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Deal or No Deal Poker
Introduction
I first saw Deal or No Deal video poker on October 3, 2018, at the Red Rock in Las Vegas. The game is based on Super Double Double Bonus video poker, but with two twists. The first twist is a multiplier on the next hand for any win of two pair or greater on the draw. The second is a "Banker Offer" to trade whatever you might win, as the cards on the draw are revealed in situations with at least a high pair.
Rules
- The player may play 60 to 300 credits*, in increments of 60.
- The base game is Super Double Double Bonus. The specific pay table is shown below.
- After making a bet, the player will be given five random cards and may choose any ones he wants to hold, as in conventional video poker.
- Directly above the five cards on the draw will be 20 suitcases, four for each card.
- After pressing the "draw cards" button, the suitcases in the columns of held cards will be opened and the cards inside revealed.
- The player will be prompted to choose one of the four suitcases above the position of each discarded card. Each suitcase shall contain one of the 47 remaining cards in the deck. As the player picks suitcases, they shall be opened to reveal his replacement cards, as well as the other three in each column to show the cards the player didn't pick.
- As the player chooses his replacements cards, if he forms a hand of a high pair or higher, he will get a call from the Banker with an offer to sell any direct winnings from the hand. The player will still win any multiplier earned, whether he accepts the Banker offer or not. It is possible the Banker also makes an offer on high expected value situations, like four a to royal flush, but I didn't play it enough to see such a situation.
- Hands on the draw of a two pair or higher win a multiplier on the next hand of 2x to 5x. The player must still make a bet on the subsequent hand of the same amount as the hand that earned the multiplier.
- Each multiplier has a weighting and the probability of winning that multiplier is proportional to its weight. There are different settings available to the casino operator. The most liberal set of weights I'm aware of is shown below.
- Multipliers are not multiplied by each other. For example, if the player wins a 4x multiplier in a hand that already had a 3x multiplier, then the next hand will have a 4x multiplier (not 12x).
The following table shows what each hand pays on the draw by the amount bet. Note there is no incentive to bet max coins.
Pay Table
| Win | Bet of 60 | Bet of 120 | Bet of 180 | Bet of 240 | Bet of 300 |
|---|---|---|---|---|---|
| Royal Flush | 24,000 | 48,000 | 72,000 | 96,000 | 120,000 |
| Straight Flush | 1,500 | 3,000 | 4,500 | 6,000 | 7,500 |
| Four Aces with any 2,3,4 | 12,000 | 24,000 | 36,000 | 48,000 | 60,000 |
| Four Aces with any J,Q,K | 9,600 | 19,200 | 28,800 | 38,400 | 48,000 |
| Four 2s, 3s, 4s with any A,2,3,4 | 4,800 | 9,600 | 14,400 | 19,200 | 24,000 |
| Four Js, Qs, Ks with any J,Q,K,A | 4,800 | 9,600 | 14,400 | 19,200 | 24,000 |
| Four Aces | 4,800 | 9,600 | 14,400 | 19,200 | 24,000 |
| Four 2s, 3s, 4s | 2,400 | 4,800 | 7,200 | 9,600 | 12,000 |
| Four 5s thru Ks | 1,500 | 3,000 | 4,500 | 6,000 | 7,500 |
| Full House | 210 | 420 | 630 | 840 | 1,050 |
| Flush | 180 | 360 | 540 | 720 | 900 |
| Straight | 120 | 240 | 360 | 480 | 600 |
| Three of a Kind | 90 | 180 | 270 | 360 | 450 |
| Two Pair | 60 | 120 | 180 | 240 | 300 |
| Jacks or Better | 30 | 60 | 90 | 120 | 150 |
Footnotes:
* While the game at the Red Rock went up to 300 credits per met, Gamblink, the game maker, tells me there is a configurable setting, allowing for a wider range of bets.
The following table shows the weighting for each multiplier under the most liberal setting for the game.
Liberal Weighting Table
| Multiplier | Weight |
|---|---|
| 2 | 492 |
| 3 | 600 |
| 4 | 2,100 |
| 5 | 2,550 |
| Total | 5,742 |
Analysis
The following table shows the win (before considering the multiplier), number of combinations, probability, and contribution to the return, assuming optimal player strategy. The lower right cell shows the player can expect to win 55.97% of the amount bet, before considering the multiplier.
