The house money effect: why a win changes the next bet

The 1990 experiment

Thaler and Johnson asked a simple question that standard economics could not answer: does a prior win or loss change how much risk a person will take next? A rational agent treats money as money; thirty dollars is thirty dollars whether it came from a pay cheque or a coin flip an hour ago. So the next gamble should be judged on its own terms, regardless of what came before.

It is not. In a series of questionnaire and cash experiments with MBA students, the authors gave subjects a prior outcome and then offered a gamble. After being told they had just won $30, a majority accepted a fair coin flip for $9 that fewer than half would accept with no prior outcome. After being told they had just lost $30, most refused the same flip. But offered a gamble whose winning outcome would exactly erase the $30 loss, subjects who had refused ordinary risks took it readily; the chance to close the account outweighed the odds.

The paper gave both patterns names that stuck. Risk seeking after a gain is the house money effect, from the gambler’s phrase for playing with winnings as though they belonged to the casino. Risk seeking for a gamble that would restore the starting point is the break-even effect. Neither fits the standard model, and both fit ordinary experience at a table.

Prior outcomes matter. Winners take more risk, and losers avoid it, unless the risk offers a way back to even.the two findings, compressed

Mental accounting

The mechanism Thaler proposed is mental accounting: people do not hold one pot of money but several, labelled by source and purpose, and they apply different rules to each. Winnings go into an account marked “house money”, and losing house money does not feel like losing. A loss goes into an account that stays open, painfully, until something closes it, which is why a bet that could close it looks attractive out of proportion to its odds.

The accounts are fiction, and the fiction is expensive in a specific way. Money in the “house money” account is bet larger and at worse odds than money in the “my money” account, so an evening that starts well is more likely to end with a bigger loss than an evening that starts badly. The loss account produces the mirror error: the one bet a person should not make after losing, a long shot sized to get everything back, is the one they most want to make. Archie Karas is the effect at the scale of forty million dollars.

• The ledger does not know where the money came from. A unit won a minute ago and a unit deposited a week ago buy exactly the same bet with exactly the same odds.
• The edge does not know either. A game’s return is a property of the game, not of the player’s history. Betting house money at a 3% edge costs 3% of it, in expectation, just as betting rent money would.
• Breaking even is not a special price. A gamble that returns you to zero is priced like any other gamble; the round number is meaningful to the player and to nobody else.

One balance

It is worth checking what the site itself does, because software can encourage the accounts or refuse them. The wallet here keeps a single balance. When a round pays, the payout is credited to the same number that a deposit sits in; there is no field for winnings, no counter for the session, no separate pot that the interface treats differently. The demo engine that runs the signed-out games is built the same way, and the code is short enough to read.

The engine is even less interested in history than the wallet. Each round is a hash of the committed server seed, your client seed and the round number, and the previous result is not an input. A win does not make the next round more generous and a loss does not make it kinder; there is no state on the house side in which “you are up” or “you are down” is recorded for the game to see. Whatever the house money account is, it lives on one side of the screen only.

What to do with it

The practical answer follows from when the effect operates. It acts on the bet after the outcome, so the defence has to be set before the outcome. A stake size or a loss limit chosen while the balance is flat is a decision made by the version of you that has not yet won or lost; the same decision made after a big win is made by someone playing with house money, and after a big loss by someone trying to break even. The limits on the settings page exist to let the first person overrule the other two.

• Decide the stake as a fraction of the balance before the session, and keep the fraction when the balance rises. A stake that grows with a win is the house money effect in numbers.
• Treat break-even as a number like any other. A bet whose only merit is that it would return you to zero is a bet whose merit is zero.
• Use the tools that lock the earlier decision in. The responsible play toolkit lists the limits and pauses this site offers and what each one does.