The Math Behind Winning: How to Size Your Bets on Peer-to-Peer Exchanges
- Feb 3
- 10 min read
When it comes to betting, how much you bet matters more than how often you win. Even with a 60% win rate, poor bet sizing can lead to losing your entire bankroll. Overbetting increases volatility and makes it harder to recover from losing streaks. This is where strategies like the Kelly Criterion come in.
The Kelly Criterion is a formula that calculates the ideal percentage of your bankroll to bet based on your edge and the odds. It’s designed to maximize growth while minimizing the risk of going broke. On peer-to-peer platforms like BettorEdge, where there’s no sportsbook margin, proper bet sizing becomes even more effective.
Key Takeaways:
Why Bet Sizing Matters: Overbetting leads to volatility and potential bankruptcy, even with a winning strategy.
The Kelly Criterion: A formula to determine optimal bet size based on your edge and the odds.
Fractional Kelly: Betting smaller fractions (like Half or Quarter Kelly) reduces risk while maintaining steady growth.
Peer-to-Peer Betting: Better odds on platforms like BettorEdge amplify the importance of disciplined sizing.
In short, disciplined bet sizing is essential for long-term success, regardless of how good your odds or predictions are.
The Kelly Criterion: How to Calculate Optimal Bet Size
The Formula and What Each Part Means
The Kelly Criterion is a mathematical approach designed to maximize the growth of your bankroll over time. It helps determine the ideal percentage of your bankroll to wager on a specific bet. The formula is as follows:
f* = (b · p – q) / b
Here’s what each term represents:
f*: The fraction of your bankroll to bet.
b: The net odds, which is the profit per $1 staked. For decimal odds, calculate this as Decimal Odds – 1.
p: The probability of winning, expressed as a decimal (e.g., 55% becomes 0.55).
q: The probability of losing, calculated as 1 – p.
The formula only suggests placing a bet when your edge (b · p – q) is positive. If it’s negative, the formula advises skipping the bet altogether.
Converting Odds to Probabilities
To use the formula, sports betting terms like odds need to be converted into a usable format. For American odds, here’s how to do it:
For positive odds (e.g., +150): Convert to decimal using (Odds + 100) / 100.
For negative odds (e.g., -110): Use (|Odds| + 100) / |Odds|.
Once you have the decimal odds, subtract 1 to get the net odds (b).
In peer-to-peer markets, prices often appear as share costs. For example, a share priced at $0.45 for a $1.00 payout reflects a 45% win probability. To calculate the net odds in such cases, use: b = (1.00 – Price) / Price. If "Yes" shares cost $0.45, the net odds would be (1.00 – 0.45) / 0.45 = 1.22.
Let’s break it down with an example. Say you find a bet with a 55% win probability (p = 0.55) and American odds of -110. First, convert the odds to decimal: (110 + 100) / 110 = 1.91. Subtract 1 to get the net odds: 1.91 – 1 = 0.91. Now, plug the values into the formula: f* = (0.91 × 0.55 – 0.45) / 0.91 ≈ 0.055. This means you should wager 5.5% of your bankroll.
Why Most Sharp Bettors Use Fractional Kelly
Betting the full Kelly amount can lead to high volatility. A full Kelly wager gives you a 50% chance of halving your bankroll before doubling it. To manage this risk, many experienced bettors use a fractional approach, such as Half-Kelly or Quarter-Kelly.
With Half-Kelly, you bet half the amount suggested by the formula. This reduces volatility by 50% while only cutting expected growth by 25%. For example, a Half-Kelly bettor faces just an 11.1% chance of halving their bankroll before doubling it, offering a much safer path compared to full Kelly.
Michael Shackleford, founder of Wizard of Odds, explains:
Betting half the Kelly amount, for example, reduces bankroll volatility by 50%, but growth by only 25%.
Fractional Kelly also helps mitigate the risk of overestimating your edge, as the formula is highly sensitive to your win probability. By using a smaller fraction, such as Quarter-Kelly, you gain an even greater safety margin - though at the cost of slower bankroll growth.
Up next, we’ll dive into how to calculate your actual edge to refine your bet sizes further.
How to Calculate Your Edge
Finding Your Edge in Peer-to-Peer Markets
Your "edge" represents the gap between your prediction and the market's expectations. In peer-to-peer markets, share prices reflect the market's implied probability. For instance, if a "Yes" share is priced at $0.45, the market is suggesting a 45% likelihood of that outcome.
To calculate your edge, subtract the market-implied probability (based on share price) from your own estimated probability. If your estimate is higher than the market's, this could signal a betting opportunity. However, if your estimate matches or falls below the market's, tools like the Kelly Criterion suggest skipping the bet.
Platforms like BettorEdge offer a peer-to-peer model with pricing that's 3–5% better than traditional options, giving you a small built-in advantage before you even start analyzing. Look for price inefficiencies caused by factors like news, market sentiment, or limited data. Once you’ve done a qualitative assessment, it’s time to quantify your edge.
