You’ve found a +EV bet. Now how much do you stake?<\/p>\n
Most retail bettors flat-stake \u2014 1% of bankroll on every pick, regardless of edge or odds. Sharps use the Kelly Criterion \u2014 a formula that tells you the optimal<\/em> stake to maximize long-run bankroll growth, given your edge and the decimal odds on offer. Bet too little and you leave growth on the table. Bet too much and variance wipes you out.<\/p>\n This post builds a Python Kelly calculator that uses Pinnacle’s no-vig lines as the “fair probability” benchmark, tested on three live fixtures pulled from the OddsPapi API. Includes the fractional Kelly variant every professional uses in practice, and a full scanner that finds +EV Kelly bets across today’s slate.<\/p>\n For a two-outcome bet at decimal odds Three things to notice:<\/p>\n The formula is easy. The hard part is estimating the true probability Option 3 is the professional default. Pinnacle takes bets from sharps without limiting them, which forces their lines to reflect true probability more tightly than any soft book. Here’s the Python:<\/p>\n Pinnacle’s moneyline on Dallas Stars vs Minnesota Wild (NHL, market 151 \u2014 Winner incl. OT\/SO):<\/p>\n Now check every US sportsbook \u2014 is any of them offering better<\/em> than Pinnacle’s fair odds?<\/p>\n Every US book is pricing worse<\/em> than Pinnacle’s fair line. Kelly says bet zero on every one of them. That’s the discipline \u2014 most games don’t have an edge, and Kelly’s job is to tell you that.<\/p>\n Contrast this with flat-staking, where a retail bettor might slap 1% on Minnesota at DraftKings because they “like the value.” Kelly says no \u2014 you’re giving up 5.7% in expected value before the puck drops.<\/p>\n Manchester City vs Arsenal, Premier League, 1X2 market. Pinnacle’s three-way line:<\/p>\n Compare to Betfair Exchange’s draw price of 3.80 and Unibet.nl’s Arsenal price of 4.60:<\/p>\n This is what a realistic +EV Kelly bet looks like. Tiny edges, tiny stakes. On a \u00a310,000 bankroll, full Kelly on Arsenal at unibet.nl is \u00a346. Quarter Kelly is \u00a311. That’s not glamorous \u2014 but compound it across 2,000 bets a year and you’re ahead.<\/p>\n If a Kelly calculator ever tells you to bet 10%+ of your bankroll on a single event, your probability estimate is almost certainly wrong. Which brings us to Example 3.<\/p>\n Paddypower was offering 2.20<\/strong> on Manchester City in the same match \u2014 a huge price compared to Pinnacle’s 1.877 fair odds. Plug it into Kelly:<\/p>\n Full Kelly says stake 10.99% of your bankroll. Do not do this.<\/p>\n A 13% edge over Pinnacle on a marquee Premier League game is not real. Paddypower’s 2.20 is almost certainly a price boost<\/strong> \u2014 a marketing promotion with a tiny max-stake cap (often \u00a310\u201325) and a TOS clause that voids arbitrage-style betting. Kelly has no way to know this. It just sees “price + probability” and crunches.<\/p>\n This is exactly why professional bettors use fractional Kelly<\/strong> \u2014 typically 1\/4 or 1\/2<\/strong> \u2014 to protect against the two things Kelly can’t see:<\/p>\n Fractional Kelly caps your downside when either of those assumptions breaks.