Loss Aversion in Poker

“According to my calculations, winning a razz hand at showdown feels about 1/5 as good as losing one at showdown feels bad.”

I sent out this message -- with tongue only partially in cheek -- sometime Friday afternoon on Twitter towards the end of a moderately frustrating online session of razz. Nothing especially profound there, I don’t think, although I was glad to see some respond agreeably and/or sympathetically to my declaration. As someone who mostly plays pot-limit Omaha, fixed limit hold’em, mixed games, or NLHE tourneys, I was recognizing (i.e., whimpering about) what seemed to me to be a kind of imbalance in the relative “emotional EV” of the games. At least in my experience, anyway.

I’ll play razz as part of H.O.R.S.E. or rotation of mixed games (8-game on Stars, 10-game on Full Tilt), though only now and then will sit down at a razz-only table. One reason why I did so on Friday was in preparation for playing in the PokerGrump’s inaugural home game event later that night, which in recognition of April Fool’s Day he’d perversely made a razz tournament.

Turned out to be a very enjoyable tourney to play, made especially so because of the frequent chatbox witticisms being contributed by the participants. One of my favorite comments was when someone early on said he kept expecting the game to change (as in H.O.R.S.E.), and we all continued to joke about the collective misery being caused by being dealt yet another razz hand. I managed to catch hands frequently enough for a runner-up finish in the sucker, a nice turnaround from the earlier cash game woes.

Still, I found myself thinking further over the weekend about my little pronouncement about the “emotional EV” of razz. What exactly makes razz such a downer?

One who responded to my tweet on Friday was John “JimmyLegs” Wray, the CardRunners instructor and one of the minds behind “The Micros.” He first pointed me to a Wikipedia page on “loss aversion” which explains how studies have shown that many experience the pain of loss more than twice as powerfully (psychologically speaking) than they do the pleasure or satisfaction of winning. In other words, my reference to feeling more “bad” about losing a razz hand than “good” about winning one was unwittingly evoking an actual phenomenon.

Wray additionally pointed me to a whole series of vids he’d made for CR -- titled “Brain Fail” -- the first part of which was an application of this idea of loss aversion to poker. Here’s that video, available for viewing over at Poker News Daily.

I liked learning more about this phenomenon, but I still found myself wondering about razz in particular and why it seemed (to me, anyway) to be a game in which it was much more frustrating to lose than enjoyable to win when compared to games like PLO or LHE. What factors are relevant here that might explain why the pain of loss in razz relative to the satisfaction of winning could be proportionately greater than the ratios I experience in other games?

One way to start out comparing the “emotional EV” of different games would be to identify relevant factors in each of the games that might significantly affect our mood when playing them. Off the top of my head, I thought of four:

personal experience/knowledge of game

amount of win/loss per hand and/or session(s) (i.e., the “swinginess”)

expectation of winning/losing during course of hand

luck vs. skill component in game

The first two items are obviously going to be particularly subjective in nature. Each player brings a different skill set to a given game. Each player also is going to be affected differently by the relative “swinginess” of a game. I still think it might be possible, though, to consider those two factors objectively when assessing each particular game -- e.g., the swings are going to be greater in PLO than in razz, no matter how a player individually responds to that fact.

Meanwhile, the latter two factors can certainly be discussed objectively, I think. Even mathematically, if you have the brain for that sort of thing. For instance, under the heading of “expectation of winning/losing,” an example to explore might be “starting good” in razz versus “starting good” in other games.

Say by fourth street in razz you hold 2-4-A-6 and you’re up against an opponent with x-x-8-9. There are three betting rounds left, and your expectation to win is quite high -- not to mention obvious to all. Then you draw nothing but face cards and pairs to the end and somehow lose to a crummy 9-8.

Compare that to having a strong starting hand in pot-limit Omaha, say A-A-J-10 double-suited. You raise from the button and get a caller, and again three betting rounds remain. But here you’re expectation of winning isn’t nearly as great (or shouldn’t be, anyway).

I deliberately added the qualification “at showdown” to my statement about winning or losing a razz hand, since by the time you fight your way to seventh street you had to have had some expectation -- perhaps quite high -- along the way of winning. (Indeed, you almost never get to the end of a razz hand without having bet most or every street to get there!) My sense is that we find ourselves at showdown in PLO or hold’em a lot more often without necessarily having had such high expectations.

The fourth factor -- measuring the relative importance of luck and skill in each game and comparing them -- also seems like it could be approached mathematically, although it would be a challenge to do so. (I’m remembering David Sklansky once making a list of ten poker games and ranking them according to the relative luck involved in each, although at the moment I cannot put my finger on where that list appears.) It does seem as though a game that involves more luck would be one in which winning would probably be less satisfying (to most) while losing would perhaps be more frustrating.

Anyhow, call these tentative thoughts to be refined and collected as a proposal toward a larger study regarding differences between poker games and how loss aversion might work in each. My apologies to those who made it to the end of the post with an expectation of finding something more conclusive on this subject.

Hey, you can't win ’em all.