Average or Home Runs?

Assuming a full-pay jacks or better machine, how would you play the following hand?

Hopefully, you're only seeing 2 realistic ways to play this. You can either hold the 2-Card Royal or just the single Ace. Let's take a close look at each of these possible plays.

Looking at the above table, it appears to be almost a toss-up in terms of which one to play. Of course, according to expert strategy, we would play the single Ace because of the slightly higher expected value. But, looking into the numbers a bit more deeply, we realize that the A-10 Royal has more than 10% of it's expected value coming from the Royal Flush. It's a 1 in 16,215 shot, but it's going to pay big when it happens. It's our Home Run!

The single Ace on the other hand spreads out its wins a bit more evenly. 55% of the wins will actually be pushes. 20% will come from Two Pairs. 15% will come from Three of a Kind. In the long run, the single Ace will return a little more and it will be far less volatile than the more risky 2-Card Royal.

So, have you decided if you're out there looking to lead in batting average or Home Runs? Do you want to hear the crowd screaming when you hit the big Royal Flush or are you content with a lot of small victories?

As I said earlier, expert strategy dictates how this one should be played. However, this particular play isn't going to bankrupt you if you choose to play it, especially if you're an occasional player. The key, as always, is knowing what to expect and knowing what you are giving up if you choose to take a big swing and always go for a Home Run. For example, there might be some that would advocate throwing a High Pair in favor of a 3-Card Royal. This particular play will cost you far more if you choose to play for it.

As a final note, the above situation only applies to an A-10 Royal. If it were an A-J Royal, the expected value of this Royal would 0.59, and any play aside from the 2-card Royal will cost you significantly.