Disregarding rake, let's say it's
heads-up and there are 4 small bets in the pot after the first betting round. If Hero can only win half of the pot and if Villain is not going to fold whatever Hero bets, then any money going into the pot on the second, third, and fourth betting rounds is a wash. (Do you understand "wash"?)
If Hero plans to check/call it will cost Hero 3 more small bets to see the next two cards. (It will also cost Villain 3 more small bets to see the next two cards, but that's immaterial).
• 36% of the time, Hero will make the flush and will win 2 small bets, half of what was in the pot after the first betting round.
- my math:
+0.36*2=+0.72 small bets.
• 64% of the time, Hero will miss and will fold. Hero will lose 1.92 small bets when he loses.
- my math:
-0.64*3=-1.92 small bets.
Hero's net figures to be about -1.20 small bets.
- my math:
0.72 small bets-1.92 small bets = -1.20 small bets.
Since Hero figures to lose more than he will gain, he should not draw purely to a flush after a play where we presume Villain has flopped a wheel. (But the bugaboo is Villain may not have flopped a wheel).
Disregarding rake, let's say it's
three way and there are 6 small bets in the pot after the first betting round. If neither opponent is going to fold, then when Hero wins, he wins half of the original pot plus half of whatever the third person puts in the pot.
If only one opponent bets... that is if one opponent bets aggressively while the other and Hero both play passively, it will again cost Hero 3 more small bets to see the next two cards. (It will also cost both Villains 3 more small bets to see the next two cards, and that's not immaterial).
• 36% of the time, Hero will make the flush and will win 3 small bets plus half of what one opponent bets on the second, third, and fourth betting rounds.
half of what was in the pot after the first betting round.
- my math:
+0.36*3+0.36*5+0.36*5=+4.68 small bets.
• 64% of the time, Hero will miss and will fold. Hero's loss subtotal figures to be about 1.92 small bets (when he loses).
- my math:
-0.64*3=-1.92 small bets.
Hero's net figures to be about +2.76 small bets.
- my math:
4.68 small bets-1.92 small bets = +2.76 small bets.
Of course there are all sorts of possibilities. One opponent can fold at any time, or there could be a betting war between the two opponents.
But so long as you are guaranteed at least two opponents who will both see the showdown, or two opponents, one of whom will see the showdown and the other of whom will fold on the last betting round, you can draw for the flush. With only one opponent after the flop who will go to showdown, you should not draw for the flush.
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Little short cut: when you win 36% against one, double that against two, to get 72%. Meanwhile, your loss, regardless of the number of opponents, is 64%. You can see that 72% is greater than 64% (while 36% is less than 64%).
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If, instead of 4 small bets in the pot after the first betting round, there were 8 small bets in the pot after the first betting round, then there still wouldn't be enough in the pot to justify continuing heads-up with only a flush draw.
+0.36*4-0.64*3=
+1.44-1.92 =-0.48 (the sign on the net is still negative).
But if there were 12 small bets in the pot after the first betting round, then
+0.36*6-0.64*3=
+2.16-1.92=+0.24
Buzz