adding outs for the possibility of being ahead

[rjc199]

I'm interested in finding a way to compute "virtual" outs (outs that account for the fact that you may already be ahead). A simple way to explain what a virtual out is as follows. You are in a hand with a pot size of X BBs on the turn, you bet and have been raised and are getting pot odds of X:1. You determine that if you are behind to a certain hand (say two pair) that you have Y outs. You can look at a chart to see if you have the pot odds to call. What happens if some percentage of the time, Q%, you are actually ahead? This would add some number to your outs, so your outs term would be Y=(Y_actual + Y_"virtual"). I know how to do this calculation if you are further behind, ie you discount a certain percentage of your outs. This would be the reverse of that, you add a certain percentage of your outs.

How do I determine Y_"virtual" as a function of X and Q?

[Paul2432]

I think the best way to do this is figure a percentage to win the hand and then convert to odds. For example, suppose you have 11 outs and 44 unseen cards. That would be a 25% chance of hitting your outs. Suppose also, you have a 15% chance of having the best hand. Overall you havea 40% chance of winning, so you would need 60:40 pot odds or 1.5:1.

Paul

[rjc199]

The answer came to me in the shower yesterday morning.

Y_"virtual" is only a function of Q and is rather simple.

Y_"virtual" = 46 * Q, where Q < 1.

For example:
I get raised on the turn and figure if I'm behind I have 5 outs to beat two pair, but there is a 20 percent chance that I'm still ahead. In this case Q = 0.2 and so Y = 5+0.2*46 = 14.2 outs

[Lost Wages]

This was the answer that I thought of at first. Unfortunately, it only works for all-in situations. Otherwise it can lead you to call the turn incorrectly.

Changing your example a bit: suppose that you have 5 outs and Q = 0.1. There are 4BB in the pot when you have to decide whether to call. With 5 outs you are 8.2:1 against so based on your "regular" outs you would have to fold. Then you add your virtual outs and arrive at 9.6 (5 + 4.6) which is 3.8:1 against so you have an easy call. The river is a blank and your opponent bets making the pot 6BB. Here is the problem. You are getting 6:1 to call the river but since we said that Q = 0.1 you are 9:1 against having the best hand so you have to fold.

Since you were unable to call a river bet if you missed your "regular" outs, your virtual outs were actually worthless.

Lost Wages

[GlemZurg]

A thorough (but not necessarily manageable) way to consider this is that

1. You have a number of outs (or partial outs) that will make you the winning hand.
2. Of the cards that are left some of those are your opponents outs that will make them a winning hand even if you have the best hand at the moment. (Allows you to calibrate to a coordinated board.)
3. Of the cards that are left, you could take a proportion of them as your winning outs.

So if you had 8 winning outs and figured you were a 2:1 underdog and there were 9 outs for your opponents (even if you have the best hand at the moment), then...

47 - 8 = 39 cards that are *not* your outs
39 - 9 = 30 cards that are nobody's outs

since you will win 1/3 the time with 2:1 odds you could "claim" 10 of the 30 cards that miss everyone and set your outs to 18.

Now, I don't know how this holds up to actual odds. Although I may do an analysis of it in a couple weeks on the computer. So use at your own risk (obviously).

I figured I should post though since you left out the effect of your opponent outdrawing you.

Good luck,
Justin

[rjc199]

You could get around the problem of having to fold the turn by way of figuring your implied odds and your reverse implied odds.

You know that if you hit your hand on the river you will be able to win an extra bet on that round, plus whatever is in the pot. This should make up for the times that you have to call the river when you don't hit your draw. If the pot is small on the turn you will have to realize that you won't have the pot odds to call the river bet so if you don't have the pot odds on the turn you can't call on the turn.

Regardless there is nothing wrong with calling on the turn then folding on the river when you miss your draw. You do it all the time with flush and straight draws. My main thrust with this virtual odds idea is to find when is it correct to re-raise for value in a multiway pot vs. an opponant who may have you beaten a certain percentage of the time and there is/are mulitple callers coming along all of whom you most likely are ahead of. It is intended to give you an idea of when to raise for value multiway, and also to give you an idea of when a close fold can be converted into a call.