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.
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Speaking for myself, I believe that this column will be very appreciated by your intended audience since it hits the sweet spot with Double Double Bonus being the most popular video poker variant and the most debated 5 card deal. I personally hope there will be some more of these novice columns in the future.
If someone is indeed playing a Double Double Bonus pay schedule that offers 40 credits for a Full House, most likely they are playing the 8/5 variant since I never seen 8/6 in existence. This concept does apply to most of the break even payout for 2 Pair on Bonus games.
I agree that understanding “why” than to just memorize something will help people in various things in the long run.
The last two columns have been very helpful to a rookie, such as myself. Thank you sir.
Great article!
This is good advice for any beginner who cares about optimizing his results. However, anyone who is playing 9/6 DDB in the first place clearly doesn’t care about EV (as in, not losing), so it’s hard to imagine such a person spending the time or effort to comprehend the rationale behind a given play. Most players, of ANY game, want to just leave their brains in the glove compartment and hope to get lucky.
Also, it seems counterproductive to expend any real effort learning how to play a LOSING game as well as possible when the best advice anyone could receive is not “AA>Two Pair > KK-QQ-JJ” but rather, “Don’t play this game at all.” I realize that teaching the recreational player to lose as little as possible is a laudable goal, but on the other hand, if you teach someone to play a 98.9% game well (and thus encourage him to play it), you really aren’t doing him any favors.
Since when is pure EV the sole basis of judging a play? There are many places where the higher EV is not the preferred play. One location I’ve played has 9/6 Jacks and also 7/5 Super Aces. Believe me when it comes to optimizing mailers the 7/5 Aces is preferred by far. Anyone who plays VP for serious money will understand the reasons why. Once you evaluate the play in full context, then it is important to maximize the return of the pay table in question. Don’t dismiss DDB just because it has a 98.9% return.
You make a valid point. I’ve played places where 9/5 Jacks or Better is a smarter play than 9/6 Jacks or Better even though the pay schedule by itself says the 9/6 version is 1.1% looser..
Rather than go into depth about that right now, this seems an excellent subject for a subsequent blog. Thanx for the suggestion.
For now, just say I was assuming “everything else equal” and this is a case of everything else NOT equal.
Good article. I think some follow-ups are in order for other two pair combos in which the small pairs are contained (2’s, 3’s, and 4’s). I’ve seen countless players be dealt a hand like 9922x or JJ33x and only hold the 2’s or 3’s.
I play DDB multiline. It is then easy to see that holding two pair is much the better play. The chance of getting a quad is only 1 in 360.
Thank you, but no.
I’m trying to not write the same article twice. My goal is to show my readers how it’s done, and leave it to them to use the same technique to look at similar hands. With 2.6 million unique hands, I’m never going to get through all of them. The best I can do is to show you the way for you to do your own analysis.
We know it’s 1 in 360, but the average gambler doesn’t. To them, the “possibility” is more important than the “probability.” Why do you think so many people play Power Ball or Mega-Millions?
Understandable.
Oh the irony. Was playing TDB earlier and on the very first hand I played I was dealt 22AA7. Held the A’s as the right play only to draw 224!! Just have to shrug it off and keep chugging away knowing I made the right play.