Deal or No Deal Poker

Introduction

On October 3, 2018, I encountered Deal or No Deal video poker at the Red Rock Casino in Las Vegas. This game is influenced by Super Double Double Bonus video poker, yet it introduces two unique elements. The first feature includes a multiplier that applies to the next round for any winning hand that is two pairs or better. The second feature is a 'Banker Offer' that allows players to exchange their potential winnings as the drawn cards are revealed in scenarios where a high pair is present.

Rules

1. Players can wager between 60 to 300 credits*, in increments of 60 credits.
2. The foundational gameplay is based on Super Double Double Bonus. The detailed payout table is provided below.
3. Upon placing a bet, players receive five random cards and can selectively hold onto any of them, similar to traditional video poker rules.
4. Above the five cards drawn, there will be 20 suitcases, each corresponding to a specific card.
5. After pressing the 'draw cards' button, the suitcases associated with the held cards will open, revealing the cards hidden inside.
6. Players will need to select one suitcase from the four options located above each discarded card. Each suitcase will contain one of the 47 cards still remaining in the deck. As players pick suitcases, they will be opened to disclose the replacement cards, along with the other three in each column that weren't chosen.
7. As players select their replacement cards, if they manage to create a hand of a high pair or better, they will receive a call from the Banker with a proposal to cash in on any potential winnings from that hand. Importantly, the player will still accumulate any multipliers earned, regardless of whether they accept the Banker's offer. There’s also a chance the Banker might propose an offer based on high-value situations, such as when aiming for four cards towards a royal flush, but I didn’t play extensively enough to encounter that.
8. When players draw hands of two pairs or better, they will receive a multiplier for the subsequent hand, ranging from 2x to 5x. However, players must continue to bet the same amount for the next hand that earned the multiplier.
9. Each multiplier has a specific weight, and the likelihood of winning that multiplier corresponds to these weights. Casino operators can select from various settings available. The most generous configuration I am aware of is detailed below.
10. Multipliers do not stack with each other. For instance, if a player wins a 4x multiplier on a hand that also had a 3x multiplier, the next hand will simply maintain a 4x multiplier (not multiply to 12x).

The table below indicates the payouts for each hand based on the amount wagered. It's important to note that there is no advantage to betting the maximum coins.

Footnotes:
* While the game at Red Rock allowed bets up to 300 credits per round, Gamblink, the manufacturer, informs me that there is a customizable option permitting a broader range of bets.

The table that follows illustrates the weighting for each multiplier under the most generous game settings.

Analysis

The subsequent table highlights the win (disregarding the multiplier), the number of possible combinations, the probability, and the contribution to the overall return, assuming optimal strategy is played. The lower right cell indicates that players can typically expect to win back 55.97% of their bet amount before accounting for any multipliers.

The above table reveals that the chance of acquiring two pairs or better sits at 0.242657.

The next table provides insight into the probabilities and contributions to averages for multipliers under the most generous settings. The lower right section indicates an average multiplier of 4.168234.

As previously mentioned, the likelihood of achieving a multiplier is 0.242657. The average multiplier, under the most favorable conditions as indicated earlier, is 4.168234. This overall average multiplier can be expressed as:

Probability of multiplier × Average multiplier + Probability of no multiplier =
0.242657 × 4.168234 + (1-0.242657) = 1.768795.

The overall return for the game can be summed up as the product of the base return and the average multiplier =
0.559671 × 1.768795 = 0.989944.

I want to remind readers that the average multiplier utilized in these calculations pertains only to the more lenient setting. There are configurations available that yield lower average multipliers, which will consequently decrease returns. Without extensive sampling, pinpointing the average multiplier of any specific game is impossible.

Strategy

Using my Video Poker Strategy Maker , I present this strategy for Deal or No Deal Video Poker.

If you wish to adopt a different strategy, you should add to the total for all hands with two pairs or better an amount equating to the product of 1.773170 and your bet amount. This constant of 1.773170 is derived from the probability of obtaining a multiplier and the additional multiplier gained beyond the base 1x entitled for your wager, meaning 0.242657 × (4.168234 - 1).

Regarding the acceptance or rejection of the Banker’s offers, I've been informed that in the most favorable conditions, the Banker tends to present offers equivalent to 95% of the expected value, rounding down to the nearest credit. It appears that in stricter settings, the Banker’s offers might be a smaller percentage of the expected values. In the most favorable settings, players should always refuse the Banker’s offers. I suspect that in tighter configurations, the Banker’s offers are lower than the base game itself and should thus be declined as well.

External Links

• Video demonstration. It's advisable not to hold a 10 kicker when you have a pair of nines.
• Discussion discussing Deal or No Deal Video Poker on my forum at Wizard of Vegas.

Written by: Michael Shackleford