"Discounted" Outs: Discussion and Questions

[brianmarc]

I recently came across the concept of "discounted" outs. It is a measure of the likelihood your hand will actually win the pot if your draw hits. For example, there are 6 outs to a flush draw; if the board is paired the likelihood of your flush standing up, should it hit, is less than if the board is unpaired. This is due to the increased likelihood of a FH in the former situation. So, if the chances of you winning the pot with an unpaired board is, say, 95% (not 100% since the board could still pair), you would use 6*85%= 5.7 outs (these are your discounted outs) in your assessment of the required pot odds; in the case of the board being paired, your likelihood of success may now be 85%, so your discounted outs are 6*85%=4.8.

My questions are: What do you thik of this concept? Has anyone created or seen a table that shows the correct discount values for various hand combinations for the flop and for the turn? Can anyone describe a method for correclty calculating the discount values, beyond the "gut feel" approach?

[brianmarc]

The example I gave used the incorrect number of outs! For a flush draw, the '6" should be '9', making the correct discounted outs 8.6 and 7.7, respectively.

Apologies.

[LetsRock]

Well, this seems to be making it harder than it needs to be. If I have a flush draw, but I feel that 2 of my flush cards will give someone else a better hand, I consider myself to have only 7 outs instead of 9.

While it's good to have a solid understanding of odds, I think it's best to keep it as simple as possible. Having a table for every possible odds situation (your outs with every hand, with every board vs. every possible opponent's hand) would be a book and therefore be little more than interesting(?) reading.

[brianmarc]

You're right on your points. But given the huge amount of attention players pay to draw odds I was curious to see what level of thinking had been applied to this refinement. Apparently it is very little.

[Louie Landale]

Its a very useful concept especially since it encourages folks to notice the difference between "improving" and "winning". Yes, use your discounted outs (your "chance of winning") in your pot-odds calculations.

No, its not possible to calculate it exactly since its usually impossible to know for sure the exact distribution of all active players hands.

I would also like to point out that your "chances of winning" are USUALLY worse than they appear. If you are NOT drawing to the nuts you need to auto-discount your outs; and I generally start with a 50% figure and adjust from there, often higher.

The difference between your "raw outs" and "discounted out" (perhaps called "discredited outs" or better "losing outs") also reduces your implied odds since you are likely to lose one or more bets if you DO improve but still lose. This cost should be calculated into your "pot odds" calculations on the "cost" side: if you have 3 "losing outs" and will lose 3bb when you hit one, then your increast cost is 3/45*3BB = .2bb. Add .2bb to your cost of calling.

You also need to adjust for your chances of winning if you do NOT improve: drawing to the A-flush means you stiff A may be the best hand, and snagging an A may also win.

- Louie

[brianmarc]

I agree. But what is interesting is that I have seen none of the "experts" who write on HE ever suggest that outs should be so modified. Is this because it's so obvious that it doesn't bear mention; or because they have overlooked it?

[MaxPower]

You don't need to modify your outs. You just have to be getting better pot odds than normal to draw to your hand. If you have a 4:1 shot and you are getting 6:1 on your call, you will still make a profit even though you will occasionaly lose when you improve. I believe S&M talk about it in this context.

[uuDevil]

If I recall correctly, the concept is discussed along with specific hand examples in Ciaffone & Brier's "Middle Limit Holdem Poker" and Mathew Hilger's "Internet Texas Hold'em."

[ACPlayer]

Ciaffone and Brier discuss this. Perhaps they even overdiscuss this point. Although they dont make it mathematical.

[brianmarc]

This is a pretty imprecise response. What hamds are you talking about? What if you are getting 5.9/1; or 4.1/1? You get my drift?