house money effect
n. The premise that people are more willing to take risks with money they obtained easily or unexpectedly.
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According to Kahneman's "prospect theory," most of us find losses roughly twice as painful as we find gains pleasurable. This radical precept subverts much of "utility theory," the longstanding economic doctrine that says we weigh gain and loss rationally. When combined with the reality that some market winners display the same recklessness as some victorious gamblers — a phenomenon that Richard Thaler, an economist at the University of Chicago, calls "the house-money effect" — the market is often revealed to be downright loony.
—Dirk Olin, “Prospect Theory,” The New York Times, June 08, 2003
The Flemings lot are now talking about "regret aversion," investors' inclination to sell their winners and stick by their losers, and the "house money effect," where people are more likely to bet recklessly in casinos with money they have recently won.
—“The Psycho Path,” Investment Week, March 17, 2003
1996 (earliest)
[E]conomic theory rested for a long time on the concept of humans as rational individuals, acting in the light of perfect information. In fact, emotions play havoc with the decision-making process.

One experiment gave 10 students $ 30 each and offered them the chance of doing nothing or flipping a coin to win or lose $ 9. Seven opted to take the gamble. Another set of students was given no money and offered the chance of $ 30 for certain, or a coin flip which gave $ 39 on heads and $ 21 on tails. Only 43 per cent went for the flip, even though the range and prospect of the possible outcomes was the same.

This is described as the "house money" effect: people who have money in their pockets will choose the gamble; those who start with empty pockets will reject it.
—“A winning way with odds and evens,” Financial Times, November 21, 1996
This phrase was first used by the economists Richard Thaler and Eric Johnson in their paper, "Gambling With the House Money and Trying to Break Even: The Effect of Prior Outcomes on Risky Choice," which appeared in a 1990 edition of the journal Management Science.