When is it right to call with a 3 flush

[Doctaprofit]

Say i raise with Ace Queen Diamonds the flop hits.. and its King 5 and 8 of diamonds... now assuming someone has a king that would more or less eliminate my queen but i still have the ace... and the backdoor flush .. what pot odds do i need to call in this situation.

[cold_cash]

Seems like I heard somewhere you cant count a backdoor straight or flush for approximately 1.5 outs.

Don't quote me on that though.

Search around. I know there are a few posts that have mentioned this.

[sublime]

Flush draws (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Board=holdem&Number=560368&P HPSESSID=&fpart=)

[HighRolla81]

Thanks for the post of those threads. I found them to be very useful

[sublime]

No problem, Illunious deserves the credit for putting it togther. I carry around a copy of a few of them in my gym bag and read them when I am on the train etc....

/images/graemlins/laugh.gif

[Mike Haven]

i wrote this a few weeks ago because i believe a backdoor flush should be counted as 2 outs - some people agreed; some disagreed:

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with a two-outer on the flop you bet 0.5BB 45 times out of 47 and miss, so you have to bet another 1BB to hit twice out of 46

if you play 47x46=2162 hands, you hit 2x46=92 times and miss 45x46=2070 on first card, and on the 2070 misses you hit 2070/46x2=90

or 182 hits out of 2162 hands = odds of 10.9 to 1, or 8.4% success rate

the COST to hit a two-outer 182 times per 2162 hands = 1081BB + 2070BB = 3151BB = 17.3BB per hit

************

with a backdoor flush you bet 0.5BB to hit the four-flush 10 times out of 47 and then have to bet another 1BB to hit the full flush 9 times out of 46

or, if you play 47x46=2162 hands, you hit 10x46=460 and miss 37x46=1702 on first card, and on the initial 460 four-flush hits you then hit the full monte 90 times, giving 90 flushes out of 2162 hands = odds of 23 to 1, or 4.2% success rate

the COST to hit a backdoor flush 90 times per 2162 hands = 1081BB + 460BB = 1541BB = 17.1BB per hit

************

hence, as the cost is exactly the same, you can count a backdoor flush draw to be EQUIVALENT to a two-outer, ON THE FLOP (as soon as the turn is dealt, you either have a new nine-outs or a new zero-outs, as far as the flush draw part of your hand is concerned)

******************

rewrite:

every time we look at our hand we compare it with the hands we deduce our opponents to have

normally we can see that we have nine outs, or eight outs, or five outs, or whatever, for our hands to catch up and overtake the leading opponent's hand

when we have a backdoor flush or straight we can't use the conventional outs-counting method because the ten outs or eight outs we need to improve our hand to a four-flush or an OESD still leave us well behind even if we catch and still leave us with only a draw

therefore we need to establish a sensible and realistic comparison between drawing to a standard finite draw and to one of these rather imprecise situations

looking at my previous calculations we can see that AT THE MOMENT OF STARTING TO DRAW TO A BACKDOOR FLUSH YOUR EXPECTATION OF SUCCESS IS ALMOST EXACTLY THE SAME, IN MONETARY EXPENSE TERMS, AS THAT OF STARTING TO DRAW TO A TWO-OUTTER

whether you finish drawing to improve to the flush, as with whether you finish trying to hit your two-outter, is irrelevant

the backdoor flush's outs-value of 2 applies only at the moment you have to decide whether or not you have enough outs to warrant drawing to your inferior hand when comparing the bet to be made with the pot odds available

finally, let's use a specific example to prove that the 2 outs is correct (we have to wonder why the pot is so large, but, whatever!)

we have Ac2c and our opponent has AdKd on a flop of Kc9h6s in a 2-4 game

ignoring runner-runner twos we have only our backdoor flush as a winner

the pot is 50

37x46=1702 times we lose our 2 = 3404 loss

10x46=460 times we have to call 4 and we lose 370x4=1480 loss

3404+1480=4884

90 times we win 50+4= 4860

this is proof that the minimum pot odds needed were 50 to 2 or 25 to 1, which is the same odds as a 1.8 outter on the flop QED

incidentally, now that you accept that a backdoor flush is worth (almost) two outs, you can choose whether or not to build in implied odds, (say, perhaps in a multiway pot), if you feel that you can win a bet or two on the river, after you make your flush; in which case on occasions you might even consider counting say Axxs as 2.5 outs in some types of games