<\/p>\n Professional sports bettors almost universally use some variant of fractional Kelly, typically 0.25. A 1\/4 Kelly bettor gives up about 3\/4 of Kelly’s theoretical growth rate in exchange for dramatically<\/em> lower variance \u2014 and most importantly, survives the inevitable runs where their probability estimates are systematically wrong.<\/p>\n Single bets are fine. The real workflow is looping the calculation across every game on the slate, every market, every book \u2014 and surfacing only the +EV bets worth taking:<\/p>\n Pipe the output to a CSV, filter by your book whitelist, and size your bets. That’s a complete +EV workflow in 80 lines of Python.<\/p>\n Things the formula won’t tell you but that will save your bankroll:<\/p>\nThe Formula (60 Seconds)<\/h2>\n
d<\/code>, with your estimated true probability p<\/code> of winning:<\/p>\nf* = (b * p - q) \/ b\n\nwhere:\n b = d - 1 (net decimal odds, i.e. profit per \u00a31 staked)\n p = true probability of winning\n q = 1 - p (probability of losing)\n f* = fraction of bankroll to stake\n<\/code><\/pre>\n\n
b*p < q<\/code>, Kelly returns negative.<\/strong> This means the bet has negative EV \u2014 don’t bet. Clip to zero.<\/li>\nThe Hard Part: Where Does
p<\/code> Come From?<\/h2>\np<\/code>. You have three options:<\/p>\n\n
def devig(decimal_odds):\n \"\"\"Power-method de-vig: normalize implied probabilities to sum to 1.\"\"\"\n implied = [1\/p for p in decimal_odds]\n total = sum(implied)\n return [i\/total for i in implied], total\n\ndef kelly(decimal_odds, true_prob):\n \"\"\"Kelly stake as fraction of bankroll. Clips negative to zero.\"\"\"\n b = decimal_odds - 1\n p = true_prob\n q = 1 - p\n f = (b * p - q) \/ b\n return max(f, 0)\n<\/code><\/pre>\ndevig()<\/code> uses the simplest normalization \u2014 divide each implied probability by the overround. For 3-way markets (soccer 1X2), power methods or Shin’s method give slightly more accurate results, but normalization is good enough for 95% of use cases and is what we’ll use throughout this post.<\/p>\nExample 1: When Kelly Says Bet Nothing<\/h2>\n
import requests\n\nAPI_KEY = \"YOUR_API_KEY\"\nBASE = \"https:\/\/api.oddspapi.io\/v4\"\nfixture_id = \"id1500023470558100\" # Dallas vs Minnesota\n\nr = requests.get(f\"{BASE}\/odds\",\n params={\"apiKey\": API_KEY, \"fixtureId\": fixture_id})\nbooks = r.json()[\"bookmakerOdds\"]\n\npin = books[\"pinnacle\"][\"markets\"][\"151\"][\"outcomes\"]\ndal_odds = pin[\"151\"][\"players\"][\"0\"][\"price\"] # 1.847\nmin_odds = pin[\"152\"][\"players\"][\"0\"][\"price\"] # 2.07\n\nfair_probs, vig = devig([dal_odds, min_odds])\nprint(f\"Pinnacle raw: {dal_odds} \/ {min_odds}\")\nprint(f\"Vig: {(vig-1)*100:.2f}%\")\nprint(f\"Fair probs: Dallas={fair_probs[0]:.4f} Minnesota={fair_probs[1]:.4f}\")\nprint(f\"Fair odds: Dallas={1\/fair_probs[0]:.4f} Minnesota={1\/fair_probs[1]:.4f}\")\n<\/code><\/pre>\nPinnacle raw: 1.847 \/ 2.07\nVig: 2.45%\nFair probs: Dallas=0.5285 Minnesota=0.4715\nFair odds: Dallas=1.8923 