A guy on Reddit is pretty confident that EV+ methods can be used to generate consistent profits in gambling. First it’s not true. Never was. Second, I’m not going to make fun of him for believing so. That’s not my style. Instead, I’m going to answer him through using logic.
EV+ on gambling
Everyone can start winning on gambling, there are ways of gambling that can be profitable, i guess everyone knows that, i looked for EV+ strategies to maximize profit and worked really well for some time, i miss the days that i was gambling, and winning. Gambling seems to be a good way to make an income, but it is not guaranteed of course, sometimes you will lose, others you will win, but overall end up in profit.
Gambling is often perceived as a potential income source, particularly when leveraging positive expected value (EV+) strategies. This article explores the technical underpinnings of EV+ gambling, their limitations, and why gambling is not a sustainable income strategy.
Expected Value in Gambling
Expected value (EV) is the average outcome of a bet over many trials:
[ EV = \sum (P_i \cdot O_i) ]
where ( P_i ) is the probability of outcome ( i ), and ( O_i ) is the payoff. EV+ bets yield positive returns on average, but most gambling games are EV- due to the house edge.
EV+ Strategies
1. Card Counting in Blackjack
- Mechanism: Tracks high-to-low card ratios (e.g., Hi-Lo system: +1 for 2-6, 0 for 7-9, -1 for 10-A). True count = running count ÷ decks remaining. Bet more when true count is high.
- EV Impact: Can shift house edge to 0.5-2% player advantage.
- Challenges: Casino countermeasures (shuffling, bans), high variance, skill demands.
2. Poker Advantage Play
- Mechanism: Exploit opponents’ mistakes using pot odds, positional play, and psychology. EV per decision is calculated, e.g., calling $100 with 25% chance of $400 pot:
[ EV = (0.25 \cdot 400) + (0.75 \cdot -100) = 25 ] - EV Impact: Skilled players achieve consistent profits.
- Challenges: Rake, variance, skill ceiling.
3. Sports Betting Arbitrage
- Mechanism: Bet on all outcomes across bookmakers with misaligned odds. Example: 2.10 odds on both tennis players yields 4.76% profit.
- EV Impact: Guaranteed profit if executed correctly.
- Challenges: Account limits, capital intensity, rare opportunities.
4. Bonus Hunting/Matched Betting
- Mechanism: Clear bonuses with hedged bets. Example: Hedge $100 bonus with 5x wagering via betting exchanges.
- EV Impact: Near-guaranteed profit from bonuses.
- Challenges: Limited bonuses, account restrictions.
Why Gambling Fails as Income
- House Edge: Most games ensure EV- outcomes.
- Variance: Risk of ruin persists, mitigated by Kelly Criterion:
[ f = \frac{bp – q}{b} ]
(Kelly, 1956). - Countermeasures: Bans, limits, rule changes.
- Psychological Risks: Addiction, loss-chasing.
Expected Value (EV) strategies in gambling aim to maximize long-term gains by making decisions where the expected payoff outweighs the cost.
Here’s an example for a typical sports bet using such a strategy:
The EV+ (Positive Expected Value) strategy in sports betting involves identifying bets where the implied probability of the odds offered by a bookmaker is lower than the bettor’s estimated true probability of the outcome occurring. This creates a theoretical edge, as the bet is expected to yield a positive return over time.
Example: EV+ Strategy in an NFL Game
Game Context
Let’s consider a hypothetical NFL game in Week 5 of the 2025 season between the Kansas City Chiefs and the Buffalo Bills. The Chiefs are favored at home.
Step 1: Gather Odds and Information
You’re analyzing the moneyline odds from a bookmaker:
- Chiefs to win: -150 (implied probability = 60%)
- Bills to win: +130 (implied probability = 43.48%)
Implied probability calculation for Chiefs:
- Odds of -150 mean you need to bet $150 to win $100.
- Implied probability = [Odds / (Odds + 100)] = [150 / (150 + 100)] = 60%.
For Bills:
- Odds of +130 mean a $100 bet wins $130.
- Implied probability = [100 / (100 + 130)] = 43.48%.
The bookmaker’s odds include a vig (house edge), so the probabilities sum to more than 100% (60% + 43.48% = 103.48%). Without vig, the “true” implied probabilities would sum to 100%.
Step 2: Estimate True Probability
Using your analysis—considering team performance, injuries, weather, home-field advantage, and historical data—you estimate the true probability of the Chiefs winning at 65% (Bills at 35%). Your sources include:
- Team stats: Chiefs have a top-tier offense, averaging 30 points per game; Bills’ defense is strong but inconsistent on the road.
