Picking the right cards not often easy

Dec 5, 2005 5:14 AM

Most decisions in video poker are really a choice between the lesser of two evils. As most pre-draw hands are net losers, the player rarely has to make any "real" decision between a net winner and a net loser, because there are no hands that have an expected value of just about 1.00. So, in the end, he is really choosing the play that will cause him to lose the least amount of money.

So, it’s hard to have any anguish when faced with which way you should play a sure-winner hand. Yet, these hands do pop up from time to time, and just because you are deciding between two winning choices, doesn’t mean that a wrong decision won’t cost you some money in the long run.

This is exactly what happens when you are playing Double Double Bonus Poker and you are dealt three aces. When the two remaining cards are between a 5 thru K, and not a pair (i.e. a full house), the decision is pretty straightforward.

But what happens when you are dealt one or two of the low-kickers that cause the potential quads to go into bonus mode, upping the payout from 160 to 400? Or, if you are dealt a full house, either made up of these low kicker cards or otherwise?

As always, the math doesn’t lie. Let’s take a look at the possible outcomes. We won’t rely solely on the strategy table, because the information in the strategy table for Double Double lumps all of these hands together to give us an average expected value. In reality, each situation has a slightly different expected value that perhaps should be looked at individually.

Let’s look at the following hand:

 

A« Aª A¨ 2© Jª

 

If you hold only the three aces, you will wind up with 66 Full Houses, 969 Trips, 11 quads paying 400 and 35 quads paying 160. When we add all this up, we get an expected value of 12.49. Had the 2© been a 6©, the impact would have been that the expected value would have been 12.71. Conversely, if the Jack were a 4, the expected value would have fallen to 12.27. So, from this we learn that discarding a low kicker will cost us about .22 in expected value. But is this enough to change the way we want to play the hand?

If we choose to hold the three aces AND the low kicker, we will wind up with three full houses, one four of a kind paying 400 and 44 three of a kinds. The expected value of this is 11.89. So, the choice is to play the three aces with an expected value of 12.49, or to hold the low kicker as well, with the expected value of only 11.89. Not much of a choice, huh? If you hold the low kicker, you will double your chances of winding up with the bonus quads (1 in 47 or just over 2% vs. 11 in 1081, or just over 1%). Of course, you’ll also reduce your chances of a regular aces quads from about 3% to ZERO. In my mind, the "choice" is rather simple. Don’t hold the kicker!

What about when you are dealt a full house where the pair is a 2, 3 or 4. The choice here is even simpler. The full house has an expected value of 9.00. The expected value of holding the three aces hasn’t really changed much from our earlier example. In the example above, a hand containing three Aces and two low kickers has an expected value of 12.27. If the two low kickers make up a pair, giving us a full house, the expected value actually creeps up a little bit as we will wind up with 1 more Full House and one less three of a kind. The impact is not even seen going out to two digits, and the expected value is 12.273 (vs. 12.267 for the earlier example).

Now that we’ve shown that the right play is to ALWAYS play only the three aces, no matter what the other two cards are, we can better understand why our strategy table doesn’t separate each one out. It doesn’t matter if the kickers are low cards or high cards, or even a low pair or high pair. The hand should still be played as three aces. With a 4% chance at quads and a 6% chance at a full house, it’s a pretty happy decision to make.