Minnesota=2.1207\n<\/code><\/pre>\nUS_BOOKS = [\"draftkings\", \"fanduel\", \"betmgm\", \"caesars\", \"betrivers\", \"bovada.lv\"]\n\nprint(f\"{'Book':<12} {'Side':<10} {'Offered':<8} {'Fair':<8} {'Edge':<8} {'Kelly':<8}\")\nfor book in US_BOOKS:\n b = books.get(book, {}).get(\"markets\", {}).get(\"151\", {}).get(\"outcomes\", {})\n for oid, name, fair_p in [(\"151\", \"Dallas\", fair_probs[0]),\n (\"152\", \"Minnesota\", fair_probs[1])]:\n price = b.get(oid, {}).get(\"players\", {}).get(\"0\", {}).get(\"price\")\n if not price: continue\n fair_odds = 1 \/ fair_p\n edge = (price \/ fair_odds - 1) * 100\n f = kelly(price, fair_p) * 100\n print(f\"{book:<12} {name:<10} {price:<8} {fair_odds:<8.3f} \"\n f\"{edge:+6.2f}% {f:.2f}%\")\n<\/code><\/pre>\nBook Side Offered Fair Edge Kelly\ndraftkings Dallas 1.83 1.892 -3.29% 0.00%\ndraftkings Minnesota 2.00 2.121 -5.69% 0.00%\nfanduel Dallas 1.83 1.892 -3.29% 0.00%\nfanduel Minnesota 2.00 2.121 -5.69% 0.00%\ncaesars Dallas 1.833 1.892 -3.13% 0.00%\ncaesars Minnesota 2.00 2.121 -5.69% 0.00%\nbetrivers Dallas 1.82 1.892 -3.82% 0.00%\nbetrivers Minnesota 2.07 2.121 -2.39% 0.00%\nbovada.lv Dallas 1.82 1.892 -3.82% 0.00%\nbovada.lv Minnesota 2.02 2.121 -4.75% 0.00%\n<\/code><\/pre>\nExample 2: A Real (Tiny) Edge<\/h2>\n
pin = books[\"pinnacle\"][\"markets\"][\"101\"][\"outcomes\"]\nraw = [pin[oid][\"players\"][\"0\"][\"price\"] for oid in [\"101\", \"102\", \"103\"]]\n# [1.877, 3.65, 4.37]\n\nfair_probs, vig = devig(raw)\n# Fair probs: H=0.5145 D=0.2646 A=0.2210\n# Fair odds: H=1.9438 D=3.7798 A=4.5254\n<\/code><\/pre>\n\n\n
\n \nBet<\/th>\n Offered<\/th>\n Fair<\/th>\n Edge<\/th>\n Full Kelly<\/th>\n 1\/4 Kelly<\/th>\n<\/tr>\n<\/thead>\n \n Draw @ betfair-ex<\/td>\n 3.80<\/td>\n 3.780<\/td>\n +0.53%<\/td>\n 0.19%<\/td>\n 0.05%<\/td>\n<\/tr>\n \n Arsenal @ unibet.nl<\/td>\n 4.60<\/td>\n 4.525<\/td>\n +1.65%<\/td>\n 0.46%<\/td>\n 0.11%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n Example 3: When Kelly Lies (Enhanced Prices)<\/h2>\n
offered = 2.20\nfair_p = 0.5145 # Pinnacle no-vig\n\nedge = (offered \/ (1\/fair_p) - 1) * 100 # +13.18%\nfull_kelly = kelly(offered, fair_p) * 100 # 10.99%\n\nprint(f\"Edge: {edge:+.2f}%\")\nprint(f\"Full Kelly: {full_kelly:.2f}%\")\nprint(f\"Quarter Kelly: {full_kelly\/4:.2f}%\")\n\n# Edge: +13.18%\n# Full Kelly: 10.99%\n# Quarter Kelly: 2.75%\n<\/code><\/pre>\n\n
p<\/code> is wrong.<\/strong> Pinnacle isn’t a perfect oracle. Public news, lineup changes, and weather move true probability between scrapes.<\/li>\nStep 5: The Fractional Kelly Function<\/h2>\n
def fractional_kelly(decimal_odds, true_prob, fraction=0.25):\n \"\"\"Bet `fraction` of what full Kelly recommends.\n\n Standard choices:\n 0.5 - Half Kelly. Sharper but still aggressive.\n 0.25 - Quarter Kelly. Professional default.\n 0.1 - Tenth Kelly. Ultra-conservative, common for model uncertainty.\n \"\"\"\n return kelly(decimal_odds, true_prob) * fraction\n\n# Usage on the Arsenal unibet.nl bet\nstake_pct = fractional_kelly(4.60, 0.2210, fraction=0.25)\nbankroll = 10_000\nstake = bankroll * stake_pct\nprint(f\"1\/4 Kelly stake: \u00a3{stake:.2f} ({stake_pct*100:.2f}% of bankroll)\")\n# 1\/4 Kelly stake: \u00a311.49 (0.11% of bankroll)\n<\/code><\/pre>\nStep 6: Full +EV Scanner Across Today’s Slate<\/h2>\n
