How Bad Players Like Sucker Hands Profit/Loss from 122,031,244 Hands

PokerRoom Hands"There's a sucker born every minute." - P. T. Barnum

During the poker boom, released the profit/loss statistics from 122,031,244 of Limit Texas Hold'em hands played at their online poker room. The table at right lists the actual results for all card combinations for those 122 million hands. PokerRoom didn't specify any disclaimers. The numbers represent pocket cards dealt in real money limit ring games regardless of the number of players, and including when players are in the big blind unraised.

The results are expressed in "average profit in big bets". So assuming a 5/10 limit game, a pocket pair of Aces won an average of 2.32 big bets, or $23.20... while the worst hand averaged a loss of -.16 big bets, or $1.60.

Both PokerRoom and others who looked at this data absurdly referred to these results as the expected value (EV) for each hand. Nonsense. These numbers merely express how the universe of chucklehead poker players as a group performed while holding these cards, not what their expected value is in general or under any specific circumstances.

Instead of expected value, the better way to look at these results is in terms of "sucker value". What this table amply demonstrates is that online poker players played certain kinds of "pretty" hands much more poorly than they should have. Some specific observations:

-- Winning hands range up to +2.32, while the losing hands only range down to -0.16 BBs. There are 20 different hands that averaged +0.17 or more.

-- There are 40 hands with a positive result, plus four more that breakeven. There are 125 losing hands. So, about three out of every four hands was a loser, while even an average chucklehead player was able to breakeven or turn a profit with about one-quarter of the hands dealt. Players playing almost every hand in these games were burning money, but so were players who only played 10% of their hands. Too loose is bad but so is too tight.

-- There are eleven hands in the +0.02 to -0.02 range. Many players obsess over things with a tiny impact, like a small difference in rake. The difference in skillful play of these seven tiny winner/losers and the four breakeven ones is more likely to have a bigger impact on a player's bottom line than the things that mediocre/breakeven players who are trying to win usually obsess over. Turning these eleven hands into meaningful winners -- by playing them in the right circumstances with the right opponents while folding against tougher players and in bad position -- should be a greater focus of a mediocre player's mental energy.

-- Compare K8s and K7s to K6s. The first two are the only oddball breakeven hands. Every other winning hand is contains either Broadway cards, pairs, or has a suited Ace or are two suited cards in the J-T-9-8 range. But even though K8s and K7s are breakeven hands, K6s loses a significant -0.04. That is quite a drop-off for hands that don't seem so different... K8s to K7s is only a drop-off of .01, but the drop-off from K7s to K6s is four times larger. The drop-off from K6s to K5s and K4s is again only .01. In contrast, the drop-off from K9s to K8s is a huge .08.

-- A9s is a very profitable +0.18 while A9o is an unprofitable -0.03. That is a large difference reflecting what should be a universal poker truth: mediocre chuckleheads do much better when playing hands that can make the nuts in multi-way pots than they do with hands that commonly only make medium-strength hands like one or two pair.

-- Similarly K8o and K7o are major losing hands at -0.11, while suited they are breakeven. Suitedness is a big deal for mediocre cards, and the nuts aspect of suitedness is very helpful to mediocre players. This is also reflected in the superiority of J8s and 87s (smallish losers) to hands like J5s or 84s (much bigger losers).

-- Offsuit baby cards are the graveyard of average Limit Hold'em players -- especially offsuit baby cards that give the illusion of being stronger than they are. Notice that while 85o loses -0.11, 87o loses -0.12. There is no way 85o is a "better" hand than 87o, especially in the hands of a top player, but the data here demonstrates that average players play 87o worse than they play 85o.

Likewise, look at the five worst hands... four are suited cards, and one is A2o. Nine of the next ten worst hands are also suited, plus the "connected" hand of 32o. Similarly, K2o and K3o perform worse than 43o. The kryptonite for average players are these hands that look better than they are, that look somehow "prettier" or more inviting than they are. An average player should be folding A2o and 32o just as fast as they do 72o, but instead they play 72o more successfully than they do A2o and 32s because they don't fold the latter hands like they do 72o.

Texas Hold'em was designed to be a simple game that any gamble-y newbie could pick up in minutes. And, when played in a low limit structure, there is a basic winning approach to the game that can easily be explained to a newbie... play any two cards ten or bigger and raise if they are paired or suited, also play pairs 55 and bigger, as well as Ace-suited hands. There is a lot more to advanced play than that, but those three simple rules manage to include only two losing hands, QTo and JTo, while missing out only on some suited hands that include a 9 or 8.

Advanced Limit Texas Hold'em play includes a lot of other considerations like adjusting hand value for position or for implied action in a lively game if you are getting in cheaply, and many other tactics to pick up small bits and pieces of value all over the place, but the statistics from PokerRoom show that during the poker boom, at least at this one cardroom, poor players self-destructed by overvaluing negative value hands that looked "prettier" than they are.

And I'd be willing to bet that around the world today, in every game type including No Limit Hold'em and Pot Limit Omaha, a similar phenomenon is in play. 1) The group of losing hands is large, even as the range of the negative value of losing hands is smaller than that of winning hands, but 2) the group of "pretty but lousy" hands like those at the end of this list transfer far more value from below average players to above average players than they should.

See also The Secret of Omaha High-Low and more on Starting Hands, Charts, etc.