Monte and Blackjack

by Daniel on October 14, 2003

Here’s my contribution to the “M-Type versus C-Type” debate. Basically, just as it’s a useful analytical distinction to make that all UK Prime Ministers are either bookies or vicars, it’s always worth remembering that all economic policy debates of interest can be usefully analogised either to blackjack or to three-card monte.

I’m assuming everyone knows a little bit about blackjack, but monte is known by other names in other jurisdictions, so I provided the link above so that everyone knows what I’m on about. Note that the maintainers of that site are inclined to be suspicious of monte as a game, but you shouldn’t damn a game just because most of the players are cheats; in principle, 3CM is a perfectly legitimate game of skill. What I’m concerned with is the optimal strategy for playing 3CM and how it differs from the optimal strategy for playing blackjack.

First, consider the “house edge” for the two games under the simplest possible strategy; random play. For monte, this means just picking a card at random, which pretty intuitively means that you win double your money one time in three for an expected return of minus 33%. For blackjack, you flip a coin to decide whether to hit or stand – I couldn’t be bothered to work out the precise odds on this one, but the inexcusably crude Monte Carlo simulation macro I just wrote in Excel suggests that if you were playing blackjack with an infinite number of perfectly randomised decks and no aces, the house edge would be about the same.

Now, how do you do better than the return to a perfectly random strategy? In blackjack, there are various levels of sophistication you go through. You can play basic strategy under which you condition your hit/stand decision on the probability of a randomised deck getting you nearer to (but not over) 21. You can count cards, and take advantage of the fact that the deck is not a random number generator; if a lot of high cards have already been dealt, the expected value of a random deal is lower (thus making the deck slightly more favourable to you; if you increase and decrease your bet size in proportion to your advantage, your expected return is much better). Or, at the limit, you can do what Scott Hagwood does, and just memorise the entire deck – at this point, blackjack is no longer a game of chance for you, and you should be able win every time the deck has a winning hand for you, and place a zero bet when it doesn’t, making your potential return infinite and risk free (unsurprisingly, Mr Hagwood isn’t allowed in any casinos).

How do you improve your odds at three-card monte? Well, you watch the cards carefully, look for the slieght of hand and misdirection and aim to develop an eye that is quicker than the dealer’s hand. It sounds pretty difficult, but I daresay that there are people out there that can do it; my guess is that a body language expert like Geoffrey Beattie would be able to train himself to do well at 3CM, because I’d guess that a lot of “tossers” (no stop sniggering that’s what they’re called) leak their intentions pretty plainly as to where they’re going to throw the red lady. Beattie also has some pretty tasty mates, which might come in handy if he were to take this up as a career.

So anyway, what’s the point of this? Well basically, look at it this way. In blackjack, there is a perfect strategy, but there are also lots of less-than-perfect strategies which still deliver a much better expected return than random play (decent card-counting strategies often have positive expected return). In 3CM, there’s the strategy which if perfectly executed delivers perfection, and basically nothing else.

It gets worse. If you adopt one of the blackjack strategies and make a few mistakes, then it doesn’t usually matter a huge amount. If you get the trailing count wrong by a couple, or if your memorisation of the decks is less than perfect, you most likely still have a decent grasp of the overall position of the deck; whether things are good or bad for you as a player. In three-card monte, if you try to track the lady and make a single mistake, then you’re going to do worse than you would by simply playing randomly.

And this is the analogy to economic arguments. Some kinds of economic argument are relatively robust; they deal with broad truths to which even a basic-level understanding of the theory is a reasonable approximation. Other results in economics are incredibly fragile, and the “Economics 101” style of reasoning can lead you inexorably to exactly the wrong conclusion. That’s why it pays to be hugely suspicious of economists who have simple and appealing answers to complicated questions, whether they want to spend a load of government money on something or whether they want to “get the government out of it”. This line of argument is plainest in Ronald Coase, but it’s there in Hayek.

Furthermore, when some people argue economics, they argue it like a three-card monte tosser. Steel tariffs a bad idea your honour? Well maybe in a perfect world you’re right but you have to consider intra-industry trade, the global pattern of industrialisation, adjustment costs and the Cancun agenda. Pensions privatisation transfers risk to the workers? But what about the concentration of defined benefit plans on a single employer, trends in labour mobility, efficient capital markets and the Demographic Timebomb? Step right up, find the lady, look for the faces watch out for the aces, you look lucky this evening sir! When you’re dealing with people who want to use genuine complexities in the economic theory as a smokescreen, then you would be faced with the alternative of either oversimplifying yourself, or weakening yourself rhetorically by conceding ground on tangential issues. In this case, the only sensible choice is not to play.

That’s why it often makes sense to make those “M-Type” arguments. If a friend asks you for help playing blackjack, you can teach him about card-counting. But if you’re trying to give advice on a game of three-card monte, all you can legitimately do is point out that it is, in fact, a game of three-card monte. And if someone points out that this isn’t getting us any closer to a reasoned analysis of where the red queen actually is on the table, then so be it.



Harry Tuttle 10.14.03 at 9:23 pm

I’ll stick with the E-Type thanks.


Shane 10.14.03 at 10:28 pm

An analogy worthy of theft. So much better than the one from my Micro teacher. In his, there are two types of model airplanes. One realistic, which doesn’t fly. The other unrealistic, which does. Econ 101 is like the latter. …


dwight meredith 10.15.03 at 2:25 am

It is hard to see how there can be a perfect strategy at Blackjack. If we assume that a player memorized the exact order of an entire deck, the dealer would simply shuffle.


pj 10.15.03 at 3:12 am

I spent all that time reading just to find that I was being shown a shell game. Lots of words, little substance. I suppose my best response is now to attack your motives?


dsquared 10.15.03 at 6:55 am

If we assume that a player memorized the exact order of an entire deck, the dealer would simply shuffle.

Not if you didn’t tell them you were doing it …


Paul Orwin 10.15.03 at 3:49 pm

Just a quick note on the blackjack case. It turns out that if you are counting cards, and you make a small mistake, you can utterly ruin your advantage. Even worse, if you bet thinking you have an advantage, but you don’t, you will get creamed (note; learned from experience, the hard way!). So while there are varying strategies that will give you different odds of winning, they are not particularly robust. The so-called “basic strategy” is robust, in the sense that small variations in it will change your expected outcome slightly (there is a math word for this, but I can’t remember it; stable to perturbation or something like that). The strategies that attempt to gain significant advantage over the house are much less stable, however.


john c. halasz 10.15.03 at 10:37 pm

So what I want to know is: which one is Tony Blair- a vicar or a bookie?


marc 10.16.03 at 7:25 am

An interesting blogpost. What struck me is how conservative, in the litteral meaning of that word, your arguement is. Because there are so many interdependencies between different parts of our society, we should be wary of attractive sounding bold ideas; they will likely have more unintended consequences than you have bargined for. Let’s err on the side of the status quo.

When applied to the issue of privitising pensions, the conservatism is on behalf of an established social welfare policy, and thus is leftist in today’s political alliance.

I am not saying that this makes you wrong, it is just intereting to see conservative arguements for leftist causes. Hmmm.


dsquared 10.16.03 at 11:02 am

I think I could pretty fairly describe myself as an egalitarian conservative if the term didn’t carry such a strong flavour of oxymoron.

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