# A Sure Thing

Several weeks ago, I wrote about a friend who texted me late one night looking for some video poker advice.  I wound up taking a picture of a strategy chart and texting him back.  Just to be clear, this was a good personal friend.  Please don't send me e-mails expecting immediate turnaround!  This past week, he needed more help and call this time.  He was a dealt a 4-Card Straight Flush which was also a Straight and wanted to know what the right play was.  Just to make sure I gave him the right answer, I looked it up and told him the correct play and what the expected values of each hand was.

The expected value of the Straight is very 'straight' forward.  The payout is 4, the expected value is 4.  The Straight Flush isn't really all that hard to calculate if you need to on the fly either.  There are 2 ways to complete the Straight Flush, 5 ways to complete the Straight again and 7 ways to wind up with a Flush.  So if we take (2 x 50) + (5 x 4) + (7 x 6) we get 162.  Divide this by 47 and we get 3.45.  A strategy chart might say 3.55, but this is an average of all hands of this type, including those with High Cards.  My friend described a hand with no High Cards.  So, the decision is not all that close.  An expected value of 4.0 vs. 3.45 leaves little doubt.  Take the sure thing and take the money.

I would like to point out however, two things about this.  The first is that even if my friend was playing max-coin \$1 machine, he is taking about \$2.75 difference over the long run each time this hand comes up.  I certainly don't recommend you go for the Straight Flush, but this is not a life altering amount.  Second, this not a hand that occurs often.  A 4-Card Straight Flush only happens about every 2500 hands.  Of these, only about 1 in 6 will be a Straight as well.  So, in the grand scheme of things, if you play it wrong, you're not going to do major damage to your bankroll.  Again, this does not justify playing it the wrong way, it just means that if you just found out you've been playing it wrong, don't go beating yourself up!

Now, if the hand had been a 4-Card Royal and a Straight, the impact becomes much greater and the hands flip flop.  A 4-Card Royal has an expected value of 18+.  When compared to the expected value of a Straight, the impact is far more significant.   It will hurt those times your draw an off-suit Low Card and miss completely, but this will be greatly offset by the 1 in 47 times you hit the Royal!

As you can see from these numbers, having a Flush instead of a Straight doesn't change our strategy.  The impact of the original situation becomes a bit greater.  An expected value of 6.0 is significantly higher than the 3.45 of the 4-Card Straight Flush.

A significant number of 4-Card Straight Flushes and 4-Card Inside Straight Flushes will be a guaranteed winner.  Roughly 1/3 of all of these hands will be High Pairs.  A High Pair has an expected value of only about 1.5.  So, in these cases, even a 4-Card INSIDE Straight Flush warrants being played over the High Pair.

As powerful as the Royal is, however, we find that a 3-Card Royal is NOT worth playing over a High Pair, although the gap in the expected values are only 0.13 apart.  This is especially important if you are playing a Progressive where the Royal may pay more than 800 per coin in.  As this amount rises, the 3-Card Royal will get closer to the High Pair and eventually overtake it.  This is despite the fact the that Flush has been lowered to pay 5 to help fund the Progressive.

All of what I have written here applies to jacks or better - and many other of the most popular games.  But, you must pay attention to the paytable to know for sure.  While very few video poker variants increase the Straight Flush, a few do.  If the Straight Flush pays 100 instead of 50, the expected value on our 4-Card Straight Flushes will increase significantly and they may overtake the expected value of the Straight.  Of course, in similar fashion, we may find that the Straight pays more than 4 and then the Straight will have a higher expected value.  One thing that is unlikely to change is that a 4-Card Royal trumps every other hand EXCEPT a Straight Flush.  If you're dealt a suited 9 thru K, you're just going to have 'settle' for your 50 for 1 payout.