Hippos Handicapping Preview Panel (Arc)

The Hippos Handicapping Panel — where memory and mechanisms collide, but only the horses decide.

Our ongoing exploration of the role of Large Language Models (LLM) in sports trading.

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Welcome to the Hippos Handicapping Panel — a virtual round‑table of racing minds brought to life with the help of an LLM. Each Hippo has a distinct voice:

1. Mick – Aussie handicapper and professional punter
2. Pearl – Canadian academic and causal analyst
3. Philip – British host who keeps them honest and sneaks in his own Weekend Warrior longshots

Together they blend events and explanations into a lively debate that is equal parts analysis and paralysis.

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Prix de l'Arc de Triomphe Preview - Longchamp, Sunday 5th October 2025

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Note

Late changes (going, jockey, withdrawal) may make the following analysis less valuable. Tread carefully!

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PHILIP (Host)

Good day, racing fans, and welcome to a special edition of the Hippos Panel. We are previewing Sunday's Qatar Prix de l'Arc de Triomphe – Europe's championship middle-distance test, worth over £2.3 million to the winner. Seventeen declared, soft ground, and the racing world watching.
The Arc is a maze you run with a compass, not a map:

1. Low draw + honest pace is a course configuration gift.
2. Low + slow can be a trap.
3. From stall 1, Minnie Hauk owns the shortest path if Soumillon finds an early escape.
4. Aventure is Longchamp-proof off the Vermeille.
5. Sosie (3) is the tidy causal line if pace is even.
6. Japan’s main hopes (Byzantine Dream and Croix Du Nord) in stalls 15/17 pay a “wide tax” unless the race lifts mid-straight. But, Alohi Alii has a sweet-spot draw!

Mick, you have a good long-term memory, what does the race base tell you?

MICK (Memory Lane)

No worries mate! I got this covered.

Right, the Arc – seventeen renewals I've backed in with intent, won on four, placed on another six. Pattern's pretty clear, mate:

What Works

1. Vermeille winners – see Aventure, just won the Vermeille at this track.
2. Three-year-old fillies on the upgrade – Minnie Hauk, Kalpana, Gezora all fit. Weight-for-age swing of 6lb from the older horses is massive over 2,400m.
3. Proven soft-ground form – This is Soft, capital S. Sosie has handled cut, Aventure won the Vermeille on soft.
4. Aidan’s fillies – O’Brien has landed the Arc with a filly before (Found, 2016). Minnie Hauk is unbeaten this season, five from five, and her Yorkshire Oaks win by 3.5L looked like a stroll.

What Does Not Work

1. Japanese raiders without the right Euro prep – Byzantine Dream did win the Foy, fair play, but he’s still a hybrid style. Croix Du Nord and Alohi Alii? Both talented, but I’ve seen Japanese closers get done for toe when it gets messy in the Arc. If the pace collapses and they’re six wide, game over.

The Kicker

Aventure (12). Won the Vermeille here, on this ground, at this track, two weeks ago. Beat Gezora, who’d won the Prix de Diane. That’s French Pattern gold, mate. Wertheimer & Frere, Fabre’s other Arc runner alongside Sosie. Sosie’s the talking horse, but Aventure’s the form horse.

I’m race-matching to Zarkava (2008), Enable (2017), Treve (2013 & 2014) – all Vermeille winners who went on to Arc glory. Aventure’s older, but she still ticks the Longchamp and ground boxes.

Verdict: Aventure is my selection, and Minnie Hauk for the romantics.

PEARL (Meaningful Musings)

Thanks Mick! I will take it from here.

1. Supplemented As Strong Signal (Mediator)

   €120k late entry is a real, noisy mediator: it does not cause class, but it reveals strong stable belief.
   2024’s Bluestocking is a live example of a supplement that paid off; Minnie Hauk mirrors the intent (and she’s landed stall 1).

   Caveat: selection bias — only already-good are ever supplemented.

2. Draw / Pace / Tactics (Collider)

   • The Arc’s shape means the draw interacts with early speed and traffic:

     • Low + slow can be a coffin (boxed)
     • Low + honest lets you save ground and angle out
     • High + slow is survivable
     • High + honest risks a fuel-burning cross

   • The long-run data favour stalls 2–7 — that’s causal via path length & interference costs, not magic. Winners’ cluster in 2–7 (~60%+) since 1988 backs it.

