[Derek in NYC]

Interesting idea valuing "runner runner" outs on a discounted basis. I suppose the idea is that the turn and river have to be viewed as dependent events, and thus the true value of the runner runner is the product of the probability of hitting your turn, times the probability of hitting your river out.

So to take the flush example, if the odds of the turn being a [img]/images/graemlins/spade.gif[/img] are 10/47 and the odds of a [img]/images/graemlins/spade.gif[/img] also falling on the river are 9/46, then the odds of a turn and river [img]/images/graemlins/spade.gif[/img] are going to be 90/2162, or roughly 4%. So using the rule of thumb that 4% = 1 out, I agree that the runner runner flush is worth 1 out. (I know that independently, of course, the odds of the runner runner flush is about 23:1 against).

Now for the runner runner str8 the odds are actually worse, since I can no longer count the K [img]/images/graemlins/spade.gif[/img] or the 9 [img]/images/graemlins/spade.gif[/img] as outs. So again, without going through the math, the value of the runner runner str8 (assuming you've already calculated the runner runner flush) is going to be 1 out at most, probably less.

So back to the decision at the flop--each of your runner runners are worth 1 out, plus your overcards of Q and J give you 6 more outs. So at best you have 8 outs, but as you said, you need to discount these outs substantially because the overcards may be dominated, and the flush runners will most likely not be to the nuts.

So I can now follow where your rule of thumb of 6 outs comes from. Wow! Very helpful, and I suspect that I have been substantially overvaluing these "double runner runner" situations, since 6 outs on 47 cards to come is not great at all.

Did I get the logic right?