Return Table
| Hand on Draw | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal Flush | 400 | 35,233,752 | 0.000021 | 0.008484 |
| Straight Flush | 25 | 180,308,491 | 0.000109 | 0.002714 |
| Four Aces with any 2,3,4 | 200 | 92,242,314 | 0.000056 | 0.011106 |
| Four Aces with any J,Q,K | 160 | 97,568,842 | 0.000059 | 0.009398 |
| Four 2s, 3s, 4s with any A,2,3,4 | 80 | 247,317,223 | 0.000149 | 0.011911 |
| Four Js, Qs, Ks with any J,Q,K,A | 80 | 316,807,768 | 0.000191 | 0.015258 |
| Four Aces | 80 | 168,847,716 | 0.000102 | 0.008132 |
| Four 2s, 3s, 4s | 40 | 667,438,461 | 0.000402 | 0.016072 |
| Four 5s thru Ks | 25 | 2,341,297,690 | 0.001409 | 0.035237 |
| Full House | 3.5 | 18,603,466,086 | 0.011199 | 0.039198 |
| Flush | 3 | 18,212,391,017 | 0.010964 | 0.032892 |
| Straight | 2 | 20,207,073,329 | 0.012165 | 0.024330 |
| Three of a Kind | 1.5 | 125,979,020,716 | 0.075841 | 0.113761 |
| Two Pair | 1 | 215,929,781,064 | 0.129992 | 0.129992 |
| Jacks or Better | 0.5 | 336,162,430,695 | 0.202373 | 0.101187 |
| All Other | 0 | 921,861,317,936 | 0.554970 | 0.000000 |
| Totals | 1,661,102,543,100 | 1.000000 | 0.559671 |
The table above shows the probability of getting a two pair or better is 0.242657.
The next table shows the probability and contribution to the average for the multiplier, under the most liberal setting. The lower right cell shows an average multiplier of 4.168234.
Multiplier Table
| Multiplier | Weight | Probability | Expected Multiplier |
|---|---|---|---|
| 2 | 492 | 0.085684 | 0.171369 |
| 3 | 600 | 0.104493 | 0.313480 |
| 4 | 2,100 | 0.365726 | 1.462905 |
| 5 | 2,550 | 0.444096 | 2.220481 |
| Total | 5,742 | 1.000000 | 4.168234 |
As stated above, the probability of getting a multiplier is 0.242657. The average multiplier, under the most liberal setting, as shown above, is 4.168234. The overall average multiplier can be expressed as:
Probability of multiplier × Average multiplier + Probability no multiplier =
0.242657×4.168234 + (1-0.242657) = 1.768795.
The overall return of the game can be expressed as the product of the base return and the average multiplier =
0.559671 × 1.768795 = 0.989944.
I would like to remind the reader that the average multiplier used in these calculations is for the more liberal setting only. There are settings available with lower average multipliers, which would obviously lower the return. Without taking a large sampling, there is no way to know the average multiplier of any given game.
Strategy
Using my Video Poker Strategy Maker, I present this strategy for Deal or No Deal Video Poker.
If you wish to use another strategy maker, you should add to the win for all hands of two pair or better an amount equal to the product of 1.773170 and the amount bet. This 1.773170 constant is the product of the probability of getting a multiplier and the additional multiplier won above the 1x the player is entitled to for his bet, i.e. 0.242657 × (4.168234 - 1).
As far as accepting or rejecting the banker offers, I'm told in the most liberal setting the Banker offers are 95% of the expected value, rounded down to the nearest credit. In tighter settings, I believe the banker offers are a lower percentage of expected value. I can say that in the most liberal setting, the player should always decline the Banker offers. I suspect in tighter settings the Banker offers are a lower percentage than the base game itself, and thus should always be rejected as well.
External Links
- Video demonstration. I would advise against holding a 10 kicker with a pair of nines.
- Discussion about Deal or No Deal Video Poker in my forum at Wizard of Vegas.