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Old 09-18-2005, 10:53 AM
ALL1N ALL1N is offline
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Join Date: May 2003
Posts: 156
Default Calculations

I was wrong initially. The backdoor straight is the equivalant of about 0.45 of an out; still much less than most people seem to think. In your calculations, you're running it as if we're allin on the turn. The bet we'll have to pay to draw on the turn must be considered.

If a T hits it allows us to call instead of folding the turn (raising the T would clearly be silly):

We call the turn with what I'll assume is 11 outs (3 K's, 4 A's, 4 9's.. sometimes the 8 will be clean, somtimes the K won't, and sometimes the straight draw will be splitting.. 11 seems generous if anything).

Assuming a pot size of 6: 4.5 + the villain's turn bet + 0.5 implied odds (seems reasonable), the EV of this turn call will be:

EV = (6 + 1) * (11/46) - 1
= 0.67 BB

Since there's 4 T's, the # of outs added by the T is:

Extra outs = (No. of T's) * (EV when T comes) / (Assumed pot size)
= 0.67 * 4 / 6
= .45

Btw, the backdoor straight via an A or 9 coming on the turn needn't really be considered, because hitting either card on the turn sets up a pretty EV-neutral call.
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