How accurate is Clonie Gowen's estimate?

nightlyraver · #1 07-25-2005, 01:38 PM

I read this little tip in Cardplayer the other month and I was wondering exactly how accurate it is. So here it goes:

I'm pretty certain that this tidbit was authored by Clonie Gowen. She advises that you can estimate your probability of making your hand using a very simply technique. Simply multiply your outs, assuming they are all good, by 2 and then multiply the product by the number of cards to come. For example, if you have a flush draw on the flop and nothing else, multiply your 9 outs to the flush by 2 (18% to make it by the turn) and then multiply that by 2 (36% to make it by the river). This sounds pretty head on for the flush draw since every says you have about a 35% chance to make your flush by the river. Does this technique work all the time assuming your outs are good? Exactly how accurate is this in other cases? Can you use this technique as-is if you have discounted outs?

LetYouDown · #2 07-25-2005, 01:48 PM

It's a decent, beginner's rule of thumb. It does give you a reasonable approximation...assuming all of your outs are live and there are no redraws. For instance, if you have an open ended straight on a flop with 2 of a suit, and someone holds two overcards of that suit, you're presented with a problem.

Long story short, if you're just looking for an estimation of making whatever hand you're drawing to...it's helpful. If you're looking for it to be the best without another occurence (another flush card coming, or a board pair, etc.)...it's likely to be off by a significant margin.

nightlyraver · #3 07-25-2005, 01:58 PM

OK, so let's take this one step further. Going back to my example with the flush draw on the flop, could we use this technique to approximate the probability of the flush being made by the river AND winning with the flush (assuming we lose when the board shows a 4-flush)? I guess we would also need to lower that percentage a little since we lose as well when top pair makes a runner-runner full house, but that can't happen enough to really affect this approximation, can it?

LetYouDown · #4 07-25-2005, 02:01 PM

[ QUOTE ]
but that can't happen enough to really affect this approximation, can it?

[/ QUOTE ]
The problem is that it doesn't take into account what other players likely hold. If you're up against a set and a higher flush draw, you could very well be drawing dead. So I'd say from 36% to 0% is pretty significant.

nightlyraver · #5 07-25-2005, 02:50 PM

I think you misunderstand. What I meant was the following: How, if possible, can we adapt this estimation to reflect 1 card of your suit hitting but not 2. For example, say the flop is Ks7h2h and Villian has AhKd while you have something like Th9h. We win when 1 heart falls, but we we see runner-runner hearts. What I meant when I said, "that can't happen too often" was the same scenario except that the board shows Ks7h2hKhAc where we also loose. Like I said, I can't see this hapenning often enough for it to affect any sort of approximation, correct?

LetYouDown · #6 07-25-2005, 03:05 PM

Assuming you hold a four flush...I think this is right.

Odds that ONLY one of the remaining cards will be of your suit:
[C(9,1) * C(38,1)]/C(47,2) = 342/1081 = 31.6%

Odds that BOTH of the remaining cards will be of your suit:
C(9,2)/C(47,2) = 3.33%

Which would put her estimate off by a few percent...but that's obviously not what the rule of thumb is for.

Bulldog · #7 07-28-2005, 04:07 PM

You need a heart for a flush, but your opponent needs two hearts for a higher flush, correct?

You have 9 outs twice, or a 36% chance (estimate based on this method) to get there. Odds of runner runner flush are about 4%*. So 36% - 4% equals 32%.

*Actually 4.16% when you know five cards (the three on the flop and the two in your hand) and three of the suit are accounted for in those five. In this specific scenario, where we know seven cards and five of that suit are accounted for, it's 2.83%.

jccookjr · #8 07-25-2005, 03:38 PM

The only time it won't be real close is when you have lots of outs.

nightlyraver · #9 07-25-2005, 04:07 PM

OK, so tell me more. Say you flop a monster draw - an open-ended str8-flush draw w/ 2 over cards. That's 21 outs I believe to top pair or better. Assuming they are all good outs, do we not have about an 84% chance of making top pair or better (not including redraws)?

LetYouDown · #10 07-25-2005, 04:24 PM

You hold K[img]/images/graemlins/heart.gif[/img]-Q[img]/images/graemlins/heart.gif[/img] and the flop is: J[img]/images/graemlins/heart.gif[/img]10[img]/images/graemlins/heart.gif[/img]2[img]/images/graemlins/club.gif[/img]

I come up with

1 - C(26,2)/C(47,2) = 1 - 325/1081 = ~70% that you'll make at least a pair of Q's.