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Kahneman and Tversky observed that bets on long shots at horse races increase towards the end of the day, evidently because people are looking for a cheap opportunity to win back what they lost earlier in the day. They concluded that a “person who has not made peace with his losses is likely to accept gambles that would be unacceptable to him otherwise.”
Two students and I looked at this question by analyzing hundreds of thousands of Texas Hold ‘Em poker games at an online poker site with blinds (initial bets) of $25/$50, which are considered high-stakes tables and attract experienced poker players. We considered a hand where a player won or lost $1,000 to be a significant win or loss. After a big win or loss, we monitored the player’s behavior during the next 12 hands—two cycles around a six-player table. We followed two cycles because experienced players often make no voluntary bets, and twelve hands are still reasonably close to the time of the big win or loss. We restricted our attention to individuals who played at least 50 hands in the 12-hand window following big wins and at least 50 hands in the 12-hand window following big losses.
Our final data set included 346 players who met these criteria. The median number of hands played was 1,738, with half of the players playing between 717 and 4,549 hands. Half of the players won or lost more than $200,000, ten percent won or lost more than $1 million.
At the beginning of each hand, the player sitting to the left of the dealer puts a small blind of $25 into the pot, and the player two seats to the left of the dealer puts in a big blind of $50. Each player is then dealt two “hole cards” that only they see. Players who have not put money in the pot decide whether to fold, “call” the $50 big blind, or raise the bet above $50, forcing the other players to match the highest bet on the table. Bets go clockwise around the table until the highest bet is called by all players who wish to remain in the hand, or all but one person folds.
If more than one player is still in, three community cards (“the flop”) are dealt, which are visible to everyone and can be used by each player to build the best possible hand. After another round of betting, a fourth community card (“the turn”) is dealt, and there is another round of betting. Finally, the fifth community card (“the river”) is dealt, and there is a final round of betting. The player with the best five-card hand from the two hole cards and the five community cards wins the pot.
The generally accepted measure of looseness is the percentage of hands in which a player voluntarily puts money in the pot. This can include a call or a raise, but does not include blind bets since these are involuntary. After a hand is dealt, everyone other than the big blind must either bet or fold before they see the three-card flop. Thus, looseness measures how often a person puts money into the pot in order to see the flop cards.
Tight players fold when their two hole cards are not strong; loose players stay in, hoping that a lucky flop will strengthen their hand. At 6-person tables, people are typically considered to be very tight players if their looseness is below 20 percent and to be extremely loose players if their looseness is above 50 percent. For our data set, the average looseness value was 26 percent at six-player tables.
In theory, experienced poker players have a style that they feel works for them based on hundreds of thousands of hands they have played over years or decades. Once they have settled on their optimal strategy, they should stick to it, no matter what the outcome of the last few hands. If they suffer a big loss, they should recognize that it was bad luck and stick to their strategy, counting on their ability to eventually win back the money they lost.
We found that, in practice, players typically changed their style of play after winning or losing a big pot—most notably, playing less cautiously after a big loss, evidently hoping for lucky cards that will erase their loss quickly. For example, at six-player tables, 135 people played looser after a big loss than after a big win, while the reverse was true for only 68 players.
Despite having played many, many poker hands, these experienced players felt compelled to play more speculatively hoping to win back what they lost quickly. Was this change in strategy profitable? If experienced players are using profitable strategies to begin with, changing strategies is a mistake. That’s exactly what we found. Those players who played looser after a big loss than they normally played, did worse than they normally did.
If investors are like poker players, their behavior might well be affected by large gains and losses, for example, making otherwise imprudent long-shot investments with the hope of offsetting prior losses cheaply. It has, in fact, been found that Treasury bond traders and professional stock day traders who lose money in the morning trade more aggressively in the afternoon. There have also been several catastrophic wagers placed by “rogue” traders who were trying to cover earlier losses.
A 2009 Wall Street Journal article reported that many investors were responding to recent stock market losses by making increasingly risky investments:
the financial equivalent of a ‘Hail Mary pass’—the desperate attempt, far from the goal line and late in a losing game, to fling the football as hard and as high as you can, hoping it will somehow come down for a score and wipe out your deficit.
For poker players, investors, and others who have sound strategies, patience is better than a Hail Mary.
