Anything can happen in poker, but don't expect it

Aug 6, 2013 3:00 AM

There are many things I remember about my father. One of his favorite lines that always sticks in my brain is, “even a blind pig can find an acorn.”

This quote tells us even the worst baseball player might hit a home run at some clutch moment. Or perhaps it explains how that fat guy is dating a Sports Illustrated swimsuit model.

Essentially, at any point, the least likely event might occur, but that doesn’t mean you should start expecting it.

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Video Poker helps to prove this point continually. Several weeks ago, I got a Razgu and threw all five cards. I was dealt Four of a Kind in the draw. It was a beautiful thing to behold. But, it doesn’t mean I should start discarding all five cards under some belief I’m likely to be dealt Quads!

In a similar vein, you might have heard a story where someone threw a High Pair to hold a 2-card Royal and hit the Royal. Hey, it will happen. But, it is rare and not the smart play in this case.

Here’s why. Say you are dealt jack-hearts, jack-spades, queen-spades, 3-clubs, 6-diamonds. The right play to anybody who knows anything about video poker strategy is to keep the High Pair. It’s expected value is 1.54.

The 2-card Royal is a paltry 0.60. If you hold the pair of Jacks and the three drawn cards are the 10, K and Ace of Spades, does this mean the right play would have been to keep the 2-Card Royal?

One could argue that in this particular case (and in hindsight) this would’ve been the right play. But, there are 16,215 different possible 3-card draws and only one will produce the Royal Flush.

Obviously, there are many others that will produce a Straight or a Flush. There are also many that would lead to a High Pair, Two Pair, Three of a Kind, Full House and Flush. There are also many that would leave the hand as a complete loser.

When you hold the Pair of Jacks, your only possibilities are High Pair, Two Pair, Trips, Full House and Quad. You have no chance to get a Royal. But, you also have a guaranteed winning hand.

When we look at all 16,215 possible draws and the resulting hand, the math tells us that while you give up the shot at the Royal, the guaranteed winner is simply too compelling to throw away.

Yes, in hindsight, you may have wished you did something different, but we cannot rely on this for determining our strategy. We must rely on the probability of all the outcomes, not the hindsight of one particular outcome.

The goal (at least of Expert Strategy) is not to hit as many Royals as possible but to maximize our overall payback. So, let’s look at another example, such as: 3-hearts, jack-spades, queen-spades, 3-clubs, 6-diamonds.

Here we have only a Low Pair and a 2-card Royal. If we go for the 2-card Royal, we will no longer be giving up a sure winner. The Low Pair only has an expected value of 0.82. The 2-card Royal is still stuck at about 0.60.

The decision is a little less lopsided, but we still stick with our Low Pair. The likelihood of Trips and Quads simply outweigh the likelihood of the Royal by enough to overcome the higher payout of the Royal.

Just as in our prior example, the Royal will occasionally occur (1 in 16,215 draws), but it is not about the blind pig finding the acorn.

Another example: jack-hearts, jack-spades, queen-spades, king-spades, 6-diamonds. Now, we are looking at a High Pair vs. a 3-card Royal. The likelihood of hitting the Royal skyrockets to 1 in 1,081.

We also greatly increase our chances of hitting a Straight or a Flush by needing to pick up only 2 cards and not 3. The decision becomes a bit harder, but the result is the same.

The High Pair has an expected value of 1.54 and the 3-card Royal has an expected value of 1.41. Even though the probability of hitting the Royal has increased 15-fold, the power of the sure winner still wins the day.

The last example: 3-hearts, J-spades, Q-spades, 3-clubs, K-spades. This time we have only a Low Pair vs. a 3-card Royal. As already stated, the 3-card Royal has an expected value of 1.41 and the Low Pair has an expected value of 0.82. The lack of the sure winner brings us to the conclusion we should discard the Low Pair and go for the 3-card Royal.

If you are interested in hitting as many Royals as possible, then your decision in each of these examples is pretty much the same – discard the Pair. If you wish to follow Expert Strategy and maximize the payback of the game, then all that matters is the expected value of each hand.

It does not matter one little bit that you once saw or heard of a case where a player made the wrong decision but it led to a big winner. The blind pig will occasionally find that acorn, but regrettably, he is more likely to starve to death before he does.

Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at [email protected].

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