The martingale index: A measure of self-deception in betting and finance

Valentin Dimitrov and Glenn Shafer

Judgment and Decision Making, 2025, vol. 20, -

Abstract: People who repeatedly risk money, whether they be traders for financial institutions, corporate executives, day traders, or sports bettors, sometimes appear to do better than chance only because the risk of large losses is hidden or overlooked. As students of casino gambling know, one way to obscure the risk of large losses is to bet more when you are losing and less when you are winning. In 19th century casinos, betting strategies that did this were called martingales. Following such strategies, whether deliberately or unwittingly, was called martingaling. Traders in financial instruments often martingale; in fact, they are martingaling whenever they respond to a margin call. A businessperson who doubles down on an apparently losing investment is martingaling. Opinionated sports bettors easily fall into martingaling. The martingale index, defined in this paper, measures the portion of the apparent success of a betting, trading, or investment strategy that can be attributed to martingaling. We calculate the martingale index for some popular casino strategies and also for some strategies that model random trading in S&P 500 futures and in stocks. And we discuss how educating the public about the martingale index might help both businesses and individuals avoid the temptations of martingaling.

Date: 2025
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