Draw Poker with Dream Card

Introduction

Draw Poker featuring the Dream Card (Do not confuse with Dream Card Poker ) is a variant of video poker I first came across at the Red Rock casino on December 15, 2009. This feature is optional and can be found on some multi-hand and Spin Poker machines. When playing, if you wager ten coins instead of the usual five, you might be dealt four standard cards along with a 'dream card.' In this case, any of the remaining 48 cards can replace the dream card to complete your hand. The game attempts to identify the best option, although it may not always provide accurate recommendations. If the suggested card isn't to your liking, you can click on 'Dream Card Enabled' to cycle through other options until you find one that suits your preference.

The image below illustrates an example scenario. In this particular hand, I received four cards of different ranks, which included a queen and the dream card. The game replaced the dream card with the queen of hearts. After the draw, I did not enhance the high pair on my top two hands, but the lower hand improved to show four of a kind.

In the screenshot below, from VideoPoker.com , the player initially had four cards towards a royal flush, and was fortunate enough to have the Dream Card feature active, which ultimately completed the royal flush.

When I first reviewed the rules, I was uncertain whether the Dream Card was guaranteed when landing either three of a kind or four to a royal in the initial four cards dealt. The specific rule clarifies:

If you have a three-of-a-kind after the first four cards, the dream card feature will guarantee you that fourth card for a four of a kind. If you have four to a royal, you can be assured that you will receive that fifth card.

However, as depicted in the screenshot below, it is indeed possible to achieve three of a kind in the first four cards without receiving the Dream Card. The probability of obtaining the Dream Card remains constant for any game scenario, for example, 50.5% for jacks or better.

There has been some discussion regarding whether players are consistently shown the best card available when they activate the Dream Card feature. In his article A Look at DreamCard — Part II of II, Bob Dancer asserts, \"In my extensive gameplay experience, I have never encountered a scenario where the Dream Card was not optimal — or at least one of the best choices." That said, at VideoPoker.com, the guidance can occasionally be misleading. For example, here is a screenshot from the 9/6 jacks game hosted on videopoker.com.

In the aforementioned game, I was offered the Q♣, positioning me with three cards towards a royal flush. However, selecting any jack or king would have been more advantageous for forming a high pair. The following outlines the expected value for both the advised play and the correct play:

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

I have compiled additional instances of poor Dream Card recommendations at VideoPoker.com toward the conclusion of this page.

Generally, the game does provide sound advice. Bob Dancer's article A Look at DreamCard — Part I of II suggests that if several cards have tied values, the game might tempt players with a card that could lead them to make a less optimal play. For instance, inspect the following two screenshots from VideoPoker.com. In the first image, the game accurately provided a card that completed my straight; however, any six or jack would suffice. It seems more than coincidental that it offered a heart, luring me into aiming for a straight flush. In the second image, the game correctly completed the flush with any spade, yet chose to provide the jack of spades, making it enticing to pursue a royal flush.

The table below summarizes the returns for both the standard 5-coin play and the Dream Card feature across all pay tables supplied by Action Gaming, the game manufacturer. It is noteworthy that the Dream Card returns are consistently higher, though the extent of improvement can differ significantly, ranging from 0.02% to 1.55%.

The games offered at the Red Rock casino are listed below, with the Dream Card return figures indicated in parentheses.

• 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%)

Now, let’s delve into the mathematics behind the 9-6 jacks or better game. Below is the pay table for the standard game, which players will encounter 49.5% of the time.

This table represents the payout expectations when players successfully obtain the Dream Card. Therefore, the players will engage with this return table 50.5% of the time. The bottom right cell reveals that the expected return with the Dream Card stands at 2.98 times a 5-coin wager.

The next table aggregates the two previous tables. The second column illustrates the likelihood of each Dream Card state occurring. The third column showcases the expected return of each state, relative to a five-coin wager. The fourth column is the product of the second, third, and fourth columns, divided by one half. This division by two accounts for the necessity of doubling the bet to enable the Dream Card option. The lower right cell indicates an overall return rate of 99.56%.

The following table incorporates all essential factors and reflects the overall return for each hand during the draw phase. The return column represents the product of probability, winnings, and one half. Again, we divide by two to accommodate for the double bet requirement.

Following this, I present return tables for various other games and their corresponding pay tables.

More Instances of Poorly Recommended Dream Cards from VideoPoker.com

In the previously mentioned game, I was presented with the Q♥, allowing for a high pair. It would have been much smarter to select the 5♠ or 6♠ for a chance at 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 this game, I encountered the Q♥ once more, which again provided a high pair. However, opting for any spade would have enabled a guaranteed flush.

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

In the game shown, I was offered the 2♠, which led to a potential pat straight or four to a straight flush. Choosing the ten of clubs would have been the superior selection, as it would have granted me 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 this game, the card presented was the Q♠, suggesting three to a natural royal flush or a high pair. The better option would’ve been selecting any two or jack to complete 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 authored by Bob Dancer.
• A Look at DreamCard — Part II of II authored by Bob Dancer.
• VideoPoker.com features a comprehensive demo of the Dream Card concept. Registration is necessary for participation.

Acknowledgement

I extend my gratitude to 'J.B.' for his thorough mathematical examination of this game, which aligns exceptionally close within 0.01% to the return figures from IGT, referenced in the aforementioned Bob Dancer article. J.B. attributes minor discrepancies to rounding errors.

Written by: Michael Shackleford