import time\nfrom datetime import date, timedelta\n\ndef scan_sport(sport_id, market_id, outcome_ids, min_edge=0.01,\n kelly_fraction=0.25, min_pin_vig=0.01, max_pin_vig=0.06):\n \"\"\"Find all Kelly-positive bets for a given market on today's slate.\n\n Args:\n sport_id: OddsPapi sportId (10=soccer, 15=NHL, etc.)\n market_id: int, e.g. 101 for soccer 1X2 or 151 for NHL moneyline\n outcome_ids: list of outcome IDs for this market\n min_edge: require this much edge vs Pinnacle fair to flag\n kelly_fraction: 0.25 = quarter Kelly\n min\/max_pin_vig: reject fixtures where Pinnacle's overround is\n suspiciously low or high (data quality filter)\n \"\"\"\n today = date.today().isoformat()\n tomorrow = (date.today() + timedelta(days=1)).isoformat()\n r = requests.get(f\"{BASE}\/fixtures\", params={\n \"apiKey\": API_KEY, \"sportId\": sport_id,\n \"from\": today, \"to\": tomorrow,\n })\n fixtures = [f for f in r.json() if f.get(\"hasOdds\")]\n results = []\n\n for f in fixtures:\n time.sleep(0.2)\n r2 = requests.get(f\"{BASE}\/odds\",\n params={\"apiKey\": API_KEY, \"fixtureId\": f[\"fixtureId\"]})\n books = r2.json().get(\"bookmakerOdds\", {})\n\n # Need Pinnacle as our fair benchmark\n pin = books.get(\"pinnacle\", {}).get(\"markets\", {}).get(str(market_id), {}).get(\"outcomes\", {})\n pin_prices = []\n for oid in outcome_ids:\n p = pin.get(str(oid), {}).get(\"players\", {}).get(\"0\", {}).get(\"price\")\n if not p: break\n pin_prices.append(p)\n if len(pin_prices) != len(outcome_ids):\n continue\n\n fair_probs, vig = devig(pin_prices)\n if not (1 + min_pin_vig <= vig <= 1 + max_pin_vig):\n continue # Pinnacle data looks bogus, skip\n\n # Check every other book for +EV on every outcome\n for slug, b in books.items():\n if slug == \"pinnacle\": continue\n outs = b.get(\"markets\", {}).get(str(market_id), {}).get(\"outcomes\", {})\n for oid, fair_p in zip(outcome_ids, fair_probs):\n player = outs.get(str(oid), {}).get(\"players\", {}).get(\"0\", {})\n if not player.get(\"active\"): continue\n price = player.get(\"price\")\n if not price: continue\n fair_odds = 1 \/ fair_p\n edge = price \/ fair_odds - 1\n if edge < min_edge: continue\n stake = fractional_kelly(price, fair_p, kelly_fraction)\n results.append({\n \"fixture\": f\"{f['participant1Name']} vs {f['participant2Name']}\",\n \"book\": slug,\n \"outcome_id\": oid,\n \"price\": price,\n \"fair_odds\": round(fair_odds, 3),\n \"edge_pct\": round(edge*100, 2),\n \"kelly_pct\": round(stake*100, 3),\n })\n\n return sorted(results, key=lambda x: -x[\"kelly_pct\"])\n\n# Scan soccer 1X2 for today\nbets = scan_sport(sport_id=10, market_id=101, outcome_ids=[101, 102, 103])\nfor b in bets[:10]:\n print(b)\n<\/code><\/pre>\nPractical Guardrails<\/h2>\n
\n
p<\/code> estimate is whether your bets beat the closing line on average. OddsPapi’s historical odds endpoint<\/a> is free \u2014 pull closing prices and track CLV on every bet.<\/li>\nFractional Kelly Cheat Sheet<\/h2>\n