This column is written primarily for beginners and low-intermediate players. Readers more advanced than that should give it a once-over as well. There’s a chart here you’ve likely never seen before.
You’re playing Double Double Bonus, receiving 45 for a full house. How much you get for the flush is irrelevant to this discussion. If you get only 40 for the full house in the game you typically play, you’re permitting yourself to play such a bad game that no amount of advice from me is going to help you be a winning player.
You’re dealt K♠ K♥ 6♣ 6♦ 5♠. You’re debating holding just the kings or holding the two pair. You’ve read from people like me that holding two pair is correct by a mile, but it’s counterintuitive to you. After all, you get the same “even money” for a pair of kings as you do for two pair and if you hold the kings you might get lucky and receive four kings. So why not go for it?
Let’s talk dollars and sense. Assume you’re playing dollar single line DDB, five coins at a time. Holding two pair, you have the following possibilities — and the value of those possibilities.
The frequency numbers from the chart may be found in Video Poker for Winners or other quality software. The dollar figures aren’t generally seen, although you do get the sum of them, shown in green. And notice I didn’t include columns for straights, flushes, straight flushes, or royal flushes simply because you can’t get one of those when you start out by holding a pair or two pair.
Let’s take the line corresponding to KK66. You have 47 possible draws, which is the normal number when you’re drawing one card from a 52-card pack and you’ve already looked at a five-card deal. You’ll end up with two pair 43 times and a full house four times. You can probably do this much in your head if you start with figuring how many full houses you can get. After all, the only time you’re going to get a full house is when you draw one of the two remaining kings or one of the two remaining sixes. In all other cases, you’re going to end up with the same two pair with which you started.
What’s new in this chart, shown in blue, is how much each of these hands is worth. The two-pair final hand contributes $4.57 to your total EV and the full house adds $3.83. Rather than give a definition for how I figured out those numbers, I’ll show you the calculations: $3.83 = (4 * $45 / 47). $4.57 = (43 * $5 / 47). The $45 and $5 in the formulas are the amounts you receive from a full house and two pair respectively in this game.
In the line corresponding to holding the kings, there are now 16,215 possible draws. For most of us, including me, there are way too many possibilities to figure this stuff out in our heads, or even with paper and pencil, with a high degree of confidence. Fortunately, software to do this for us is very fast, accurate, and inexpensive.
The number that really pops out at me on this line is the 69¢ that the chance at a 4-of-a-kind is worth. Yes, the quad is worth $250 when you get it, and that’s the number beginning players focus on, but you only get it a little less than one chance in 360. Multiply it out and it comes to 69¢.
Also, note that the chance for a full house is 47¢ when you hold a pair, compared to the $3.83 it’s worth when you hold two pair.
It’s easy to think of possibilities — like you COULD get a four-of-a-kind. It’s much harder to think of probabilities — which means how often does it happen percentage-wise. It’s even harder to multiply out the VALUE of the hands which means the probability multiplied by the pay schedule.
Players sometimes confuse this hand with A♠ A♥ 6♣ 6♦ 5♠. To put this into the above chart we need to add another column for four aces with a kicker. If we do that, we’ll find all the numbers in the chart stay the same, except the value of the four aces without a kicker is worth $1.63 and the value of four aces with a kicker is worth $1.48. Adding those together gives us $3.11 — compared to the 69¢ the kings were worth. This makes holding the aces worth more than holding two pair, aces up.
The strategy for this part of the game is AA > Two Pair > KK, QQ, JJ. If you can read the strategy and just follow it no-questions-asked, then you don’t need columns like this one. If you ever wonder “why,” and haven’t figured out the answer to this particular question, maybe this column will be useful to you.
As for me, I’m always wondering “why?” Once I figure that out (which I normally can do in video poker — not so much in certain other parts of life), it makes it much easier to keep strategies memorized.