Raising your draw to increase EV/ Caveat

[KDF]

Numerical wizards, your kindly insight is required:

In a previous string on this section (probability) a question was asked and answered regarding raising an already large pot with a flush draw when you know you will get many calls. The idea being that you increase your EV by doing so. I can see how this works well when nobody else is holding anything that can beat you when you hit. (I suppose it applies for straight draws with non-flush board against you).

However, if this situation were to take place in a real game where there are five callers staying for the river and even calling a raise to see the last card, what is the probability that one or more hold either a set or two pair where 1 or more of your 'outs' are hand killers? (i.e. making a full house for one of your five callers.) And how do you adjust your outs accordingly?

It is not unrealistic to have 4-5 callers going to the river in some loose low limit games, so this is a practical scenario. I am wondering if it would be truly increasing your EV if you were only to employ this move when you are drawing to the nut flush with no pairs on the board (or nut straight for that matter, with no flush possibility on the board). Or, when you have only two callers and you are in late position with the nut draws (no pairs out).

Thank you for paying attention in Math class!
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[pudley4]

</font><blockquote><font class="small">In reply to:</font><hr />
I am wondering if it would be truly increasing your EV if you were only to employ this move when you are drawing to the nut flush with no pairs on the board

[/ QUOTE ]

It would increase your EV for that hand; however, you would be passing up many more +EV scenarios. Also remember that even though the board hasn't paired, you could still be up against someone with a set, so it's still possible 2 of your outs would give him a full house.

Finally, notice that if the board hasn't paired, at most 2 of your outs are "tainted".

[Dynasty]

When you've got KcQc and the flop is: 9c,6d,2c, your tainted outs (somebody has 9h6h) in some hands are compensated for in other hands when you win the pot when the final board is: 9c,6d,2c,2s,Kh and you win with top pair.