   • Implication:

     • Sosie (3) and Giavellotto (5) gain structural advantages
     • Minnie Hauk (1) needs an early extraction plan
     • Byzantine Dream (15) pays a “wide-tax” unless pace collapses

3. Going / Stamina (Mediator)

   Current read good-to-soft (3.4–3.7) reduces the top-end speed premium and increases value on efficient cruisers with 12f stamina. That keeps Aventure’s Vermeille profile robust; Sosie’s run style benefits if they do not dawdle. Japanese closers (Byzantine Dream, Croix Du Nord) are exposed to a tactical mismatch if they’re shuffled wide before the turn-in.

4. Jockey Skill (Moderator)

   Soumillon on Minnie Hauk and Murphy on Byzantine Dream are positive moderators: positioning + decision rules under uncertainty. They do not erase the configuration — they reduce variance conditional on a trip.

5. Causal Selections:

   • Primary: Sosie (3) — clean pathway: draw → tactics → performance; minimal confounders.
   • Secondary: Aventure (12) — robust to pace; mid-gate tax manageable.
   • Conditional: Minnie Hauk (1) — ceiling high, but collider risk at rail; needs luck/skill to open the path.
   • Risky: Byzantine Dream (15) — strong motor; causal path requires cross + cover + late slingshot.

PHILIP (Host, Summary)

Well, the Hippos have spoken and it only remains for me to summarize their selections and give you my Warrior bet!

1. Minnie Hauk (1) — O'Brien filly; shortest route and best recent 3G1* body of work; needs an early escape route.
2. Aventure (12) — Vermeille winner; proven at Longchamp; profile screams Arc; mid-wide draw is the only tax.
3. Sosie (3) — Fabre filly; Longchamp experience; tidy draw; honest-pace – likely winner.
4. Byzantine Dream (15) — engine is real (Foy); but draw complicates it. Needs pace collapse and luck in running.

Weekend Warrior (10/1+)

Alohi Alii (4) — Japanese runner with a sweet-spot draw; market still yawns at him; I’m EW at the bigger quotes (16/1).

If he sneaks a place, I’ll be insufferable until (at least) Tuesday.

"Character is destiny," said the ancients; for the Arc, draw, going, and pace are the paths.

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Hippos Handicapping Review Panel (LLM)

The Hippos Handicapping Panel — where memory, models, and mechanisms collide, but only the horses decide.

Our ongoing exploration of the role of Large Language Models (LLM) in sports trading.

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Welcome to the Hippos Handicapping Panel — a virtual round‑table of racing minds brought to life with the help of an LLM. Each Hippo has a distinct voice:

1. Mick – Aussie handicapper and professional punter
2. Dominic – Irish quant and market analyst
3. Pearl – Canadian academic and causal analyst
4. Philip – British host who keeps them honest and sneaks in his own Weekend Warrior longshots

Together they blend events, equations, and explanations into a lively debate that is equal parts analysis and paralysis.

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Philip

“The Cambridgeshire is run and done. Boiling Point, trained by Karl Burke and ridden by Clifford Lee, made virtually all from stall 6 and held off Indalo by a nose at 14/1. The Hippos must face the music. Let’s hear it.”

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Mick

“Well Philip, I leaned toward Fifth Column and Real Gain. The crowd weren’t shouting Boiling Point, but a few sharp punters had him. Burke’s yard was flying, and I should’ve trusted that. Sometimes the old bookmaker’s instinct gets dulled by the noise.”

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Dominic

“The model actually had Boiling Point as value, and the Betfair WOM was steady — no drift, no panic. Rated 105, tactically versatile, and underestimated from a low draw. The model didn’t predict the draw reversal, but it did highlight his ability to control pace. That was the edge.”

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Pearl

“The key driver was tactical speed. Boiling Point raced far side, made virtually all, and wasn’t challenged until late. The pace didn’t collapse — it was controlled. That’s why Treble Tee faded and Real Gain never got going. Mechanism over narrative, once again.”

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Philip

“So there you have it: Mick trusted the crowd, Dominic trusted the model, Pearl trusted the mechanism. This time, the model and the mechanism aligned — and Boiling Point delivered. The Cambridgeshire reminds us that in a field of 23, sometimes the winner is hiding in plain sight. Until next time, the Hippos remain humbled — and a little wiser.”

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Lessons Learned

• Boiling Point → tactically sharp, ignored draw bias, model pick vindicated.
• Treble Tee → faded late, hype not matched by race shape.
• Real Gain → high draw didn’t help, pace setup didn’t materialize.
• Fifth Column → well backed, but never landed a blow.

