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" of 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 kicker.

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 game and 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 hold 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 holds. 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 number represents the odds for a royal flush in one particular suit such as spades or hearts. There are four possible suits so the odds against getting any one of them are one fourth that number, which is 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 which 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 * 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 against 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 that 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 * 46/2 * 45/1 = 16,215 (i.e., odds of one in 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 * 46/3 * 45/2 * 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.

Okay, let's assume that your favorite video poker game is Double-Double Bonus poker as it is for a great many video poker players. In this game there is more than one monster hand compared to Jacks or Better. There are also hands containing four aces and a "kicker". What are the odds of completing a hand containing four aces and a "kicker" consisting of a 2, 3, or 4?

Initially it might appear that there are 16 cards in the deck that are in play: the four aces, four 2's, four 3's and four 4's. You need all four of the aces and only one of the remaining 16 kicker cards. The actual odds of completing the hand, however, could be skewed by the fact that proper strategy dictates that the player saving for four aces (and the possible kicker) only save the ace or aces and ignore any kicker cards that may be in the initially dealt hand.

Okay, first scenario - you are dealt four aces but no kicker. What a great hand to be dealt. You are already guaranteed a win of 160-for-1. What are the odds of completing the hand with a kicker? Since you only threw away one card and it is not a kicker, there are 12 cards out of the remaining 47 that will complete the hand. That is about a one in four chance (25.5 percent) of completing the hand.

Let's say you are not quite as lucky and are only dealt three aces. There are 1,081 possible hands that can be made with the remaining 47 cards. The correct hold is the three aces only so it is possible to throw away one or two kickers. If you threw away no kickers there are 12 possible combinations that will complete the hand; the fourth ace with one of four 2's, one of four 3,s or one of four 4's. The odds of completing the hand are 12 in 1,081 or about 1 in 90 tries. If you discarded one kicker card there are 11 possible combinations that will complete the hand. The odds of completing are 11 in 1,081 or about 1 in 98 tries. And if you discarded two kickers there are 10 combinations in 1,081 possible hands or about 1 in 108 tries.

Let's continue with the more rare completion rates. There are 16,215 possible hands that can be made from the remaining 47 cards if you save two aces. If you threw no kickers there are 12 possible combinations that will complete the hand (the remaining two aces along with one of the 12 kickers remaining in the deck). The odds of completing the hand are 12 in 16,215 hands or about 1 in 1,351 hands. If you discarded one kicker, there are 11 combinations that will complete the hand for about a 1 in 1,471 chance. If you discarded two kickers there are only 10 combinations remaining for about a 1 in 1,621 chance of hitting the jackpot.

When saving one ace there are 178,365 possible hands that can be made with the remaining 47 cards in the deck. If you threw away no kickers, there would be 12 quad-aces-with-a-kicker hands out of 178,365 so the odds against getting your final hand in this case is 178,365 divided by 12 or about 14,864 to 1. If you threw away one kicker you would have one less chance of completing the desired hand and the odds against would be 178,365 divided by 11 or 16,215 to 1. Throw away three kickers and the odds against completing your hand increase to 178,365 divided by 10 or about 17,837 to 1. If you are playing proper strategy you would never throw away four kickers as they would include a low pair and you would save the low pair.

Finally, what are the odds against drawing to four aces with a kicker if you threw the entire first hand? There are 1,533,939 possible combinations in the remaining 47 cards and there are still the 12 possible winning combinations in these 1,533,939 combinations if you threw no kickers. The odds against getting four aces with a kicker in this case are 127,838 to 1. If you discarded one kicker, you have 11 combinations out of 1,533,939 which work out to about 13,945 to 1 against completing the hand. Discarding two kickers increases the odds against you to about 153,394 to 1. If you had four or five kickers in the initial hand, you would save at least two of them so you would not be attempting the four aces and a kicker on those hands.

As you can plainly see from the numbers, monster hands are rare. They are also quite lucrative. Quite probably that is why Double-Double Bonus video poker is so popular.

All the best in your casino and life endeavors.