CHASING THE MONSTERS
The rare hands that keep video poker players coming back
By Jerry “Stickman” Stich
Maybe Jacks or Better is the video poker game of choice for you. It has low volatility and generally has a high return, approaching 100 percent. Maybe Double Bonus Poker is more your speed with its bonus for quads and sometimes (though rare) a better-than 100 percent return. Or maybe you like it even more edgy and you opt for Double-Double Bonus with its jackpot for four aces with a “kicker” or a 2, 3 or 4. If this isn’t enough to whet your appetite for monster hands, you may opt for Triple Bonus Poker or even Triple Double Bonus poker with its royal- flush-sized payoff for four aces and a 2, 3 or 4.
Whatever your game of choice, it contains one or more “monster” hands. These hands are able to pay high returns because they are very rare. How rare? Let’s take a look at some of them and see.
The overall occurrence rates vary depending on the rest of the pay table because strategy charts are built to get the maximum return out of each possible hand that is dealt. Sometimes hands that might result in a royal flush or four aces (such as a lone ace) are not saved for the monster hand because another hand (such as a low pair) might return more money in the long run. The odds of being dealt a monster hand or completing a monster hand from a particular saved hand are always the same, however, since the decision has already been made.
Let’s start with a royal flush. Many players know that the odds of completing a royal flush overall are one in about 40,000 hands. This number takes into account all strategy plays for all possible hands and saves. In this article, all the hands discussed have already been dealt and held. The odds are determined based on the hold. The strategy doesn’t matter and the pay table doesn’t matter as they will not change anything once the hold is made.
Many of the more serious players also know that the odds of being dealt a royal flush are one in 649,740. Wikipedia may show the number as one in 2,598,960 but this shows the odds for one particular royal flush such as spades or hearts. There are four possible royal flushes so the odds of getting any one of them are one fourth that number—649,740.
Whenever a player is dealt four of a royal, a jolt of excitement fills the air. There is only one card needed to win the jackpot. So what are the odds of drawing it? There is exactly one card left in the deck of 47 cards that will complete the hand. This makes the odds one in 47 of completing the royal flush.
Many times a player will be dealt three cards of a royal. This is usually enough to make them sit up and take notice, but what are the odds of completing this hand? There are two cards left in the remaining deck of 47 that will complete the hand. There is a two-in-47 chance of getting one of those two cards as the first card drawn, and a one-in-46 chance of getting the last card needed as the second card. The math is 47/2 x 46/1 = 1,081. The odds of completing a royal flush when holding three are one in 1,081.
When holding two of a royal, the odds of completing the hand climb. There are three cards in the remaining 47 that will complete the hand. There is a three-in-47 chance one of those three will be the first card drawn, a two-in-46 chance one of the remaining two will be the next card drawn, and a one-in-45 chance the last card drawn will complete the hand. The math is 47/3 x 46/2 x 45/1 = 16,215.
Finally, what are the odds when only one card of a royal is saved? Using the same logic as above, there are four cards in the remaining 47 that will complete the hand. If one of those is drawn as the first card, there are three cards in the remaining 46, then two in the remaining 45, and finally only one card in the remaining 44 that will complete the hand. The math is 47/4 x 46/3 x 45/2 x 44/1 = 178,365. There is a one-in-178,365 chance of completing a royal flush when saving one card. This is a rare event indeed, but it can and does happen. That is why video poker is so popular—any given hand can be a huge winner.
