A Double 'Boo'nus Tale

As you begin to play, you pretty much use the same strategy you learned for Jacks or Better. After all, how much different can it be? After getting a few Two Pairs on the Pre-Draw hand, not having them improve, and collecting only even money, you begin to wonder if maybe you should only keep 1 Pair if its Jacks or Higher. After all, your chances of getting that Bonus Four of a Kind is much higher by holding a pair (it's obviously impossible holding 2 Pairs!), so you begin to try holding just the High Pair.

Suddenly, you notice the gentleman at the machine on your left. His hair is blonde with streaks of gray and white. He's tall and scholarly looking. He recognizes the look of anguish on your face, and kindly tells you the proper play is to hold the Two Pairs, even if one of the Pairs is a Pair of Aces. He continues, "The expected value of a Pair of Aces is just a little below that of Two Pair, 1.763 vs. 1.766. Pairs of other High Cards have an EV of about 1.46, so you certainly don't want to be breaking up Two Pairs for THAT!"

You nod approvingly and thank your neighbor as you notice a worn copy of Winning Strategies for Video Poker by Lenny Frome in his hand. You figure this gentleman must know what he's talking about. As you continue playing, you realize the gentleman is not playing the machine next to you, but just watching you play. Normally, you hate this, but for some reason, tonight, it has a calming effect.

In a very matter of fact, professor-like voice, the gentleman continues to explain how important it is to realize that different Paytables can mean very different strategies. Even slight changes can mean changes to strategy. In the case of Double Bonus, there are some significant changes to the strategy table. Some don't really matter at all, some matter a little, some matter more than that, and in some cases, such as the Two Pairs, it's just as important to realize there is NO change in our strategy.

You give a smile to the gentleman as you hit your second Full House on the Draw from Two Pairs. "How can a change in the strategy table not matter at all?" you ask him. The gentleman explains how some hands don't overlap, so if they swap places from one strategy table to the next, it doesn't matter. For example, in Jacks or Better, Two Pairs is better than a 4-Card Inside Straight Flush. In Double Bonus, the 4-Card Inside Straight Flush has a higher EV than Two Pairs. However, it's impossible for any pre-draw hand to have both, so it really doesn't matter which ranks higher with these two hands. Of course, this isn't always the case. In Jacks or Better, we hold a Low Pair over all 4-Card Straights EXCEPT the 10-J-Q-K. In Double Bonus, we hold ALL 4-Card Straights (not insides) instead of the Low Pair.

The amount of the affect on the overall payback of the machine depends on two factors: how frequent the hand comes up where the choice must be made and how big the EV difference between the choices is. If the hand is VERY infrequent and the EV difference is only .01 or .02, then the overall impact will be small. For example, Two Pairs where one Pair is Aces will occur about once in every 250 hands. With an EV difference of .0025, we only cost ourselves .001% in total payback if played incorrectly. However, in the case of Low Pairs vs. 4-Card Straights, we can also expect to see this situation about once very 250 hands. With the EV difference being just above .1 (depending on how many high cards), the impact to the overall payback could be as much as .04%. Why bother playing Double Bonus with the higher volatility if your strategy may reduce the overall payback to below that of a Full-Pay Jacks or Better machine?

You're surprised that you're able to hear what the gentleman has to say while still focusing on playing your machine. You also realize that you've played the Low Pair over the 4-Card Straight at least half a dozen times in the past half-hour when you are dealt a Pair of Twos and a 3-4-5. You look over at the gentleman and then turn back to your machine and just before your hand hits the 'Deal' button, you 'un-hold' one of the Two's and Hold the 3-4-5. You hit 'Deal' and up comes a 6… a Straight! The gentleman gives you a nod of approval.

Happy with your recent streak of good luck, you think to yourself how this is much better than handing candy out to the kids at your door! You hit the 'Max Bet' button and up comes A-A-7-A-7. Great! A Full House! As you begin to hit the hold buttons, you look at the gentleman and say, "Well, if I hold a Two Pair instead of a Pair of Aces, I guess I hold a Full House instead of Three Aces!" The gentleman raises one eyebrow and gives you that 'Are you sure?' look. Effortlessly, he turns to page 53 of his book, and it shows that Three Aces has an EV of 10+ (actually, 10.11), while the Full House has an EV of exactly 10. Its close, but the proper play is to hold the Three Aces. You give him a nervous look, but he certainly hasn't guided you wrong so far, so you hold the Three Aces and hit 'Deal/Draw'. Up comes a Queen and an….ACE!!! You let out a hoot and a holler over your mini-jackpot!

You turn to your left to thank the gentleman and offer to buy him a drink. Much to your surprise, there's no one there. You look down and on the seat is a copy of Winning Strategies for Video Poker. It's brand new! You open the front cover, and it's signed 'Playerspal - 2003'.

hAppy hAlloween!