Wizard Of Odds Video Poker Hand Analyzer
Introduction
Just as in Three Card Poker, the player makes an ante to start, then, after seeing a three-card hand, must either fold or make a bet equal to the ante. If the dealer doesn't have a qualifying hand of Queen-8 or better, the ante is paid at even money and the bet ignored. Welcome to the video poker hand analyzer. Javascript must be enabled in order for it to work. Here is how you use it: The first step is to select the game category. For example, classic 5-card draw poker, Five Aces Poker, or Quick Quads. After choosing the category, you must select the game itself.
In early October 2020 I heard of a reversible royal video poker game at the Red Rock casino in Las Vegas with an enormous jackpot. To be specific, it was a jackpot over $40,000 for a 5¢ denomination game. This would be equivalent to a win of 160,000 for 1. Remember, one must make a five-coin bet to qualify for the progressive. A reversible royal pays for a sequential royal flush in either direction (10-J-Q-K-A) or (A-K-Q-J-10).
On October 17, 2020 I paid a visit to investigate. I did indeed find a bank of four games with the linked reversible royal jackpot. It is located near the Starbucks in the food court (not to be confused with the other Starbucks by the gift shop). At that date and time the jackpot was at $40,389. There were six base games the player could choose from, all of which qualified for the jackpot, as follows. The return column shows the return without the reversible royal jackpot.
| Game | Pay Table | Return |
|---|---|---|
| Bonus Poker Deluxe | 6-5 | 95.36% |
| Jacks or Better | 6-5 | 95.00% |
| Triple Double Bonus | 7-5 | 94.92% |
| Double Double Bonus | 6-5 | 94.66% |
| Double Bonus | 8-5 | 94.19% |
| Bonus Poker | 10-8-5-3-1 | 94.18% |
As the table above shows, the highest return is on 6-5 Bonus Poker Deluxe at 95.36%.
A jackpot of $40,389 for a 5-cent game is equivalent to a win of 147,722 for 1. Putting that and the rest of the pay table into the video poker analyzer at Wizard of Odds, results in the following return table.
| Win | Pays | Permutations | Probability | Return |
|---|---|---|---|---|
| Reversible Royal Flush | 807,782 | 67,567,248 | 0.000001 | 0.109525 |
| Royal Flush | 4,000 | 2,531,111,347 | 0.000025 | 0.020317 |
| Straight Flush | 250 | 10,545,248,235 | 0.000106 | 0.005290 |
| Four of a Kind | 400 | 246,151,065,684 | 0.002470 | 0.197580 |
| Full House | 30 | 811,309,337,868 | 0.008140 | 0.048842 |
| Flush | 25 | 1,067,259,148,415 | 0.010708 | 0.053542 |
| Straight | 20 | 1,275,953,861,466 | 0.012802 | 0.051209 |
| Three of a Kind | 15 | 7,722,917,814,918 | 0.077488 | 0.232464 |
| Two Pair | 5 | 10,770,132,885,066 | 0.108062 | 0.108062 |
| Jacks or Better | 5 | 22,463,692,195,905 | 0.225389 | 0.225389 |
| All Other | 0 | 55,295,592,349,848 | 0.554808 | 0.000000 |
| Totals | 99,666,152,586,000 | 1.000000 | 1.052220 |
The lower right cell in the table above shows a return of 105.22%. It should be emphasized that this return optimal strategy, including considering the order of the cards.
The image above is for the same jackpot on Triple Double Bonus.
My advice is if you have two or less cards are in position for a reversible royal, then don't muddy the waters with positional exceptions and play standard 6-5 Bonus Poker Deluxe strategy. That link will take you to the video poker strategy maker at Wizard of Odds for that game and pay table.
With three cards in position for a reversible royal, then follow the strategy for the same game, but with an average royal win of 3671. This is the weighted average of a 1.79% chance of getting a win of 161556 for a reversible royal and 98.21% chance of a regular royal win of 800. These wins are based on the total bet of 25 cents.