Implied Probability vs. Your Estimated Probability
The formula for calculating your edge is straightforward:
Edge = Your Estimated Probability – Market-Implied Probability
Here’s an example: Say you believe a team has a 60% chance of winning, but "Yes" shares are priced at $0.52, implying a 52% probability. Your edge would be 8 percentage points.
Let’s look at a real-world scenario from BettorEdge. In a Federal Reserve interest rate market, "Yes" shares were priced at $0.35, implying a 35% chance of a rate hike. After analyzing economic data, a bettor estimated the actual probability at 50%, creating a 15-point edge. Using the Kelly formula with net odds of 1.86 (calculated as (1.00 – 0.35) / 0.35), the bettor allocated 23% of their bankroll. On the other hand, the "No" side, priced at $0.65, showed a negative Kelly result, meaning it wasn’t worth betting on.
"Your edge is the difference between your probability and the market's... This edge tells you whether to bet and how much." – BettorEdge
For reference, a $0.45 share translates to net odds of roughly 1.22. If your edge is zero or negative, it means the pricing is efficient, offering no advantage. Calculating your edge is critical for applying the Kelly Criterion to determine the right bet size.
Since probability estimates are rarely perfect, experienced bettors often use fractional Kelly - such as Half or Quarter Kelly - to reduce the risk of overestimating their edge. Keep in mind that prices in peer-to-peer markets can change rapidly due to breaking news, injuries, or weather updates. Always recalculate your edge whenever market conditions shift.
Kelly Criterion Betting Explained: System to Calculate Optimal Bet Size
Risk of Ruin: Why Winning Bettors Still Go Broke
What Risk of Ruin Means in Real Numbers
Risk of ruin refers to the chance of losing your entire bankroll before your edge can lead to long-term growth. Betting too much on each wager increases your exposure to losing streaks, which can be devastating. For instance, losing 50% of your bankroll requires a 100% gain just to break even, making recovery significantly harder.
Here's the math: betting twice the Kelly amount results in zero expected growth over time. Go beyond that, and you're guaranteed to drain your bankroll, no matter how good your edge is. The main issue? Overbetting too aggressively.
Take a Full Kelly bettor as an example. They face a 50% chance of losing half their bankroll before doubling it. But if they switch to Half Kelly, that risk drops to just 11.1%. These figures highlight how adjusting your Kelly fraction can help manage risk.
Real Examples: Full Kelly vs. Half Kelly vs. Quarter Kelly
Let’s break it down with an example. Imagine you have a $1,000 bankroll and a 55% win probability on even-money bets. Betting Full Kelly (10% of your bankroll per wager) results in a 41% drawdown after five consecutive losses, leaving you with about $590. By comparison, Half Kelly (5% stakes) reduces the drawdown to 22.6%, leaving you with $774. Quarter Kelly (2.5% stakes) minimizes the damage even further, with only an 11.9% drawdown, leaving you with $881.
Kelly Strategy | Stake Per Bet | Bankroll After 5 Losses | Drawdown | Chance of 50% Loss |
Full Kelly | $100 (10%) | $590 | 41% | 50% (1/2) |
Half Kelly | $50 (5%) | $774 | 22.6% | 11.1% (1/9) |
Quarter Kelly | $25 (2.5%) | $881 | 11.9% | Minimal |
The trade-off? Lowering your stake reduces volatility significantly while only slightly decreasing your expected growth. For instance, Half Kelly cuts volatility by 50% but only reduces growth by about 25%. In one simulation with a 51% win probability (a 2% edge), betting the full 2% Kelly amount required 3,496 bets to double the bankroll. But increasing the stake to 3% (a 50% overbet) slowed progress, requiring 4,477 bets to reach the same goal. So, higher stakes don’t lead to faster growth - they just increase your risk.
This is why most professional bettors lean toward fractional Kelly strategies, typically betting between Quarter and Half Kelly. This approach accounts for estimation errors and the unpredictability of real-world betting. On peer-to-peer exchanges, where your edge depends on comparing your model to market odds, even small errors in your calculations can be amplified by the Kelly formula. Capping bets at 5% of your bankroll provides a safety net against these risks and unexpected events.
How to Size Your Bets: A Step-by-Step Guide
The 5-Step Bet Sizing Process
Figuring out the right bet size doesn’t require advanced math - just a straightforward process. Follow these five steps every time you place a wager on BettorEdge. This approach simplifies theoretical ideas into real-world decisions.
Estimate Your Win Probability Start by determining your win probability. Use your models, past data, or compare it to the market's implied probabilities. For instance, if you think a team has a 52% chance of winning, that percentage becomes your p value.
Convert Market Odds to Net Odds Take the decimal odds and subtract 1 to find the net odds (b). For example, if the odds are 2.10, the net odds are 1.10.
