(Bob Wilson founded Wilson Software in 1989. He joined Mensa in 1966 and has been playing poker and working with computers for more than 30 years. Mike Gilbert has many years of professional poker experience and works as a prop player in Los Angeles.)

Several poker authors have written negatively about the usefulness of computer simulations. By the nature of their writing, as well as by their own admission, these authors have not even seen the modern “smart” simulation programs; the Windows Turbo Texas Hold'em programs from Wilson Software. Their experience is with “dumb” simulation programs that have no resemblance to real games and, as we will show, provide misleading results.

One of the more common tests performed by a “dumb” computer model of hold’em is a 'showdown contest' between various hold’em hands These contests produce win rates. However, when there is no betting, these win rates do not accurately measure the value of the hands in the contest.

For example, when A♠ K♠ plays heads-up against 2♥ 2♦, and neither hand bets or folds, AK suited wins just over 50% of the pots. This 50%-50% computation is commonly cited as a measure of the strength of these hands when played heads-up. However, when there is betting, AK suited and a pair of 2s are not evenly matched in a heads-up contest. One of these hands wins much more money than the other. To demonstrate these points, we'll start by running a showdown test (no folding, no betting) of 100,000 deals.

Test 1 – A “dumb” simulation/showdown matching A♠ K♠ heads-up against 2♥ 2♦

Player	Hand	Total Pots	Total $ won
1	A♠ K♠	50,247	$0
2	2♥ 2♦	49,753	$0

The showdown win rates are comparable, 50.247 % versus 49.753%.

When we retest with profiles that use strategies, the difference is striking. These strategies bet according to the values of each hand, without ever knowing the actual hand held by an opponent. Profiles evaluate their own hands, the betting and the board; consequently they often fold before there is a showdown. To see this, we'll run another test with betting, raising and folding; as in a real game.

Test 2 – A “smart” simulation matching A♠ K♠ heads-up against 2♥ 2♦

Player	Hand	Total Pots	Total $ won
1	A♠ K♠	58,127	$239,610
2	2♥ 2♦	41,873	-$239,610

Seat 9 with AK suited, wins over 58% of the pots and averages over $2.39 per deal against pocket 2s.

Even played showdown, AK suited is a big favorite over unpaired hands, and at worst a slight underdog against most pocket pairs. Therefore, when betting, Player 1 plays AK aggressively, since he doesn't know which type of hand he faces. Until the action indicates that AK is not the best hand after the flop, Player 1 bets as though it is.

When betting with pocket 2s, again Player 2 does not know what hand he's up against. Played showdown, pocket 2s is a marginal favorite against most unpaired hands, and a big 'dog' to other pocket pairs, so Player 2 plays pocket deuces more conservatively than AK. AK is too busy betting to be bluffed very often, while pocket 2s is vulnerable to bluffs, value bets, and the betting of draws.

With pocket 2s, no betting strategy maintains showdown equity against AK suited, and at the same time, avoids big losses to other pocket pairs.

What happens when these two hands each play heads-up against an opponent whose hand is random? We can find out with 2 more tests.

Test 3 - A “smart” simulation matching 2♥ 2♦ against random hands

Player	Hand	Total Pots	Total $ won
1	? ?	34,683	- $31,360
2	2♥ 2♦	65,317	$31,360

A pair of 2s wins about $.31 per deal against random hands.


Test 4 - A “smart” simulation matching A♠ K♠ against random hands

Player	Hand	Total Pots	Total $ won
1	? ?	21,655.5	- $1,297,605
2	A♠ K♠	78,344.5	$1,297,605

AK suited wins almost 41 times as much money as 22 and wins over 78% of the pots.

In summary:

The tests in this article were run using Turbo Texas Hold'em for Windows.