# How Poker Imitates Academia: The case of Expected Value

The summer couldn’t come too quickly for me this year. After a very busy spring/summer semester, I couldn’t wait to go on my holidays. I was fortunate enough to spend a week on the Caribbean, and it was  just what this doctor ordered.

During my stay, I noticed that the hotel had a daily poker tournament. I had dabbled with poker before, as my brother was (and now is again) a very keen player. I’ve played in live tournaments, and even finished in the top-10 of a European online tournament a few years ago. I know my way around a pack of cards; needless to say, I signed up quickly. Below is a photo of me (with the cap) on my way to tournament victory at the resort.

## Poker is skill, NOT luck

Upon my return from holiday, I decided to read as much as I can about poker theory, and it’s been a blast. Contrary to what most people believe, poker is a game of skill, not luck. Every year, the same players top the “best player” lists, and sit on final tables of massive tournaments; this would not be possible if poker were primarily a luck game. For a statistic nerd like me, I relish in the fact that it’s all about understanding the numbers. You have to understand probabilities of certain hands occurring, odds of certain cards appearing in the future, and pitting these against how much money you can win on the current hand (so-called “pot-odds”).

The beauty of poker is that if you have a good understanding of these odds and probabilities (and can narrow down the potential cards your opponents have), you can pretty much guarantee that you can play profitably—at least at the lower stakes.  The key is to think long-term, not short-term.  When deciding whether to put all of your chips in to call someone else’s bet, you have to weigh up the utility (or profitability) of that bet over the long-term (i.e., over several occurrences) rather than worry what will happen on this specific hand. Results can vary wildly from hand-to-hand, but probabilities are probabilities, and in the long-term everything will settle down to this probability (over hundreds of hands, for example).

For example, here is a hand I played on the way to winning the above tournament in Mexico. I looked down and had the following two cards:

Now, these are not great starting cards in no-limit Texas hold ’em, but I decided to play the hand anyway. A fellow competitor looked at his cards and all of a sudden looked very excited, before putting some chips in the middle. Based on his excitement, I believed he had AA, KK, QQ, or a high connector like AK, AQ, AJ. The flop and turn appeared with no further betting:

At this stage, there were 100 chips in the pot, and there was only me and one other guy in play. At this point, he put 25 chips into the pot, making it 125 chips. I have to pay 25 chips to continue, but at this stage, I’m pretty sure he has got at least a pair of Kings, and therefore has me beat. Even worse, before the hand, I thought he had KK, which would mean he now has three Kings. The only thing that can save me is to get a card with a heart on the final card, making me an A-high flush, which beats his trip Kings.

But what are the odds of this happening? With only one more card to be drawn, the odds of this happening are 4.11:1 against (or a probability of ~.19). Should I make the call? How can I work out whether this is profitable?

The beauty of poker is that you make your decision NOT on what you THINK will happen on THIS hand; this is what gamblers do. They decide whether they feel “like a punt” and put their chips in the middle if they feel it’s their lucky day. Poker players don’t do this (at least, profitable ones don’t). They use something called expected value (EV), which is basically a statistic for how much one can expect to profit if one were to repeat the trial many times. That is, given how much I stand to win (or lose) and the probability of me winning (or losing), how much would I expect to profit over the long term if I were to repeat this scenario many times. It even has a nice formula:

EV = (pW * \$W) – (pL *\$L)

where pX is the probability of winning or losing (L), and \$X is how much I stand to win or lose (L). So, my EV for the above betting proposition is

EV = (.19 * 125) – (.81 * 25) = +3.50

So, this IS a profitable call despite my somewhat-long odds of actually getting a heart on the final card. Therefore, I should call. Over the long-term, repeating this call in identical situations will always be profitable for me. In this case, however, I missed a heart on the final card, he flipped over KK (3 Kings total), and won the pot.

## What the hell does this have to with academia?

What matters in the above example is thinking of the utility of actions over the long-term, rather than getting distracted by short-term results. I lost this hand (and a reasonable proportion of my chip stack); does this mean I shouldn’t have made the call? NO! Over the long-term, this is always the correct play; the short-term result (losing) will always be washed out in the long-term.

You can think of the hand-to-hand results as noise, and the EV as the signal. Calling is always a good idea in this situation, but not every hand will win every time. Profitable poker players know this, and don’t get (too) upset at losing these individual hands, because in the long-term, they know it was a correct play that will profit in the long-term.

As I was reading about EV and the idea of “taking the long-view” that this is much like paper rejections in academia. The “play” in this case is all the hard work and dedication that goes into a piece of research, and the “result” is a win (accept!) or a loss (reject!). Sometimes, p(win) is actually very low (as was the case in my example); many journals have an acceptance rate of ~20%, which actually matches the probability of my hand improving to the winning one above (this was purely coincidental). But, the potential reward (\$W) is actually very high (you know how good it feels to get a paper accepted, let alone the career benefits they bring!), so the play is always correct. Work hard, keep submitting, and in the long-term, your publishing EV will be positive, despite short-term set-backs. You can expect these set-backs often (almost 80% of the time), but like the poker player who doesn’t grumble about short-term losses (like mine above), keep putting your chips in.

To summarise:

1. Think long-term, not short-term: Don’t be too despondent about individual rejections.
2. Don’t be put off by low-probability of success if potential reward is high
3. Keep making plays (keep working hard!).

Now, go back to your lab, and shuffle up and deal.