Saturday, October 13, 2007

Maximum outage: 21 on the Flop, 25 on the Turn

To follow up on the discussion from last night, the most outs you can have on the flop would be 21 in the standard two overs, four to the flush, and four to the straight scenario that we are all familiar with.

Hero: KhQh
Villain: 2c2s
Flop: JhTh7c
Hero can win with:
Ah to make a Royal Flush
Ac Ad As to make a Broadway Straight
Kc Kd Ks to make Kings
Qc Qd Qs to make Queens
9c 9d 9s to make a King high Straight
9h 8h 7h 6h 5h 4h 3h 2h to make a Flush
21 outs

However, if you are talking about the Turn card, it is possible to pick up a ton more outs if the board pairs the Seven.

Hero: KhQh
Villain: 2c2s
Board: JhTh7c 7s

From the 21 outs on the flop, Hero loses the 2h and 7h since they would boat up Villain but in exchange, Hero picks up three more Jacks and three more Tens to counterfeit Villain's pair for a total of 25 outs on the Turn. Astonishingly enough, there is a situation where the player that is behind in the hand on the Turn is actually favored to win since there are 25 winning cards and only 19 losing cards in the deck.
Hero can win with:
Ah to make a Royal Flush
Ac Ad As to make a Broadway Straight
Kc Kd Ks to make Kings
Qc Qd Qs to make Queens
Jc Jd Js to make Jacks and Sevens w/King kicker
Tc Td Ts to make Tens and Sevens w/King kicker
9c 9d 9s to make a King high Straight
9h to make a King high Straight Flush
8h 6h 5h 4h 3h to make a Flush
25 outs!

So there you go, 25 outs on the turn. I cannot imagine how you could have any more than that.

5 comments:

Bob Loblaw said...

I'm a little confused by the math behind having a maximum of 25 outs on the turn. Say your opponent doesn't have 2c2s. Instead he has 6c8s. For argument's sake, let's say your opponent's name is Martin, and he's called the Hero's overly-high bet of $40 on the flop on the way-low chance that his gut shot will hit.

We've already established that our hero had 21 outs on that flop, but when the turn comes 7s, it appears that his outs have now increased to 27 outs, because the 7h and 2h are no longer giving the villain a better hand. Right?

The only cards Martin could hit to beat our hero would be 8c 8d 6s 6d.

I hope our hero hits a non-heart 9 on the river, so he gets the maximum call from Martin.

Bob Loblaw said...

OH wait. Now I see my flaw. uh, duh. You don't need outs when you're already winning.

OK, now I'm going back to sleep.

Sushi Cowboy said...

If Villain is holding 68os then Hero is already ahead in the hand and doesn't need outs.

So yes, the 2h and 7h will improve Hero's hand into something other than the King high which is already leading but they would not be "outs" in the traditional sense.

Bob Loblaw said...

Duh, Martin. Sheesh.

Sushi Cowboy said...

I don't know why that happens so much. I start a post and after I post it there is another comment there already that wasn't there before I posted. *Sometimes* I start a post and come back, like this time, but other times I type and post pretty quickly. Dunno.

Anyway, didn't mean to beat a dead horse, your realization just beat my explanation to the punch.

If we *were* just talking about improving your hand regardless of what you are up against, you can do a different scenario to get to 22 on the turn, which until this weekend was the highest I had heard of.

Hero: AhAd
Board KhQhJh Ac

Again, Hero is already winning but has 22 "outs" to improve.
As for Quads
Kc Kd Ks for Aces full of Kings
Qc Qd Qs for Aces full of Queens
Jc Jd Js for Aces full of Jacks
Th for Royal flush
Tc Td Ts for Broadway Straight
9h 8h 7h 6h 5h 4h 3h 2h for Nut Flush