# Video Poker - Deuces Wild

Royal flush - 840

Four deuces - 200

Wild Royal - 20

Five of a kind - 12

Straight flush - 9

Four of a kind - 5

Full house - 3

Flush - 2

Straight - 2

Three of a kind - 1

I would do this myself, but I am unable to use the necessary software, as I am not a windows user.

p.s. Where can I find full pay full pay deuces wild in Vegas?

The standard deviation of full pay deuces wild is 5.08. The standard deviation of the sample mean is 5.08/sqr(n), where n is the number of hands. I’ll skip over the rest of the math to the answer, which is 42,383,720 hands. That is a lot! Suppose your goal is to simply come out ahead with a 90% probability. Then you would only need 733,790 hands. This is still a lot, which just goes to show how volatile your bankroll will be in the short run. The general formula in Excel of your sample return being at least x is with a probability of p is (normsinv(1-p)*5.08/(1.0076-x))^2. In the case of my first example you would put the following in any cell:

=(NORMSINV(1-0.9)*5.08/(1.0076-1.0066))^2

This formula can be used for any game by substituting the correct standard deviation per hand.

I think all the Stations and Fiesta casinos have full pay deuces wild in the quarter coinage only. Green Valley Ranch too. When I moved to Vegas three years ago it was much easier to find.

^{14000}= 5.75%.

Almost. If more than one royal per deal in 5-play counts as only one sighting then you will have sightings slightly less than 5 times as often. This is because the total number of royals will be five times as much, but sometimes they will be clumped together in the same play, usually when you get a royal on the deal, and thus 5 on the draw.

The following table shows the probability of making a royal in 1-play according to the number of cards to the royal held, assuming full pay optimal strategy.

### Royal Flush Probability in 1-Play Video Poker

Card Held | Probability on deal | Probability on draw | Total probability |

0 | 0.19066396 | 0.0000014 | 0.00000027 |

1 | 0 | 0.00000561 | 0 |

2 | 0.01969711 | 0.00006167 | 0.00000121 |

3 | 0.01299751 | 0.00092507 | 0.00001202 |

4 | 0.0003309 | 0.0212766 | 0.00000704 |

5 | 0.00000154 | 1 | 0.00000154 |

Total | 0.22369101 | 0 | 0.00002208 |

What this table shows is that 22.37% of the time you will have a possible royal draw. The rest of the time a royal will be impossible, for such reasons as you held a wild card or a pair. The lower right cell shows the overall royal probability is 0.00002208, or 1 in 45282.

The next table shows the same thing but for 5-play, and the probability of at least one royal.

### Royal Flush Probability in 5-Play Video Poker

Card Held | Probability on deal | Probability on draw | Total probability |

0 | 0.19066396 | 0.00000698 | 0.00000133 |

1 | 0 | 0.00002803 | 0 |

2 | 0.01969711 | 0.00030832 | 0.00000607 |

3 | 0.01299751 | 0.0046168 | 0.00006001 |

4 | 0.0003309 | 0.10195134 | 0.00003374 |

5 | 0.00000154 | 1 | 0.00000154 |

Total | 0.22369101 | 0 | 0.00010268 |

Note the probability of at least one royal is 0.00010268. This is 4.65 as high as the probability for one-play. The reason is the probability of making at least one royal is always less than five times that of 1-play. For example the probaiblity of hitting a royal holding for to the royal is 1/47 in 1-play. However in 5-play the probability of making at least one royal is 1-(1-(1/47))^{5} = 0.101951341, which is about 4.79 times as high.

^{2}×(45281/45282)

^{5998}= 0.007688177, or 1 in 130.

In this case, the profit is maximized by following a strategy based on a royal win of 450. That will lower the actual return to 1.007534 and decrease the royal probability to 1 in 46415, resulting in an expected profit of 46415 ×(1.007534-1) = 349.68. The extra 4.6 bet units may not be worth the bother of learning a different strategy.

To find the optimal target royal value, you can use my video poker calculator, and keep lowering the pay for a royal until the overall return gets as close to 1 as possible. At that point, it is like playing for free until you hit the royal, at which point you get a bonus for the royal. In the full pay deuces wild example, the bonus is 800-450=350.

The situation is not entirely hypothetical. Slot managers have been known to prohibit advantage players from playing video poker, and usually such players get the tap on the shoulder shortly after hitting a royal.