- Injuries: Bills’ starting cornerback is questionable, potentially weakening their secondary.
- Advanced metrics: Chiefs rank higher in DVOA (Defense-adjusted Value Over Average) and EPA (Expected Points Added).
- Historical trends: Chiefs have won 3 of the last 4 home games against the Bills.
Step 3: Calculate Expected Value (EV)
EV compares your estimated probability to the bookmaker’s odds to determine if the bet has a positive expected value.
Formula for EV (for a $100 bet):
- EV = [(Probability of Winning × Payout) – (Probability of Losing × Amount Bet)]
For betting on the Chiefs (-150):
- Payout = $100 bet wins $100 / 1.5 = $66.67 (plus your $100 stake returned).
- Your estimated probability: Chiefs win 65% (0.65), lose 35% (0.35).
- EV = [(0.65 × $66.67) – (0.35 × $100)]
- EV = [$43.34 – $35] = $8.34 per $100 bet.
This positive EV suggests the Chiefs bet is theoretically profitable over the long term.
For betting on the Bills (+130):
- Payout = $100 bet wins $130 (plus $100 stake).
- Your estimated probability: Bills win 35% (0.35), lose 65% (0.65).
- EV = [(0.35 × $130) – (0.65 × $100)]
- EV = [$45.50 – $65] = -$19.50 per $100 bet.
The Bills bet has a negative EV, so it’s not a good wager.
Step 4: Place the Bet
Based on the EV+ calculation, you bet $100 on the Chiefs to win at -150, expecting a long-term profit due to the 8.34% edge ($8.34 EV per $100 bet).
Potential Outcomes
- Chiefs Win:
- You win $66.67 (plus your $100 stake).
- This aligns with your 65% probability estimate and reinforces the EV+ strategy’s logic.
- Bills Win:
- You lose your $100 bet.
- Despite the positive EV, this outcome reflects the 35% chance of losing, highlighting the inherent risk in single bets.
- Unexpected Factors:
- An injury to the Chiefs’ quarterback during the game or a fluke play (e.g., a pick-six) could swing the outcome, reducing the accuracy of your probability estimate.
Why EV+ Strategies Don’t Work Objectively
While the EV+ strategy is mathematically sound, it has significant limitations that prevent guaranteed success:
- Sample Size and Variance:
- EV+ assumes long-term profitability, requiring thousands of bets to realize the expected edge. A single NFL game or even a season’s worth of bets (e.g., 100 bets) is too small a sample to overcome variance. You could hit a losing streak despite positive EV, depleting your bankroll.
- Example: Even with a 65% true probability, the Bills could win this game, and similar bets could lose multiple times in a row due to chance.
- Inaccurate Probability Estimates:
- Your 65% estimate for the Chiefs is based on subjective analysis. If your model overestimates their win probability (e.g., true probability is 60% or lower), the EV may be zero or negative.
- External factors like last-minute injuries, referee decisions, or weather changes can render your analysis obsolete.
- Bookmaker Efficiency:
- Bookmakers set odds using sophisticated models and adjust them based on betting volume. Finding consistent EV+ opportunities is difficult because odds often reflect near-true probabilities, especially in high-profile markets like the NFL.
- The vig (3.48% in this example) further erodes your edge, requiring an even higher accuracy in your probability estimates.
- Bankroll Limitations:
- To capitalize on a small edge (e.g., 8.34%), you need a large bankroll to withstand losing streaks. Most bettors lack the capital or discipline to bet consistently over thousands of wagers.
- Example: If you lose five $100 bets in a row (possible even with a 65% win probability), you’re down $500, which may exceed your budget.
- Psychological and Behavioral Risks:
- Bettors often deviate from the EV+ strategy due to emotions, chasing losses, or overconfidence in their analysis. This undermines the disciplined approach required for long-term success.
- Example: After losing the Chiefs bet, you might impulsively bet on the Bills in the next game to “recover,” ignoring EV calculations.
- Market Dynamics:
- Odds can shift quickly due to sharp bettors or new information (e.g., injury reports). By the time you place your bet, the -150 odds on the Chiefs might move to -170, reducing or eliminating the EV+ opportunity.
While EV+ identifies theoretically profitable bets, it doesn’t guarantee success due to variance, estimation errors, bookmaker efficiency, and practical constraints. Most bettors fail to achieve consistent profits because they can’t overcome these challenges.
Same can be applied to slot games
Let’s take the example of Starburst; which is a 5-reel, 10-payline slot game with a Return to Player (RTP) rate of 96.09%, low volatility, and features like expanding wilds and re-spins. It’s popular for its simplicity and frequent small wins. For this example, assume you’re playing Starburst at an online casino with a $1 bet per spin.
