1. Conceptual and probabilistic foundations: “why gamblers lose on average”

What Research Says about Earning in Gambling

Below is a detailed, evidence-based overview of what theory and empirical research say about whether one can reliably earn money by gambling. It includes names of key scientists and studies. The short answer: it is extremely unlikely for ordinary gamblers to make money in the long run — though under very specific conditions some might temporarily succeed.

1. Theoretical Foundations: Why Gambling is Usually a Loss in Expectation

1.1 Expected Value and the House Edge

In most gambling games, each bet has a negative expected value for the gambler after accounting for the “house edge” (or vig). That is, when you multiply each possible outcome’s probability by its payoff (net of cost), you usually get a negative number. Over many repetitions, that negative expectation tends to dominate.

Casinos, lotteries, sportsbooks, and similar operators design their payouts and odds such that over large numbers of bets, the house wins. Even if the margin is small per bet (e.g. 1–5 %), over many plays the losses accumulate.

1.2 Martingales and the Optional Stopping Theorem

From probability theory, the optional stopping theorem (in martingale theory) implies that for “fair” or unfavorable games, you cannot reliably beat the game by choosing when to stop — unless you violate certain conditions (e.g. have infinite capital, no time limits).

In gambling settings, this is often used to show that “betting systems” like doubling-after-loss (the classic Martingale) cannot overcome the negative long-term expectation.

1.3 Kelly Criterion, Growth Optimal Betting, and Risk of Ruin

The Kelly criterion is a formula used when there is a known positive edge to optimize the growth rate of capital. However, in most gambling opportunities, **gamblers do not have a positive edge**.

Moreover, even if one applies a Kelly or fractional-Kelly strategy, misestimation of probabilities, volatility, and drawdowns can lead to ruin. Thus it is not a magic solution for gambling profit.

In short: unless you have a real and reliable advantage (better information, skill, or mispriced odds), gambling is constructed to be losing in expectation.

2. Empirical Evidence: How Do Real Gamblers Fare?

2.1 Large-Scale Studies: Most Gamblers Lose

One of the most cited empirical findings comes from a study by Kenneth C. Wilbur and coauthors, analyzing over 700,000 online gamblers. Their results showed that about **96 % of gamblers lost money**, while only around **4 % made any profit** from online betting over the study period.

This finding has been widely reported as showing that the vast majority of gamblers do not come out ahead.

2.2 Cognitive Biases, Probability Misjudgments, and Overconfidence

Research by Dickinson et al. (2023) examined how gamblers form probability judgments in decision tasks. They found that higher gambling frequency was associated with *worse* accuracy in updating probabilities, suggesting that frequent gamblers may distort or misweight new evidence and base rates.

More generally, gamblers often exhibit an “illusion of control” (believing that they can influence random outcomes) or overweight low probabilities and underweight high probabilities. These biases degrade performance and erode any potential edge.

2.3 Losses Disguised as Wins (LDWs) and Reinforcement Effects

In slot machines and multi‐line electronic gaming machines, so-called losses disguised as wins (LDWs) are outcomes where the gambler receives some feedback (lights, sounds, small credit return) but still loses net. Studies show that LDWs can prolong gambling sessions and promote persistence.

In a laboratory experiment by Graydon, Dixon, Stange, and Fugelsang (2019), gamblers were exposed to different frequencies of LDWs. They found that “moderate” levels of LDWs caused higher-risk gamblers to persist longer in gambling, even during losing streaks.

Another real-world account-based study by Leino et al. (2016) of over 2 million bets showed that LDWs increase the likelihood of continuing within a session compared to outright losses, though real wins more strongly prompt continuation.

Also, Dixon, Harrigan, Sandhu, Collins, and Fugelsang (2010) showed that novices have similar physiological arousal (measured via skin conductance) to LDWs and genuine wins, indicating that gamblers may misinterpret the signals.

2.4 Neuroscience Findings: How the Brain Processes Wins vs. Losses

In one study (Sacré et al., 2016), scientists recorded neural signals from human participants doing gambling decisions. They found that in the anterior insula, gamma-band activity increased when subjects realized a win, differentiating wins from losses in real time. This suggests that the brain processes wins and losses differently in momentary reward circuits.

2.5 Theoretical Reinforcement: “Long Bet Will Lose” in Bandit Models

A recent theoretical study by Chen, Liang, Wang, and Yan (2022) analyzed a two-armed “Futurity” bandit model to show that even when a gambler sometimes sees gains, over a long series of bets the house ultimately wins. Their formal result was that “long bets will lose” — i.e. the game may appear fair in the short term, but is fundamentally skewed.

3. Synthesis: Can Anyone Earn Long-Term? Under What Conditions?

From theory and evidence, we can derive a balanced summary:

ConclusionReasoning / EvidenceNotes & Caveats
Most gamblers lose in the long run The Wilbur et al. large-scale study supports ~96 % loss; negative expectation models “Long run” implies many repeated bets; in single events or short spans, luck may dominate
A tiny minority may profit temporarily If a gambler has a genuine skill or information advantage, or finds mispriced odds Even then, profitability is fragile and often limited by operators (limits, bans)
Variance and luck dominate short time frames Randomness in outcomes means some will have “hot streaks” These streaks are not reliable or predictive of long-term success
Cognitive and behavioral biases erode expected edge Empirical research shows gamblers misestimate probabilities, overvalue control, and misinterpret LDWs These biases reduce or eliminate any small advantage
Structural constraints limit scalability Operators may throttle or ban consistent winners; odds and margins may shift Even if you can make profit, you may be cut off
Risk, drawdowns, and ruin dominate growth strategies Kelly and related strategies require reliable edge and accuracy; misestimation is dangerous Many gamblers cannot maintain discipline or correct estimates over time

Thus, while earning from gambling is not impossible in rare cases, for the average gambler it is extremely unlikely, especially over sustained periods.

4. Implications, Open Questions & Warnings

5. Take-Home Messages

1. Mathematical and probabilistic theory strongly suggest that in most gambling systems, the expected return is negative for the gambler.

2. Empirical studies across large samples confirm that most gamblers lose money over time.

3. A few individuals may make profits under special conditions (skill, mispricing, etc.), but such cases are rare and difficult to sustain.

4. Cognitive biases, emotional traps, and behavioral reinforcement features (e.g. LDWs) worsen outcomes for most gamblers.

5. It is far safer to treat gambling as entertainment with a built‐in cost, not as a dependable income strategy.

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