# Gambler's fallacy

CFAI Vol 2 Page 151 problem 13.

The memo from the technical department says that since an event of this sort has resulted in X in the past, they believe the same would happen again. To me this sounds more like anchoring than gambler’s fallacy. As a poor poker player I can say that decisions in a gambler’s fallacy are not based on knowledge of prior events but rather driven by hope that a favorable card will show up. In achoring, however, a previous event/number drives current decisions. What am I missing here?

Thank you.

In anchoring the individual comes across a price information that she thinks is “right” - i.e. she is told that her house will sell for £500k because three other similar houses on her street have sold for £500k during the course of the previous month.

Yesterday, however, the government authorized the build of an airport at a stone throw from the house in question (something which is bound to significantly depress house prices in that area).

At this point the individual decides to put the house on the mkt @ £495k and can’t get a bid. The landscape has changed, what seemed to be a fair price is no longer, but the individual anchors herself to that level, delays the sale and misses on the opportunities to buy something else.

The tell-tale sign of the gambler’s fallacy is the mentioning of a long-term mean (which you do not have in anchoring) and the false belief on the part of the individual that, once the price pierces through that long term mean, - like it happens in the vignette - it is bound to mean-revert.

So, anchoring = one price that is thought to be “right”, some factor that changes the situation, individual who fails to adjust her valuation because she is anchored to a previous, no longer fair, price.

Gambler’s fallacy = a long term trend, price going above or below it, individual reacting in the expectation that the price is about to revert to mean.

Good luck, Carlo

Carlo

I really appreciate your taking the time to explain. Although I am not totally clear about it, for the purpose of the exam I will stick to

1. Tethering to numbers for anchoring and

2. mean-reversal for gambler’s fallacy.

Cheers.

Carlo, that is an excellent explanation and thank you for taking the time to provide a detailed answer.

As a semi-professional poker player during my college years, I witnessed several other poker playing friends cling to what is formerly referred to in the CFAI text (and many other places) as the gambler’s fallacy. Although the gambler’s fallacy is pervasive in many forms of gambling (and not necessarily just poker), I will apply it to poker since it is the game I am most familiar with.

In experienced internet poker circles, data mining software programs can be used to accumulate numerous data points and establish a sample mean / expected value, or what is effectively known as a long-term win rate. Experienced and advanced players refer to this long-term win rate as their mean, and despite fluctuations and volatility in day-to-day outcomes (i.e., having winning sessions and having losing sessions), there is a deep belief that, in the long run, performance will revert to a long-term mean, or win rate, let’s call it \$X (assumed to be > \$0 for profitable players). So despite having sessions where profit / loss is < \$X, experienced players have a thought process (referred to as the “gambler’s fallacy”) whereby they believe that their long run outcomes will “mean-revert” to X over time, making them winning players.

Hope this helps,

OMGMileyCyrus

The Gamblers Fallacy is clearest at the roulette table. If a red number comes up 10 times in a row, the gamblers fallacy is to think that now it is time for a black number to come up. So more people will bet on a black number. However, the chance that a black number will come up is always 50% (leaving out the 0). It does not matter how many times red showed up before.

The more rational choice would be to bet on a red number if they show up significantly more than 50% of the time, because then chances are that the table is rigged.