Step 1: Gather Odds and Information
In slots, “odds” are determined by the game’s RTP and mechanics, not explicit betting lines like in sports. Key details for Starburst:
- RTP: 96.09%, meaning for every $100 wagered, the game returns $96.09 on average over millions of spins.
- House Edge: 100% – 96.09% = 3.91%, the casino’s long-term advantage.
- Win Probability: Starburst’s low volatility means frequent small wins (e.g., 2x to 10x the bet) but rare large payouts (up to 50,000 coins for a max win).
- Payout Structure: Wins depend on symbol combinations (e.g., BAR symbols pay 250x for five on a payline, low-value gems pay less). The game’s paytable and random number generator (RNG) determine outcomes.
- Casino Promotion: Suppose the casino offers a 100% deposit bonus (e.g., deposit $100, get $100 bonus) with a 30x wagering requirement, which you believe could create an EV+ opportunity.
You aim to use the bonus to create a positive expected value by leveraging the RTP and bonus terms, a common approach in casino gambling to seek EV+ situations.
Step 2: Estimate True Probability and EV
Unlike sports betting, slots don’t allow you to estimate “true” probabilities for specific outcomes because the RNG ensures each spin is independent, and exact probabilities for each symbol combination are proprietary. Instead, you rely on the RTP and bonus terms to calculate EV.
Scenario: You deposit $100 and receive a $100 bonus, giving you $200 to play. The wagering requirement is 30x the bonus ($100 × 30 = $3,000 in total bets) before you can withdraw winnings. You play Starburst at $1 per spin.
EV Calculation:
- Expected Return per Spin: With a 96.09% RTP, each $1 spin returns $0.9609 on average.
- Expected Loss per Spin: $1 – $0.9609 = $0.0391 (the house edge).
- Total Wagering: To meet the $3,000 requirement, you make 3,000 spins at $1 each.
- Expected Return from Spins: 3,000 × $0.9609 = $2,882.70.
- Expected Loss from Spins: 3,000 × $0.0391 = $117.30.
- Bonus Value: The $100 bonus is “free” money but requires meeting the wagering requirement. If you have $2,882.70 left after wagering (from the expected return), you can withdraw this amount (assuming no additional losses or wins beyond the RTP average).
EV of the Promotion:
- Cost: Your $100 deposit.
- Expected Balance After Wagering: $2,882.70 (from spins) – $100 (initial deposit) = $2,782.70 in theoretical winnings, but this assumes you sustain the RTP over exactly 3,000 spins and hit no major losses.
- Bonus EV: The bonus reduces your effective cost. The EV of the bonus is calculated as:
- EV = (Bonus Amount × RTP) – (Wagering Requirement × House Edge).
- EV = ($100 × 0.9609) – ($3,000 × 0.0391) = $96.09 – $117.30 = -$21.21.
The negative EV indicates that, even with the bonus, the wagering requirement and house edge make the bet unprofitable on average. However, let’s assume you believe you can hit a big win (e.g., 250x from BAR symbols) during the 3,000 spins, which could offset the loss. This is speculative, as the probability of such a win is unknown but low due to the game’s design.
Step 3: Place the Bet
You deposit $100, claim the $100 bonus, and start spinning Starburst at $1 per spin, aiming to meet the $3,000 wagering requirement while hoping for a big win to create a positive outcome. You track your progress to ensure you stay within the bonus terms.
Potential Outcomes
- Average Outcome (RTP-Based):
- After 3,000 spins, you have approximately $2,882.70 left (per RTP calculations).
- You meet the wagering requirement but lose $117.30 on average, leaving you with less than your starting $200 (deposit + bonus).
- The negative EV (-$21.21) reflects a loss, consistent with the house edge.
- Big Win Scenario:
- During the 3,000 spins, you hit a 250x win ($250 for a $1 bet) due to five BAR symbols or multiple wild re-spins.
- This boosts your balance significantly (e.g., $250 + remaining funds), potentially allowing you to withdraw a profit after meeting the wagering requirement.
- However, this outcome is rare and not guaranteed, as Starburst’s low volatility favors smaller, frequent wins.
- Loss Scenario:
- You experience a streak of losing spins or small wins that don’t cover the $3,000 wagering requirement.
- Your balance depletes before meeting the requirement, losing the $100 deposit and $100 bonus.
- This reflects the inherent risk of slots, where variance can lead to significant losses despite the RTP.
