calculating runner runner in hold em

[benneh]

Is there an easier way of counting runner runners? like assigning a runner-runner aspect of your hole cards into your outs for use with pot odds. I can only think of using combinations to figure out the probability of it, but is there a rule of thumb for this kind of stuff?

Example:

Hole cards: (7h, 8h)
Flop: (9h, 6d, As)

Bet to you is 1 sb. pot w/ the current bet is only 3.5 sb. would the runner-runner flush be enough to justify a call to play 'correctly' here?

And just to make sure my calculations are right, when using the combination method, the forumla would be:
1 - C37,2/C47,2, right?

edit: Fixed my equation, i think

[LetYouDown]

Probability of running hearts:

47 C 2 possible turns/rivers or 1081.

10 C 2 possible running heart combinations or 45.

45/1081 = ~4.2% shot for the flush only.

[Ixnert]

[ QUOTE ]
45/1081 = ~4.2% shot for the flush only.

[/ QUOTE ]

Which is about 1.5 outs, if you prefer to think of it that way.

[Marlow]

I read once that you can calculate runner-runner str8s and flushes as one extra out. It looks like that was a little conservative.

In any case, does that seem like a good rule of thumb?

Marlow
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[BruceZ]

[ QUOTE ]
And just to make sure my calculations are right, when using the combination method, the forumla would be:
1 - C37,2/C47,2, right?

[/ QUOTE ]

No, that is 1 minus the probability that you get 2 non-flush cards = probability that you get at least 1 flush card. That's not what you want. You need 2 flush cards, so it should be C(10,2)/C(47,2).

[LetYouDown]

Because it's rarely a consideration in NL (implied odds are generally more important in the games I play in), I rarely run into a situation where I need to actually consider it. When I do, I generally use 1 out as a rule of thumb.

[RiverTheNuts]

I also consider it about 1 out, because often some straight cards or flush cards will make a better straight or flush for someone else, or will pair the board to make a boat for someone else.

[Siegmund]

The problem with counting a runner-runner as some number of outs is that "outs" are used in two different ways - deciding whether to take one card off, and then deciding again whether to take the second card off, vs. estimating your chance of making your hand assuming you stay in to the end (combining these two chances at once)

The first interpretation (a separate calculation on the flop and on the turn) is the one I find more useful. Under that interpretation, on the flop a backdoor flush is a 10/47 chance of having 9 extra outs on the turn, and should be counted as TWO outs on the flop (and then as either nine or zero on the turn, according to what has developed.) Straights are more complicated and depend on whether you anticipate being able to play the gutshots on the turn or not. (Ex. 543 now: 8 chances at 8 extra outs, and 8 more chances at 4 extra outs -> only 1.5 outs now if you will fold the gutshots, but more than 2 now if they will be playable.)

The second interpretation I charitably describe as dangerous, but for some reason it's the more common one on the forums. Under that interpretation, the runner-runner flush represents a 4.2% chance of coming in by the end, which is similar in some sense to being given two chances at a 2.1% draw, so equated with having one one-card out.

Key lesson: hands that start out with backdoor chances must be reevaluated after the turn is dealt, rather than treated as having a fixed value. Whether you represent that value as "one out twice" or "two outs once, then recount" is your choice.