# Empty Suits

I was a big fan of the tv show White Collar.  One of the characters referred to members of the FBI and just about anybody else who worked in some corporate type of job as a "suit" and he clearly did not trust "suits."  This week's column reminds me of that character (Mozzy).  But, as is probably no surprise, it's not about guys who wear suits.  It's about the value of a suited hand in Poker.   In the end, I come to a similar conclusion - I don't trust suits.

If you play Texas Hold'em, you're always rooting for a suited hand (if not Pairs).  If you look at your pocket cards one at a time and the first one is an Ace, you're almost disappointed if your second card is an unsuited Jack.  But, how much are you giving up relative to a suited Jack?

In a head's up game, you'll win with an A-J offsuit a significant 62.38% of the time.   If you have an A-J suited, you'll win 64.1% of the time.  This is a barely noticeable difference in win frequency.  In a game of Poker, of course, it is not just about win frequency.  Having a nut Flush after the Flop could potentially set up a HUGE pot and huge victory.  If you have an off-suit hand and the Flop is 3 suited cards matching one of yours, you are left somewhat dangling.  So, I won't completely discount the betting value of a suited hand, but again, how often will this occur?

If you have two suited cards the probability that the Flop will complete a Flush is 0.84% or less than 1 in 118 hands.  So, you have a slightly less than 24% chance of being dealt a suited hand and then a 1 in 118 chance of turning the Flush after the Flop.  You might play all night without having this happen to you.  And when it does, your opponents may have garbage (always seems to happen that way to me!).

If you have an offsuit pocket hand, it will take 4 cards to complete that Flush, but you'll sort of have 2 cracks at it as you will have 2 different suits you will be chasing.  This is why the impact to the win frequency is only a smidge under 2%.  No matter how you slice it, your odds of hitting a Flush is relatively small.  You're more likely to win by pulling an Ace and riding the Top Pair to victory.

So, this is the case where we have 2 cards and are being dealt 3 for the Flop or 5 for all the community cards.  What about a video poker situation.  As we all know, a 3-Card Flush is generally NOT a playable hand in video poker.  Why not?

In video poker, there are far less variables.  There is no play that goes on with other Players.  You are dealt what you are dealt and you get paid according to the paytable.  So, all that matters is your final hand, not how you get there.  You get paid the same whether you are dealt 3 to a Flush and draw 2 more or if you get a Razgu and wind up pulling a Flush.  With a 3-Card Flush, the Player has 10 more cards of the same suit.  This means there are 45 ways to draw the Flush out of 1081 possible draws.  A mere 4.16% chance of pulling the Flush.  If this is not any form of 3-Card Straight Flush, then there is no chance for a Straight either.  If the 3-Card Flush has no High Cards, then your chances for getting a winning hand are now limited to drawing the Flush, drawing a High Pair or winding up with Two Pair or Trips.   Not many chances to hit these hands and none are big payers.

When we look at all the possibilities, we find that a 3-Card Flush simply has a lower expected value than any of the other possibilites.  If you've got a 2-Card Royal in that 3-Card Flush, then you hold it.  If you even a single High Card, it has a higher expected value than the 3-Card Flush.  And even if you've card a 3-Low Card Flush with 2 other Low Cards, you're still better off throwing ALL 5 Cards then holding the 3-Card Flush.  The fact that the hand is suited just isn't worth enough to make it worth playing.

The one exception to this is if it is a 3-Card Straight Flush of any type.  Then you give yourself a some chances to get a Straight Flush.  It will be very long odds, but with a significant payout.  You also create many opportunities to draw a Straight.  These additional opportunities make the 3-Card Straight Flush a playable hand.

What about the 2-Card Royals?  We play these more for the Royal potential than the Flush potential.  The possible Flushes in these cases are what amounts to a consolation prize and help prop up the expected value a little.  But it is the 800 payout on the Royal Flush that gives these hands their true value.

The bottom line is don't overestimate the value of a suit.  You may just find out that its value leaves you a bit empty.