What’s Money Worth? Part II

Last column was a discussion about money and what it’s worth, a topic sufficiently complex to warrant another look. The key idea here is that winning and losing are asymmetrical. Losing money produces psychological pain that is greater than winning a comparable amount produces psychological happiness.

This asymmetry gives us a foundation to get a deeper understanding of some aspects of our game that often have experts scratching their heads, specifically bad beat jackpots, the popularity of tournaments, bankroll variance and nosebleed level games.

Bad Beat Jackpots: From any rational point of view, bad beat jackpots are stupid. They drain money from the game and decrease everyone’s long-term expectation. In the typical BBJ a dollar is taken from every pot over some amount.

Estimates vary but a good player probably wins about 2-3 raked pots an hour. Giving up $2-3/hr is significant and full-timers playing 2000 hours a year are having $4000 to $6000 a year filched from them.

So: Why are BBJs wildly popular? Why do players flock to casinos when the word is out that the BBJ is “over a hundred grand?” And, importantly, why is this enthusiasm not found at higher stakes?

The answers to the first two questions are found in the asymmetry of the win/loss ratios. The loss is small, in fact many low-limit players don’t realize what’s happening. A surprising number of players don’t know what the rake is in their rooms so the additional take-out doesn’t cause additional pain.

But, the possibility of a big win exists. The result is a situation where the negative element is diminished but the positive one increased dramatically, for as we noted last week, the asymmetry effect holds even when losses and wins are merely imagined.

Why do higher-stakes players hate them? Because they recognize the damage to their EV; they experience the down-side of the asymmetry more intensely and the up-side is lessened because their ‘imagined’ wins are accompanied by a footnote that says, “this is so unlikely that it shouldn’t be part of your thinking.”

This analysis also applies to other forms of gambling like lotteries and progressive-jackpot slot machines.

Tournaments: Ever wonder why tournament poker is so popular? A couple of weeks back I asked several regulars at a $90+10 NLH event why they like them. The answers were interesting, if obvious. “Well, they’re just fun.” or “I like the competition.” or “It’s just become my way of spending Wednesday evenings.” or “Hey, man, I’ve been killing this tournament for years now.” All interesting and obvious.

Then I got one that was more interesting if less obvious: “Look, you know there’s a pretty nice payout for top three spots for damn small investment.”

Bingo. The asymmetry principle in play.

The allure of tournament poker is that your loss is limited and small compared with the potential win. The negative affect is under control whereas the positive one has an imagined up-side that overcomes any qualms about losing the buy-in.

This works in face of a significant negative expectation. The $10 house vig on top of the $90 that goes into the prize pool makes it a -11% game. Factor in dealers’ tips and the EV is even lower.

The principle also gives us insight into rebuy tournaments.The vig only applies to buy-in; rebuys are zero sum gambles. However, potential loss increases adding negative affect. Hence, they are less attractive to players who are risk averse. Pros, for whom the asymmetry principle doesn’t hold quite the way it does for most of us, love these tournaments, so much so that there won’t be any in this year’s WSOP.

Variance: Virtually every good poker strategy book has a section on variance and all counsel adopting measures to reduce it. From a straightforward economic perspective it’s not clear why this is good advice. If your bottom line isn’t changed by variance, why should it matter whether your swings are wild and crazy or small and manageable? Dollars/hr doesn’t change and it’s take home pay that counts, right?

But it is good advice and the reason is the asymmetry principle. Big losses hurt more than big wins feel good; as your variance goes up so will the number of times you have very bad days in emotional terms, in subjective experience. You’re just as rich or poor as you would be with a smaller variance but you will be less happy overall.

Appreciate that this principle won’t hold for those who have little aversion to risk, which is why players like Patrick Antonius or David Benyamin can win or lose hundreds of thousands in a session and not have it have (too) much of an impact on their psychological well-being.

The Really Big Game: Some years ago Andy Beal, a Texas billionaire challenged the top pros to play heads-up for astronomical stakes. The story is fascinating (see Michael Craig’s superb book, The Professor, the Banker and the Suicide King).

The professionals who agreed to the arrangement included, among others, the Brunsons, Phil Ivey, Jennifer Harman, Howard Lederer and Chau Giang, folks whose approach to the game is such that it usually lies outside of the impact of the asymmetry principle.

But before they agreed to play, the pros first formed a consortium with each contributing to a common bankroll to be used in the game. Why, you may ask, did they do this? Why didn’t each of them just sit down and play with their own money like they normally do?

Because the stakes that Beal set were so high that these seasoned pros, who usually never experience risk aversion, were pushed to the point where the asymmetry effect kicked in.

Beal understood this. His goal was to take them out of their comfort zone, to the point where they would experience the same emotional swings as the rest of us. The consortium (partially) neutralized this move by lowering variance and reducing individual risk.

Eventually they won a huge hunk of change from Beal, but from a psychological point of view that’s almost beside the point.