣: expected value = 99.6809 coins

 

 

In the game above the card offered was the Q♠ for three to a natural royal flush or high pair. The better card would any two or jack for a pat straight.

K♠ 10♠ 9♥ Q♥ Q♠: expected value = 7.0490 coins
K♠ 10♠ 9♥ Q♥ J♣: expected value = 10.0000 coins

External Links and Resources

• A Look at DreamCard — Part I of II by Bob Dancer.
• A Look at DreamCard — Part II of II by Bob Dancer.
• VideoPoker.com has a nice demo of Dream Card. Registration is required to play.

Acknowledgement

I would like to thank "J.B." for his mathematical analysis of this game, which agrees to within 0.01% of the return figures from IGT, quoted in the Bob Dancer article linked to above. J.B. says the few differences are due to rounding.

Written by: Michael Shackleford