With four cards in position for a reversible royal, always go for the royal, even with a pat straight flush.
Assuming a playing speed of 1,000 hands per hour, the expected win of this play is $13.05 per hour. This does not include the value of points or that the meter will continue to rise as you play. The probability of getting a reversible royal is 1 in 1,475,066 per hand. Assuming the same playing speed, playing 24 hours a day, on average a reversible royal will come along once every 61.5 days.
Second Progressive
After this article was published, on October 20, 2020, a reader mentioned another 5¢ reversible royal game in the same casino with a $73,844 jackpot. Later that day, I returned to the Red Rock to investigate. It can be found near the entrance by the buffet. The bad news is that this larger jackpot requires a 10-coin bet, as opposed to a 5-coin bet for the $40,389 jackot. In other words, the ratio of the jackpot to bet amount is less. The ratio of jackpot to bet amount is 147,722. The good news is that the base pay tables were more generous. To be specific, the following table shows the base pay tables available and the return before considering the jackpot for a reversible royal.
| Game | Pay Table | Return |
|---|---|---|
| Double Bonus | 9-6-4 | 96.38% |
| Bonus Poker Deluxe | 7-5 | 96.25% |
| Jacks or Better | 7-5 | 96.15% |
| Double Double Bonus | 7-5 | 95.71% |
| Triple Double Bonus | 7-5 | 94.92% |
| Deuces Wild | 25-15-10 | 94.82% |
| Bonus Poker | 10-8-5-3-1 | 94.18% |
The greatest return is that of 9-6-4 Double Bonus at 96.38%.
The next table shows the return for 9-6-4 Double Bonus with a reversible royal jackpot of 147,722 for 1. The lower right cell shows a return of 105.27%.
| Win | Pays | Permutations | Probability | Return |
|---|---|---|---|---|
| Reversible Royal Flush | 147,722 | 67,459,882 | 0.000001 | 0.099987 |
| Royal Flush | 800 | 2,495,093,079 | 0.000025 | 0.020028 |
| Straight Flush | 50 | 10,924,785,363 | 0.000110 | 0.005481 |
| Four Aces | 160 | 22,253,946,864 | 0.000223 | 0.035726 |
| Four 2s, 3s, 4s | 80 | 52,308,875,382 | 0.000525 | 0.041987 |
| Four 5s thru Ks | 50 | 161,090,857,086 | 0.001616 | 0.080815 |
| Full House | 9 | 1,067,274,737,292 | 0.010708 | 0.096376 |
| Flush | 6 | 1,111,860,442,001 | 0.011156 | 0.066935 |
| Straight | 4 | 1,261,479,363,060 | 0.012657 | 0.050628 |
| Three of a Kind | 3 | 7,402,211,583,588 | 0.074270 | 0.222810 |
| Two Pair | 1 | 12,095,167,336,452 | 0.121357 | 0.121357 |
| Jacks or Better | 1 | 20,990,003,172,849 | 0.210603 | 0.210603 |
| All Other | 0 | 55,489,014,933,102 | 0.556749 | 0.000000 |
| Totals | 99,666,152,586,000 | 1.000000 | 1.052733 |
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While the return is close to the 5-coin game by Starbucks (105.27% vs. 105.22%), the expected win per hand is more than twice as much. To be specific, it is 2.63 cents per hand, compared to 1.31 cents per hand of the 5-coin game. Assuming a playing speed of 1,000 hands per hour, the expected win per hour is $26.37. This game is also less volatile with a standard deviation of 121.66, compared to 133.14 of the five-coin game.
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I should remind the reader that if you don't hit the reversible royal, the player can expect to lose $14.33 per hour playing the 5-coin game and $23.63 per hour playing the 10-coin game. There will also probably be a steep tax obligation on the jackpot, depending on how the winner does his taxes.
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