Game Theory Analysis
SPORTS BETTING
Sports Betting
The bet is the number.
Not the team
Sharps don't bet teams. They bet numbers.
Every bet has two parts: what has to happen, and what you get paid if it does. Most bettors only think about the first one.
Real example - Premier League match
| Outcome | Price | Implied Probability |
|---|---|---|
| Man City | 1.80 | 55.6% |
| Draw | 3.60 | 27.8% |
| Arsenal | 5.00 | 20.0% |
| Total implied probability | - | 103.4% |
Notice that the three outcomes add up to 103.4%, not 100%. That 3.4% is the bookmaker's cut built into the prices before you make a single decision. Your job is to figure out whether the true probability of any one outcome is higher than what the odds are implying.
If the odds imply Arsenal has a 20% chance of winning but you believe the real probability is closer to 25%, you have an edge. You will still lose that bet most of the time; that's what a 25% chance means. But if you're right, you're being paid for a 20% chance while holding a 25% chance. Over time it pays up.
EV of the Arsenal bet
5.00 price, 25% true probability
EV = (25% x +4.00u) + (75% x -1.00u) = +0.25u per bet. Across 1,000 bets, the expectation is +250u.
Verdict
+EV
Decimal Price
5.00
Arsenal to win
Market Implied
20.0%
1 / 5.00
Your Probability
25.0%
+5.0 pp edge
EV On 1u
+0.250u
+25.0% ROI
1,000 bet simulation
Seeded run: 252 wins, 748 losses, final profit +260u.
1u flat stake
The bet still loses 75% of the time. The edge comes from being paid at 5.00 when your number says the fair price is 4.00.
ODDS FORMATS
Odds are prices. They tell you what you get paid, and they imply how often you need to be right.
| Price | Meaning on 1u stake | Implied Probability |
|---|---|---|
2.10 | Return 2.10u total (+1.10u net) if win | 47.6% |
1.91 | Return 1.91u total (+0.91u net) if win | 52.4% |
QUICK PROBABILITY CHECK
A quick implied probability from decimal odds is:
Example: at 2.10, the market is pricing the outcome at about 47.62%.
WHY PRICE BEATS OPINION
It is not enough to be 'right about the game'. You need to be right more often than the odds require.
If two books offer 2.00 and 2.10 on the same side, 2.10 is the better long-run ticket. Small price edges compound hard.
Being right is not enough. You need to be right at the right price.
This is the concept that separates disciplined bettors from everyone else. A bet has positive expected value (+EV) when your estimate of the true probability is higher than what the odds are implying. Not just I think they'll win - you need to be more confident than the market is pricing in, specifically after the vig is removed.
EV example - same bet, different verdict
| Scenario | Market Price | Your Estimate | Edge | Verdict |
|---|---|---|---|---|
| Good price | 2.10 (47.6% implied) | 52% | +4.4 percentage points | +EV bet - take it |
| Worse price | 1.91 (52.4% implied) | 52% | -0.4 percentage points | -EV bet - pass it |
+EV bets lose all the time. -EV bets win all the time. In the short run, luck dominates. Over hundreds of bets, the math catches up - and it always does.
Most losing bettors judge themselves on wins and losses. That is the wrong scoreboard. The right question is: did you buy a good number? A well-priced losing bet is a better decision than a poorly-priced winner. Process over results, every time.
Enter decimal prices like 1.90, 2.24, or 5.00.
Add as many sides as you need, then enter your own probability for each outcome to see the implied house edge, probability edge, and EV.
EV / House Edge Calculator
Enter decimal prices like 1.90, 2.24, or 5.00. Add as many sides as you need, then compare the book's implied numbers with your own probabilities.
Valid Sides
2
House edge becomes meaningful once you have at least two prices.
Total Implied Probability
105.3%
This is the sum of the market's implied probabilities.
Implied House Edge
5.26%
Calculated as total implied probability minus 100%.
Your Probability Total
--
Enter your probabilities to start calculating EV.
Outcome 1
Implied Probability
52.6%
No-vig fair: 50.0%
Prob Edge
--
Your % minus market implied.
EV on 1u
--
Incomplete
Outcome 2
Implied Probability
52.6%
No-vig fair: 50.0%
Prob Edge
--
Your % minus market implied.
EV on 1u
--
Incomplete
WHY PARLAYS GET PUSHED
Parlays are the most aggressively marketed product in sports betting for a reason: they are extraordinarily profitable for the book. Every leg you add multiplies the vig, not just the payout. The potential return grows in a way that feels exciting, while the compounded margin grows in a way that is designed to be invisible.
EXAMPLE
3-leg parlay at 1.91 each leg (52.4% implied each)
True fair odds: 0.5 × 0.5 × 0.5 = 12.5% chance
Book payout: roughly 6.96 total price (14.4% implied for the book)
EFFECTIVE MARGIN
Effective margin on a 3-leg parlay: ~15% vs ~5% on a single
PLAIN LANGUAGE
Parlays are great ways to have fun, and to chase huge multipliers. The odds aren't the best, and if you want to bet competitively, it's better to stick to single bets.