Defining virtual or real outs
May 02, 2017 3:00 AM
by George Epstein
In deciding whether to call a bet, skilled hold’em players often count their outs, the cards that will complete a drawing hand. That’s important!
A group of us were discussing how we use our outs. The question came up: Should we include the outs for cards that are no longer available? Obviously, unavailable outs cannot help to make your hand.
In a game of $4-$8 limit hold’em with a full table, you and eight opponents vie for the pot. On the turn, you have A-9 spades in the hole, and 10-5 spades are on the board, accounting for four spades. There are nine more spades remaining. These are your “virtual” outs, any one of which will give you the nut flush.
On the turn, multiply your 9 outs by 2.2 for approximately 20% probability. Then, the card odds are: (100 – 20) ÷ 20 = 4-to-1 (approximately) against making your flush on the River. This information also is available in charts published in many sources, making it easy to translate the number of your outs directly into the card odds. Glancing at the pot shows the pot odds are much higher than your card odds; therefore, calling a bet to see the river is the wise decision.
With your two holecards (spades) and the four cards on the board (including two more spades), you actually have seen just six cards. There remain two groups of unseen cards, some of which are no longer available:
Group 1: There are 16 unseen holecards held by your eight opponents plus the three burn cards, some of which may be spades – no longer available to you – a total of 19 unseen cards that are not available.
Group 2: The dealer holds the remainder of the deck (the stub) – 27 cards – from which the river card will be dealt. How many spades (outs) can you expect in this group – the only ones still available? These are the “real” outs, from which you hope to catch another spade on the river.
There are nine spades among the two groups of unseen cards. Assuming a normal distribution, these remaining spades are dispersed among these two groups of unseen cards, of which there are 46 total (19 + 27), in the following manner: 100 x 19/46 = 41% (approx.) and 100 x 27/46 = 59% (approx.).
So, Group 2 – the unseen cards still available – has 59% of the nine remaining spades; that’s five spades available to you. Instead of the originally presumed (virtual) nine outs, the more realistic number is just five outs. Those are the only remaining spades (outs) actually available to you – the real outs.
At first glance, using the real outs – approximately 5 rather than 9 spades – the probability of making your flush would seem to be much lower. But, with the help of Tom Green (retired college math professor and author) here is the probability in each case, from which the card odds can be determined (as explained above).
Of landing another spade on the river – (1) For the 9 virtual outs: (100/46) x 9 = approx. 20%, where 46 is the number of all unseen cards; (2) For the 5 “Real” outs: (100/27) x 5 = approx. 20%, where 27 is the number of available unseen cards. Identical.
Bottom line: You can continue to use the “old” method with the “Virtual” outs; it’s much easier. And, you can comfortably use one of the many charts published in various sources to convert the number of outs to the card odds.
Acknowledgement: In preparing this column, in addition to Geen, I received much valuable support from several outstanding poker experts – Dr. Alan Schoonmaker, Linda Johnson, Jan Fisher, Jonathan Little, Ron Ross, and Robbie Strazynski.