Skilled hold’em poker players often count numbers – There are nine of spades between two groups of invisible cards. Assuming a normal distribution, these remaining spades are spread out between these two groups of invisible cards, which add up to 46 in total (19 + 27), in the following way: 100 x 19/46 = 41% (average) and 100 x 27/46 = 59% (mean).

So, Group 2 – the unseen cards still available have 59% of the nine spades remaining; that’s five spades available to you. Instead of what is initially considered a nine (out), a more realistic number is just five outs. It’s the only shovel left that’s actually available to you for real.

At first glance, using a real out – around 5 and not 9 spades – the chances of making your flush seem much lower. But, with the help of Tom Green (retired mathematics professor and college author) here are the probabilities in each case, from which the card odds can be determined (as described above).

From another spade landing on the river – (1) For 9 virtual outs: (100/46) x 9 = approx. 20%, where 46 is the sum of all invisible cards; (2) For 5 “Real” losses: (100/27) x 5 = approx. 20%, where 27 is the number of invisible cards available. Identical.

Bottom line: you can continue to use bonus138 the “old” method with “Virtual” out; it’s much easier. And, you can conveniently use one of the many charts published in various sources to convert the difference amount to card odds.

Confession: In preparing this column, apart from Geen, I received a lot of valuable support from some of the leading poker experts – Dr. Alan Schoonmaker, Linda Johnson, Jan Fisher, Jonathan Little, Ron Ross, and Robbie Strazynski