# In doubt? Hold the low pair

Feb 19, 2008 5:02 AM

As promised last week, this week, I’m going to walk through a more complex example of how an expected value is calculated and how this helps to develop the strategy for video poker.

Last week’s example was a hand that contained both a Three of a Kind and a 3-Card Royal. I doubt anyone was surprised to find that we keep the sure winner as opposed to going for the long-shot big payoff. This isn’t always the case, but the answer as to the right way to play a video poker hand always lies in the expected value of each way to play the hand.

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This week, as our example,

I’d like to use the following hand:

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While there are theoretically 32 ways to play this hand, I think we would all agree that 29 of them can be quickly discarded. That will leave us with three possibilities.

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Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  ”¡ 3-Card Straight Flush
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (0 High Cards)

Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  ”¡ 4-Card Straight (with 1 High Card)

Â Â  Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  ”¡ Low Pair

As was done last week, we need to look at all the possible hands that will result if we play out every possible draw. Unlike last week, however, the number of cards being drawn is different for each scenario, so the number of possible draws is different.

This is why when we sum up the total payouts of all possible outcomes; we divide it by the total number of outcomes so that we can average and compare the results in these cases. Let’s look at each possible draw.

With the 3-card Straight Flush, here are the possible outcomes:

 Final Hand Occurs Pays Total St. Flush 3 50 150 Flush 42 6 252 Straight 37 4 148 3 of a Kind 7 3 21 Two Pair 21 2 42 High Pair 21 1 21

The total number of coins paid out is 634. We divide this by 1,081 (the total number of outcomes) and we get an expected value of 0.59. Moving on to the 4-Card Straight, the following table shows the possible outcomes:

 Final Hand Occurs Pays Total Straight 8 4 32 High Pair 3 1 3

The total payout is 35 coins. The total number of outcomes is 47. We divide 35 by 47 to get an expected value of 0.74. Last but not least is the Low Pair.

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 Final Hand Occurs Pays Total 4 of a Kind 45 25 1125 Full House 165 9 1485 3 of a Kind 1854 3 5562 Two Pair 2592 2 5184

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The total payout is 13,356. The total number of outcomes is 16,215, which gives us an expected value of 0.82, which is the highest of the 3 possible ways to play the hand.

There is no magic with all this. There are no playing hunches. Everything is laid out before you. The choice is yours.

The proper mathematical long-term play is to hold the Low Pair. It is slightly better than holding the 4-Card Straight. There will always be those people who will swear that the right play is to go for the 3-Card Straight Flush and hope that you draw the other two cards to complete that Straight Flush.

Expert Strategy is not based on what gives you an opportunity to win the most money on any given hand. It is based on what gives you the best chance to win in the long run. The strategy for video poker is no different than the strategy for any other casino game. You make the choices that allows the best opportunity to win.

The same reason why you don’t hit a 14 looking into a Dealer bust card in blackjack is essentially the same reason why you play our sample hand as a Low Pair.

Next week: How all of this gets summed up into an overall strategy for video poker.