Royal choice?Do 3 of a kind

February 12, 2008 1:46 AM


Last week, I said I would walk through an example of a video poker hand to show how the strategy is developed and why we choose to play hands one way instead of another. Let’s look at the following example:

10 heart - 10 diamond - 10 spade - J spade - Q spade

As I stated last week, technically there are 32 different ways to play this hand. Theoretically, I could choose to hold only the JQ, but I don’t think I really need to explain why that would not be the best choice. I think most people would quickly see there are 2 ways to play this hand — hold the three 10’s or hold the 3-Card Royal. Which is the right play?

If we hold 3 cards, there are 1,081 possible draws. If we hold the Three of a Kind, we will get the following final hands:

Final Hand Occurrences Pays Total
Four of a Kind 46 25 1150
Full House 66 9 594
Three of a Kind 969 3 2907

The total units returned is 4,651. We divide this by 1,081 to arrive at an expected value of 4.30. This means that on average, we can expect to win 4.30 coins for each coin wagered when we are dealt a Three of a Kind.

In the case of the 3-Card Royal, the final hands will look like this:

Final Hand Occurrences Pays Total
Royal Flush 1 800 800
Straight Flush 2 50 100
Flush 42 6 252
Straight 45 4 180
Three of a Kind 6 3 18
Two Pair 15 2 30
High Pair 252 1 252

The total number of coins returned is 1,632. We divide this by 1,081 to get an expected value of 1.51. This is significantly below the 4.30 of the Three of a Kind. From this, we know that the right play is the Three of a Kind. The computer programs that generate strategy will actually compute the expected values for the other 30 possible ways to play the hand. Each one, will be well below even the 1.51, not just the 4.30.

While this first example may have seemed to have 2 reasonable ways to play the hand, in reality one of the ways is vastly superior to the other. While it might seem reasonable to want to try for a Royal when dealt 3 parts of one, you’re just going to have to leave that to times when you’re not also dealt Three of a Kind.

One final note: For this example, I used the paytable for a full-pay jacks or better, assuming max-coin play. In this case, almost no paytable would have caused us to play this hand any differently. However, it is very important to realize that the payout of each hand is critical to calculating an expected value.

It is very common that different paytables will generate different strategies. If, in my example, we were talking about a Progressive machine with a 4,000 units (per 1 unit wagered) jackpot for the Royal (highly unlikely that it would ever get this high), then the right play would actually be to go for the Royal, because its expected value would actually be a smidge higher than that of the Three of a Kind which would remain at 4.30.

Next week, I’ll review a more complex hand.