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Chasing down the flush.

One of the biggest mistakes rookie poker players make, is to chase after inadequate hands. Better players capitalize on such anti-skills all the time. Let’s take the following situation: Our rookie calls all the aggressive preflop betting a better player is throwing at him, just to take a peek at the flop. When the flop comes, and he realizes it missed his hand completely, he quietly folds and even congratulates himself on the excellent choice he’s just made. That, of course, leaves dead money in the pot for sharks, and slowly sucks our rookie’s bankroll dry.

This is just the milder version of the anti skill I’m trying to illustrate. Lots of players find no shame in chasing a hand all the way down to the river and then mucking it.
There are players out there who are capable of doing this on a J,3o, no doubt about that, but still, most of the "chasers” need something tangible to get them going.
Pocket pairs are such hands. They get the rookies going, yet there is a strong possibility they won’t improve at all. 4-card flushes are quite similar in this respect to pocket pairs. Both hands depend on a single right card hitting them: if the card comes, they’ll be extremely strong hands to beat, if it doesn’t, the player will pretty much end up with zilch. It’s a kind of "all or nothing” situation.

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Whenever such an "all or nothing” thing comes around, trouble is not far behind. Let’s now take a closer look on the odds involved with these hands, that spell doom for so many rookies. Maybe once you see the figures involved, you too will be able to draw a few relevant conclusions.

Let’s suppose you’re dealt a couple of 7s. What exactly do you need on the flop to improve your hand? another 7 of course, because a flush or a straight is not really an option here. Even if a 4-card flush comes up on the table, with one of your 7s fitting right into it, you’ll still have a 50% chance of being outdrawn by a player with a card higher than your 7. (50% is like coin-flip, so I don’t suppose you like those odds) The only way to hit a potentially winning straight, is if 6,5,4 comes up on the flop, and 3 on the turn. The odds of that happening are naturally, infinitely small. No other card will help you, because if 8,9,10 comes on the flop, and J on the turn, you’ll be on the low end of it, and you’ll be easy to beat.

Bottom line is, in this situation, only a third 7 will help you. There are four 7s in a deck. two of those are in your pocket, so that makes it 4-2=2 left. Out of the 52 cards in the deck, 2 are in your hand so that leaves 50 cards out there (if you don’t know what your opponent has) You’ll need 2 of 50 cards to make the break you’ve been looking for. That means a 4% chance. How do you like your pair now? You still reckon it’s worth to pay to see the flop on?

Even if there are 8 other players in the game, and – let’s suppose – you know none of them has a 7, the odds will be 2 cards in 50-18=32. That means 6,25%. I guess that says enough…
When chasing a flush though, the situation is different. You can only chase a flush after the flop, and if you have a 4-card flush ( two of the cards in your pocket and two on the table) it might just be worth chasing.

Here are the odds involved: there are 13 cards of a suit in a deck. 2 of those are in your pocket, two on the table, so that leaves 13-4 = 9 cards of the suit you’re looking for, in the deck.

You have your two cards, plus the three on the board, make 5. The deck has 52-5=47 cards left in it (you don’t know what your opponent has) That means you’ll be on the hunt for 9 cards in a 47-card deck. That’ll give you a 19.1% chance to get it right. Even if you miss it on the turn, the river comes, and that too will give you a 19.5% chance of completing your flush.

It reality it is not that simple though. These odds are greatly dependant on how many players there are in the game, (even those count who already mucked their cards) and on the cards these players hold.

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Let’s see two extreme examples. There are 9 more players in there, and none of them has another card of the suit you’re chasing for your flush. In that case, you’ll be looking for 9 needles in a much-reduced haystack. 2x9=18+your 2 pocket cards=20+3cards on the board=23.

The "haystack” you’ll be looking for your 9 needles in, is 52-23=29 cards big. That’d give you 31% real chance to get it right, on the turn alone.
On the other hand, if all those 9 players held 1 card of the suit you’re looking for, your chances would be down to 0%.
This is just to illustrate how complicated it really is to calculate truly relevant odds for different poker-situations. Bottom line is, it makes more sense to chase a flush than to chase a medium-to-low pair.

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