Flush Draws in NLHE
Correct my thinking.
10nl (FR). You are OTB with AhJh. 18/14 Villain open raises from MP1 to .35.
You decide to call. Pot is now .85. Flop comes down Tc6h5h. You just flopped a 4 Flush. Your chances of hitting the Flush on the Turn are 18%. Which means 82% of the time you miss. Just to round it off say you hit your Flush 1 out of 5 times and miss it 4 out of 5 times.
Purely by Pot odds
you need to get 4 to 1 on your money to draw profitably. so you should not call a bet larger .25. (If villain bets .25 pot becomes $ 1.10. If you call 5 times, 4 times you lose .25 for a total of $ 1.00 and 1 time in theory you win $ 1.10. That, of course is assuming you have the best Flush and villain doesn't make a Full House. Also this calculation does not include rake which increases your pot odds
Of course most villains don't make .25 bets into .85 pots. More likely villan makes an .85 bet into an .85 pot. Therefore, by pot odds it would not be profitable to call.
However in NLHE we have implied odds, whereby we call a bet that we do not have odds to call because we think we can get more of the villain's chips if we make our Flush.
So, if villain pots the flop and you call, 4 times you miss on the turn for a loss of $ 3.20. One time you make the Flush, which means you need to get, on average $ 1.50 more of villain's stack when you do. So, if vlllain check/folds to a raise you have lost $ 1.50.
Of course the other option is to re-raise the villian's c-bet with the hope that he folds. So, say you re-raise to $ 3.40. Villain needs to fold 50% of the time to be EV neutral. If villain doesn't fold at least 50% of the time you lose even more money.
So you need to pick villains who fold to re-raises at least 50%, probably because they either open too wide of a range or won't risk their stack with a medium hand. So I'm guessing LAG's or Nits, but not Solid TAGs or Calling Stations.
So, unless villain gives you a free card, you probably can't draw to a Flush based on pot odds but need a reasonable chance that villain pays you off when you hit or you need to be able to make a villain fold to a re-raise 50%+ of the time.
Now I didn't mention what happens after the Turn card is dealt, only that you go through the same odds calculations for the River if you call his c-bet or villain calls your flop re-raise.
You do have one other option, which is to re-raise large enough that villain folds or decides to shove so that you have pot odds to call a shove. You would need to call 36% or less of the pot to make this +EV. So if you both started with $ 10.00 and the pot is $ 1.70 after his c-bet and you re-raised so much that villain would feel like he had to commit his stack you would need to make sure he stacked off or folded. Say you bet $ 6.00. If villain shoves you would need to call $ 3.65 to win $ 10.00. You should win 36% of the time so this should be ~ breakeven EV. Of course this strategy requires villain to fold. If villain never
folded 36% of the time you would win $ 10.00 = $ 3.60 and 64% of the time villain wins and you lose $ 6.40. If villain calls only 10% of the time you win $ 1.35 * .9 = $ 1.22. IF he calls 10% of the time and you win 36% of then then you 3.6% you win $ 10.00 or .36. and 6.4% of the time you lose $ 10.00 = -.64. so EV if he shoves 10% of the time - .28. So if he folded 90% of the time and shoved 10% of the time your net EV is .94.
ninety-four cents. That's a lot of assumptions and risk for a small reward.
So realistically, unless you have a bunch of players who pay you off handsomely every time you hit a Flush OR who fold a high percentage of the time to a re-raise, I don't see how you can profitably draw to Flushes in NLHE.
Am I missing anything here?