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Playing no-limit hold-em cash game, I am out of position drawing at a flush against one opponent. The river card comes down without completing the flush, but it does complete a potential open-ended straight draw. Assuming I have bet the flop and the turn as a semi-bluff, how often and how much should I bluff on the river?

What parameters are relevant? For example, how does the pot size and opponent stack size effect the decision?

Example: typical example, I am holding A♥K♥ in the CO, 25c/50c blinds:

Fold to CO
CO: Raise $1.5
Button: Call
SB/BB: fold

Flop: Q♥9♥2♣
CO: Raise $3
Button: Call

Turn: 3♠
CO: Raise $6
Button: Call

River: 8♠
CO: ??

  • Using examples of other hand historys, is it possible for you to adapt a hand to show in much more detail the situation you describe? Pot size, bet sizes, all prior actions, table dynamics, are all critical to this decision. I'd like to answer but it wouldn't be as specific as this situation requires. Thanks. – Toby Booth Apr 24 '12 at 17:06
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    In addition to what Jeffrey has said, consider that it is often better to bluff a busted straight when a flush comes than to bluff a busted flush when a straight comes. This is certianly not universal, but straights have a tendancy to be more well-hidden than flushes. – John Dibling Apr 25 '12 at 20:46
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    @JohnDibling Isn't that a comment that should be placed beneath Jeffreys answer, and not the question. – Toby Booth Apr 26 '12 at 23:54
  • @TobyBooth: I didn't think so. – John Dibling Apr 27 '12 at 12:55
  • @JohnDibling Comments on questions are best used to gain "clarification" and/or additional information. Comments on answers are best used to gain clarification and, to avoid duplicating good answers, to add helpful additions to the existing response. Your response is most useful as a comment to Jeffreys answer. – Toby Booth Apr 27 '12 at 18:19
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The number one consideration here is your opponent's tendencies. Are they the type to be scared away, or are they the type to make a crying call? Also, what was the action prior to this point and what does that lead you to believe your opponent holds? What was the preflop action? How large were your bets? Exactly what community cards are we talking about also has a big impact here on how scarey things will be to your opponent. Moreover, that will determine whether you hitting the straight is even a believable story.

The more likely they are to hold a strong hand (or, worse, hold the hand you're representing), the less inclined you should be to bet.

Pot size and opponent stack size only really enter into this as factors that might affect your opponent's tendency to call. The action up to this point and the types of plays you have seen from them in previous hands are both far more relevant factors here.

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There is an optimal bluff rate from GTO (Game Theory Optimization). You bluff at a rate that call versus fold has the same outcome for your opponent. Set that EV (Expected Value) to zero and solve for the bluff rate.
pot = pot size at start of river
bet = bet as a fraction of the pot size
bluff = fraction of bluffs
EV = 0 = -bet + bluff(pot + 2bet)
bluff = bet / (pot + 2bet)
set bet = 1 (pot)
set pot = 1 bluff = 1 / 3
so for every 2 winning hand bluff 1

if they call all three the EV is 0 = -1 -1 -1 +3
if they fold all three EV = 0 + 0 + 0

It is fair to call it a raise but it would be more proper to call it open for $3 on the flop. With $3.75 in the pot that is almost a pot size open. That is a strong call. They have a piece of it (like a Q) or a strong draw. Since you have the flush covered including the Ace maybe JT for an 8 outer straight draw.

Turn fire again with an almost pot size bet. You have a flush draw and two over. You get another call. That is a very strong call. That does not fill in a draw so now you need to put them on a made hand like one pair, two pair, or even a set. JT is still a possibility.

River hits JT for a straight and 8.

Need to sell that you have a winner. Would you have played JT, Q8, 98, QQ, 99 that way? Get AQ or KQ to fold out. Or they could be on a busted draw. Your risk is here is they could be on 2 pair or better and not going to fold.

I think a better plan is to check the turn. If they bet big just get away. If they check bet the river no matter what. You have just as much fold equity with 1/3 the investment.

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