Applying an EV+ strategy to Starburst or any slot game is nearly impossible due to the following reasons:
- Fixed House Edge:
- Starburst’s 96.09% RTP ensures a 3.91% house edge, meaning every spin has a negative expected value in the long run. Unlike sports betting, where you can estimate true probabilities, slots are designed to favor the casino consistently.
- Even with bonuses, wagering requirements (e.g., 30x) amplify the house edge, as you must bet multiple times, increasing your exposure to the 3.91% loss rate.
- Random Number Generator (RNG):
- Starburst’s outcomes are determined by an RNG, making each spin independent and unpredictable. You cannot analyze past spins or game conditions (like team stats in sports) to gain an edge.
- The lack of skill or decision-making in slots eliminates the ability to find “mispriced” bets, a key component of EV+ in sports betting.
- Unknown Probabilities:
- The exact probabilities of specific wins (e.g., five BAR symbols) are not publicly disclosed, preventing precise EV calculations. The RTP is an aggregate over millions of spins, not a per-spin guarantee.
- Without accurate probability estimates, you cannot identify bets with a positive expected value.
- Variance and Short-Term Play:
- Slots have high variance, especially in short sessions (e.g., 3,000 spins). You might win big or lose everything, but the RTP only holds over millions of spins, far beyond typical player sessions.
- Even with a bonus, the wagering requirement forces you to play long enough for the house edge to dominate, negating any temporary EV+ from the bonus.
- Casino Promotions Limitations:
- Bonuses like the 100% deposit match seem to offer EV+ opportunities, but high wagering requirements and game restrictions (e.g., slots only, low RTP games excluded) ensure the casino retains an edge.
- For example, the -$21.21 EV in the bonus scenario shows that the promotion is designed to encourage play, not guarantee profits.
- Psychological Traps:
- Slots like Starburst are designed to be engaging, with vibrant graphics and frequent small wins, encouraging prolonged play. This can lead to chasing losses or overestimating the likelihood of a big win, undermining disciplined EV+ strategies.
- The illusion of “almost winning” (e.g., near-miss combinations) can make players feel they’re close to a positive outcome, but this is a psychological trick, not a mathematical edge.
Slots like Starburst are engineered to prevent EV+ strategies from working. The house edge, RNG, and bonus terms ensure the casino’s long-term profitability, and players cannot gain a mathematical advantage through analysis or skill, unlike in sports betting.
EV+ strategies can fail for several reasons:
- Variance and Short-Term Luck: Gambling outcomes are often highly variable. Even if a strategy has positive EV, short-term losses can occur due to bad luck, depleting a gambler’s bankroll before the long-term edge is realized.
- Bankroll Mismanagement: EV+ strategies assume sufficient funds to weather variance. If a gambler bets too aggressively or lacks the capital to sustain losses, they may go broke before achieving the expected gains.
- House Edge: Most casino games are designed with a built-in house edge, meaning the EV is negative for players in the long run. Even skilled strategies (e.g., card counting in blackjack) face challenges overcoming this edge consistently.
- Imperfect Execution: EV+ strategies, like those in poker or sports betting, require precise execution. Miscalculations, emotional decisions, or lack of discipline can turn a positive EV strategy into a losing one.
- Limited Opportunities: In some cases, EV+ opportunities (e.g., exploiting bookmaker errors) are rare or quickly corrected, limiting the ability to capitalize on them consistently.
- External Factors: Casinos or betting platforms may ban players using EV+ strategies (e.g., card counters), or market inefficiencies may disappear as others exploit them.
- Psychological Pressure: Gambling involves emotional and psychological challenges. Even with a sound EV+ strategy, fear, greed, or tilt can lead to poor decision-making.
Responsible Gambling Reminder
Sports betting carries significant financial and emotional risks.
- Set a Budget: Decide in advance how much you can afford to lose (e.g., $100 for the Chiefs bet) and never exceed it. Treat betting as entertainment, not income.
- Avoid Chasing Losses: If the Chiefs lose, don’t place impulsive bets to recover your $100. Stick to your EV+ strategy or take a break.
- Limit Time and Exposure: Don’t spend excessive time analyzing bets or checking odds, as this can lead to obsession. Set a weekly limit (e.g., 1-2 bets).
- Recognize the Odds: Even with an EV+ bet, you have a 35% chance of losing this wager. Accept that losses are part of betting.
- Seek Help if Needed: If betting feels compulsive or stressful, contact resources like the National Problem Gambling Helpline (1-800-522-4700) or visit www.ncpgambling.org for support.
Responsible gambling ensures you enjoy the process without risking financial stability or mental well-being. Never bet more than you can afford to lose, and always prioritize informed, disciplined decisions.