Long Odds

            When playing jacks or better video poker, all it takes is to have ONE High Card and you can eliminate the choice of throwing all five cards.  My father, Lenny Frome, called this a Razgu hand.  Shortly before my mother died, I actually found out that the term was created (or at least popularized) by a friend of theirs.  A Razgu is just a hand in which you wish you could start all over again.  It is to poker what a mulligan is to golf.

            In golf, a mulligan is a bit subjective.  If a pro hits his ball 150 yards and just slightly into the rough, he'd probably love a do-over.  If I hit that shot, it won't be my best shot, but it won't be my worse shot - and I'll probably accept the outcome.  Video poker is a bit more finite than that.  According to Expert Strategy, there is a clear definition of a Razgu.  It is a hand, in which throwing all five cards results in a higher expected value than any of the other 31 possible ways to hold cards.  This is calculated with mathematical certainly.  Unfortunately, most Players don't follow Expert Strategy.

            Players hate to throw all five cards away.  Surely, something in what was dealt must be better than throwing all five cards.  Keep 1 High Card?  Yep, that'll do it.  But, what if you don't have any High Cards and no Pairs?  Now you start scanning for partial Flushes and Straights.  You have a 4-Card Flush?  That's a solid hand worth playing.  You have a 4-Card Straight?  Well, if it isn't an Inside Straight, it is worth playing.  If it IS an Inside Straight you better have some High Cards to help raise up the expected value.  That's right, a 4-Card Straight with only 1 or 2 High Cards and you're better off just playing the High Card.  But, what if there are NO High Cards and the last card (not part of the 4-Card Inside Straight) isn't a High Card either.  In this case, there will only be 4 cards that can make you a winner - the 4 that will complete the Straight.  Straights pay 4, so the expected value would be 4 times 4 divided by 47 (number of possible draws).  This works out to just a bit over 0.34.  If we throw all five cards, we get an expected value of about 0.36.  It is not a huge difference, but enough to make it not worth it to hold the 4-Card Inside Straight.

            But what about a 3-Card Flush?  When you hold a 4-Card Flush, you have 9 cards out of 47 that make a Flush.  This is almost a 20% chance.  When you hold a 3-Card Flush, you have only 45 chances out of 1081 possible draws or about 4%.  This is offset somewhat by the fact that you now have chances to draw a High Pair or to turn a singleton into Three of a Kind.  There are also ways to wind up with Two Pair.  But, when all is said and done, the expected value will be 0.3469 and still below that of a Razgu.

            It doesn't get any better for a 3-Card Straight.  You have 4 out of 47 cards that will complete an Inside Straight.  With a 3-Card open ended Straight, you'll have 48 ways out 1081 possible draws to draw the Straight.  This means you're roughly twice as likely to draw a Straight from a 4-Card Inside Straight than you are from a 3-Card Straight.  As was the case with the Flush, this deficit of Straights is partially offset by being able draw Pairs, Two Pairs and Trips.  With the lower payout of the Straight, playing a 3-Card Straight with no High Cards rates a meager 0.2747 expected value, WELL below our Razgu.

            That leaves just one more possibility.  What about a 3-Card Straight Flush.  To test this one, we'll go with about the weakest 3-Card Straight Flush as you go.  A DOUBLE INSIDE 3-Card Straight Flush.  If you are dealt a suited 2-4-6, how does this rate?  Well, now we have the opportunity to draw a Flush OR a Straight.  Plus, one of these combinations will result in a Straight Flush.  Beyond that, we have the usual opportunities for Pairs, Two Pairs and Trips.  When the numbers are crunched we find an expected value of 0.4431 which is WELL above that of a Razgu. 

            Razgus are not fun.  They occur about 3.5% of the time when you are playing properly.  When you get a hand that you think might be one, scan for the 3-Card Straight Flushes.  They are worth keeping.  The 3-Card Flushes and 3-Card Straights need to be overlooked.  This is one time that doing 'anything' is simply not the right move.