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    • lynius
      Joined: 15.01.2011 Posts: 382
      Guys, is it acceptable to calculate your outs to give you your odds and then bluff based on whatever pot odds would give you value?

      So in a 30 cent pot, with your odds to win at 3:1 can you bet 10 cents as a bluff?

      Hand converted with online hand converter:

      Play hand

      $0.02/$0.05 No-Limit Hold'em (9 handed)

      Known players:
      MP3 (Hero):

      Preflop: Hero is MP3 with J, K.
      4 folds, Hero raises to $0.13, 2 folds, SB calls $0.11, BB folds.

      Flop: ($0.31) 3, 6, 2 (2 players)
      SB checks, Hero checks.

      Turn: ($0.31) 9 (2 players)
      SB checks, Hero bets $0.10, SB folds, Hero gets uncalled bet back.

      Final Pot: $0.31.
  • 2 replies
    • Wurble
      Joined: 04.04.2009 Posts: 457
      If you think that villain will fold to 1\3 pot bet even some of the time it is massively +EV but if not then betting bigger would still be +EV due to the $$ you make each time villain folds added to the pot you win 1 in 3 when he calls.
    • phathustler
      Joined: 03.01.2011 Posts: 23
      To directly answer your question: you probably don't want to always do that if anyone is paying attention since you'd be pretty much announcing "I have a draw with x outs" whenever you bet less than half pot. But anyway, the math behind the answer from an expected value perspective can be seen by looking at

      f*(.3) + (1-f)*((.25)(.3+.10) - (.75)(.10)) - (0.25*.3)
      where f is the probability that the opponent folds.

      This is the difference between the EV of the bet and your current pot equity. Assuming the opponent doesn't raise, and you magically get to showdown without further betting (both pretty big assumptions), that tells you how much more than your current expected value you gain by making this bet, as a function of how often the opponent folds. In this case, it simplifies to

      0.275*f - 0.05

      In particular, it's negative up until around 0.18 and then positive afterward. So as long as the opponent folds at least ~18 percent of the time, you've gained compared to checking it down. So from that perspective, it's probably okay, because your opponent is probably going to fold enough unless they're crazy. It's complicated by the fact that you need to play additional streets though.

      For comparison, a half pot size bet requires that they fold ~25% of the time or more, two-third pot requires ~30%, and a pot-size bet requires that they fold at least ~40%.

      The reason those other cases matter is that your opponents likely respond to different bet sizes differently. They might think a 1/3 pot size bet is weak and call / raise with more hands, but might think a 2/3 pot bet is strong and fold more. So it's possible they don't fold 18% of the time to 1/3 pot size bets, but fold more than 30% to 2/3 pot bets. Extreme example: a min-bet of 0.05 only needs them to fold at least 10% of the time to be better than checking. But, some players will never fold to a minbet, so against them it would always be a bad move.

      And, like I said, keep in mind that this used assumptions that aren't totally realistic. Your opponent is going to raise some percentage of the time, and you probably won't be able to check down everything all the way to showdown after this flop bet. Even worse, I compared the EV of the bet to the current pot equity, which is kind of like assuming we're comparing the EV of the bet to the EV of checking. But you might need to fold too often when you check to actually think you have a reasonable claim to your pot equity.