Calculate Your Edge Use this formula to find your edge: Edge = (Win Probability × Decimal Odds) – 1 For example, with a 52% win probability and decimal odds of 2.10, the calculation is (0.52 × 2.10) – 1 = 0.092, or a 9.2% edge.
Determine Your Kelly Fraction Divide your edge by the net odds. Using the example above, 0.092 ÷ 1.10 equals about 0.084. This means a full Kelly bet would be roughly 8.4% of your bankroll. This step applies the Kelly Criterion principles to guide your bet size.
Adjust with a Multiplier and Set a Bet Cap To manage risk, multiply your Kelly fraction by a safety factor, such as 0.25 for Quarter Kelly or 0.5 for Half Kelly. For Half Kelly, 8.4% becomes about 4.2%. Additionally, cap your bet at 1–2% of your total bankroll. If the formula gives you a zero or negative result, skip the bet altogether - this ensures you only wager when you have a statistical edge.
Using a Simple Calculator or Spreadsheet
To make this process easier, you can use a spreadsheet or BettorEdge’s free online calculator. In a spreadsheet, set up columns for Bankroll, Win %, Decimal Odds, Net Odds, Kelly %, and Final Stake. Use these formulas:
For "Net Odds":
For "Kelly %":
For "Final Stake":
If spreadsheets aren’t your thing, BettorEdge’s Kelly Bet Sizer tool is a great alternative. Just input your odds, win probability, bankroll, and multiplier, and it will instantly calculate your recommended stake. Want to see the percentage of your bankroll to bet? Enter "1" as your bankroll, then multiply the result by your actual bankroll.
One more tip: BettorEdge’s peer-to-peer model often offers odds that are 3–5% better than traditional sportsbooks, giving you an extra edge. This makes careful bet sizing even more important.
Conclusion
After examining effective bet-sizing strategies and the dangers of overbetting, one thing stands out: even the best odds won't save you if you overbet. While platforms like BettorEdge can provide a solid advantage, ignoring proper bet-sizing - especially exceeding the Kelly criterion - can wipe out your bankroll and erase any chance of long-term success. For instance, betting exactly double the Kelly amount results in 0% expected long-term growth, and going beyond that will actually shrink your bankroll over time.
Maintaining discipline with your bet sizes is what separates successful bettors from those who go broke. A behavioral study highlighted this point: even with a 60% win-rate edge on coin flips at even money, 28% of participants still went bankrupt because they ignored proper sizing rules. It’s also important to remember how difficult recovery from losses can be - a 50% loss requires a 100% gain just to break even. Adopting a Half Kelly approach can strike a balance by cutting volatility in half while only giving up about 25% of your expected growth. This method provides a steadier path toward profitability.
FAQs
What is the Kelly Criterion, and how does it help manage betting risk on peer-to-peer platforms?
The Kelly Criterion is a mathematical tool designed to help you calculate the ideal bet size based on two key factors: your edge (the expected advantage) and the odds. The goal? To maximize the long-term growth of your bankroll while keeping the risk of going broke as low as possible.
In practice, many bettors opt for a fractional version of the Kelly Criterion. For instance, they might bet only a quarter or half of the recommended amount. This adjustment helps to manage volatility, keeping swings in your bankroll more controlled. By taking this approach, you can stay disciplined, safeguard your funds, and ensure you're ready to seize future betting opportunities.
Why do many bettors prefer using a fractional Kelly strategy instead of the full Kelly strategy?
A fractional Kelly strategy is a favorite among bettors because it helps manage volatility and minimizes the chance of losing your entire bankroll (often referred to as the risk of ruin). Instead of wagering the full Kelly amount, you bet a smaller percentage - typically half or even a quarter. This adjustment allows for more controlled risk while still aiming for steady, long-term growth.
This method is particularly effective in sports betting, where outcomes can be highly unpredictable. By taking a more cautious approach, you shield yourself from significant losses and increase your ability to endure losing streaks. It’s no surprise that many seasoned bettors turn to fractional Kelly for its balance between safety and growth potential.
How do I determine my edge in peer-to-peer betting?
To figure out your advantage in peer-to-peer betting, start by analyzing the event and estimating the likelihood of it happening. Compare your estimated probability to the odds being offered. From there, you can use the Kelly Criterion to calculate the ideal bet size:
f = (b × p - q) / b, where:
b = the decimal odds minus 1 (e.g., for odds of 2.5, b = 1.5)
p = your estimated probability (e.g., 60% would be 0.6)
q = 1 - p (the probability of the event not happening)
This formula helps you determine a bet size that aligns with your edge, balancing potential gains with the risk involved. Many bettors opt for a fractional version, like half-Kelly, to minimize swings and safeguard their bankroll. Betting responsibly is crucial for staying in the game over the long run.
