- How to convert a risk-free bet?
- Optimal hedging betting strategy
- Betting strategies compared
- Betting stats
Many leisurely sportsbooks provide promotions for new users, dangling a "risk-free" bet of a hefty sum, say $500. However, the fine print reveals a catch: if your first bet flops, they compensate you with a "free bet" matching your stake.
Upon securing the free bet, you're entitled to the profits should you win, yet the initial bet's face value remains with them. So, the offer isn't entirely "risk-free," but it does significantly lower your risk, essentially offering free cash. The challenge lies in maximizing the free money from this offer.
Maximizing Expected Value: Is Taking the Risk Justified?
You might reckon that chasing the highest expected value (EV) is the way to amplify your free cash. After all, EV calculates the gamble's worth across all potential outcomes. The best strategy, by this logic, would be to go for a long shot, likely to lose, since winning the initial bet provides no benefit from the promotion.
While targeting extreme longshots might spike your EV, ensuring a better shot at the promotional free bet, it comes with heightened risk. Betting $500 on a longshot with 4.600 odds means winning roughly 20% of the time, yet it secures a substantial free bet if you lose. Placing the free bet on a similar line gives another shot at netting $1,300.
This approach also maximizes your free bet's EV, but you often risk losing as there's a two-thirds chance of losing both bets and the initial $500.
Yet, wagering on a heavy favorite might be more prudent, especially for novices with a smaller bankroll, say $1,000. This strategy, betting on a favorite at 1.500 odds, offers a 63% chance of winning $250 on your $500 risk-free bet, minimizing the risk of depleting your bankroll significantly.
However, aiming for the free bet on a loss is where the real value lies, and playing it safe might mean missing out on significant value.
Optimal Hedging: Striking the Perfect Balance
Is there a strategy that balances maximizing EV and minimizing risk? Indeed, it's called optimal hedging. Hedging involves betting on all outcomes to secure a guaranteed return, albeit at a cost due to the sportsbook's margin.
For instance, if Team A has 4.600 odds to win, and considering a typical 5% bookmaker margin, the odds for Team B would be around 1.204. The fair line is in between, but hedging at 1.204 won't maximize your EV. Betting with a low-margin sportsbook like 7x7Bets, offering 1.238 odds, trims the EV loss.
However, if profit maximization is the goal, considering the risk appetite is crucial. This requires moving beyond simple EV calculations to employing Theoretical Kelly Optimization (TKO) for identifying the strategy that enhances your bankroll's expected growth (EG) percentage. This nuanced strategy is the essence of the Kelly Criterion, adapted for complex scenarios involving hedged bets.
Below is a comparison of potential outcomes with three strategies, showing the chances of winning your initial bet, losing it and then winning your free bet, or losing both. It also highlights the average profit, or EV. Betting on 1.500 favorites yields the lowest EV ($34 on average) but with less variance compared to longshots.
The highest EV ($271) comes from not hedging on longshots, but hedging sacrifices only about $45 in EV—and just $17 when betting with 7x7Bets. So, if Team B wins, leveraging the entire payout on another longshot with your free bet minimizes your losses to $233 instead of $500, a substantial difference for those starting with $1,000.
Risk-Free Bet Odds | Free Bet Odds | % Win | Win in $ | % Lose/Win | Win in $ | % Lose/Lose | Win in $ | EV |
1.500 | 1.500 | 63.5% | $250 | 23.2% | -$250 | 13.3% | -$500 | $34 |
4.600 | 4.600 | 20.7% | $1800 | 16.4% | $1300 | 62.9% | -$500 | $271 |
4.600/hedge | 4.600/hedge | 20.7% | $1300 | 16.4% | $800 | 62.9% | -$275 | $227 |
7x7Bets hedge | 7x7Bets hedge | 20.7% | $1300 | 16.4% | $800 | 62.9% | -$233 | $254 |
Testing risk-free betting strategies
Determining the best strategy for maximizing the median long-term bankroll in risk-free betting involves practical experimentation or simulation. If sportsbooks allowed repetitive use of the same promotion, a direct comparison of strategies through multiple iterations or a Monte Carlo simulation could reveal the most profitable approach.
The highest expected value (EV) of $271 comes from betting on longshots without hedging. Adjusting the promotion rules to allow betting 50% of the current bankroll, regardless of its size, ensures that a bettor never goes completely bankrupt, providing a chance for recovery if a strategy proves superior.
A simulation conducted over numerous iterations showcases the variability of outcomes across strategies. One specific run for the first 100 trials, displayed on a logarithmic scale to accentuate differences, indicated that betting on favorites consistently could transform a $1,000 bankroll into approximately $4,000 without entering the loss zone. However, this outcome represents an unusually favorable scenario for that strategy, as the marginal benefit of each bet actually results in a negative expected growth (EG).
Conversely, betting on longshots without hedging led to significant bankroll volatility, resembling the erratic nature of a basketball during an intense dribbling session, ultimately depleting the bankroll to less than $10. This drastic decline highlights the risk of over-betting, even with a significant edge. Reducing the bet size could mitigate the risk of ruin but at the expense of diminishing the theoretical EV of $271, achievable only with a $500 initial bet.
However, by sacrificing a small portion of EV through strategic hedging on a platform like 7x7Bets, the losses during downturns are significantly lessened, ultimately leading to substantial profits. This approach underscores the viability of hedging as a strategy, particularly when applied with a large bankroll and through a sportsbook offering competitive odds and welcoming to all bettors.
With a $10,000 bankroll, betting on 4.600 odds without hedging maximizes the EG, leveraging a substantial mathematical advantage with minimal risk. Yet, a hedging strategy that involves placing a $1,575 bet on the favorite at 7x7Bets, followed by a $1,450 hedge at 1.238 odds if the initial bet wins, also achieves a 2.25% EG on the bankroll, irrespective of the outcome. This hedged approach offers a balanced strategy, combining risk management with profit maximization, ultimately aligning with bettors' preferences at higher bankroll levels.
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