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Philip – Unlikely Brag, Likely Flop

“And before we close, a word on my speculative dart. In the 5:55, I went for Elarak at 27.00. Lightly raced, bred to be better than his mark, and with Tom Marquand booked. He didn’t just win — he bossed it. So yes, I’ll be insufferable until Tuesday (at the earliest).”

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Source:

• Racing Post – Cambridgeshire Result
• Racing Post – Elarak Result

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Co‑created with Microsoft Copilot

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DMDA Probability Thresholds

A Weekend Warrior's approach to sustainable speculation using probability thresholds and illustrated with a Taleb's Barbell Strategy example

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In our previous posts, we introduced the Dual-Metric Decision Algorithm (DMDA) as a framework combining Expected Value (EV) and Likely Profit (LP) for sports betting decisions. While EV measures average profit per bet, LP captures the expected geometric growth rate of our bankroll - the multiplicative reality facing bettors with limited capital.

This post extends that work by deriving the precise probability thresholds required for positive EV and LP, using the Rugby World Cup 2023 as a worked example of Taleb's Barbell Strategy in practice.

Mathematical Framework

For a bet with stake fraction F, decimal odds O, and bettor's estimated win probability P, the DMDA calculates win-balance and loss-balance multipliers:

• Win-Balance Multiplier: $WB = 1 + F(O-1)$
• Loss-Balance Multiplier: $LB = 1-F$

From these, we derive:

• Expected Value: $EV = (WB \times P) + (LB \times (1-P)) - 1$
• Likely Profit: $LP = WB^P \times LB^{(1-P)} - 1$

Probability Thresholds

EV = 0 Threshold

Setting $EV = 0$ and solving for P gives:

$$P_{\text{EV}} = \frac{1-LB}{WB-LB} = \frac{F}{F \times O} = \frac{1}{O}$$

Elegantly, a bet has non-negative expected value only if our probability estimate exceeds the market's implied probability $1/O$.

LP = 0 Threshold

Setting $LP = 0$ yields:

$$P_{\text{LP}} = \frac{\ln(1/LB)}{\ln(WB/LB)}$$

This boundary is stricter than the EV threshold because geometric growth is more sensitive to downside volatility.

Canonical Example

We will focus initially on this canonical betting example:

Parameter	Value
Total Bankroll (B)	$10000
Markets (M)	1
Decimal Odds (O)	1.9091
Win Probability (P)	55.00%
Stake Fraction (F)	1.00%

Market Conditions:

• Implied probability: 52.38% (decimal odds 1.9091)
• Warrior assessment: >=55.00% (conservative minimum)

Threshold Calculations:

• $F = 0.01$
• $O = 1.9091$
• $LB = 1 - 0.01 = 0.99$
• $WB = 1 + 0.01(1.9091-1) = 1.00909$

Results:

• $P_{\text{EV}} = 1/1.9091 = 0.5238$ (52.38%)
• $P_{\text{LP}} = \frac{\ln(1/0.99)}{\ln(1.00909/0.99)} \approx 0.52622$ (52.62%)

Decision: Warrior assessment of 55% exceeds both thresholds and an effective lower bound s set at 53%.

Rugby World Cup 2023: Worked Example

Consider a Weekend Warrior's barbell allocation:

• Total Bankroll: $10,000
• Total Stake: $500 (5% of bankroll)
• Safe Allocation: $450 (4.5% of bankroll, 90% of stake)
• Risky Allocation: $50 (0.5% of bankroll, 10% of stake)

Safe Allocation (Favs)

Market Conditions:

• Implied probability: 80% (decimal odds 1.25)
• Warrior assessment: >=85% (conservative minimum)

Threshold Calculations:

• $F = 0.045$
• $O = 1.25$
• $LB = 1 - 0.045 = 0.955$
• $WB = 1 + 0.045(1.25-1) = 1.01125$

Results:

• $P_{\text{EV}} = 1/1.25 = 0.80$ (80%)
• $P_{\text{LP}} = \frac{\ln(1/0.955)}{\ln(1.01125/0.955)} \approx 0.8045$ (80.45%)

Decision: Warrior assessment of 85% exceeds both thresholds

Some Insights

Conservative Estimates as Lower Bounds

The warrior assessments function as conservative minimum thresholds rather than precise probability estimates. This approach provides safety margins: if actual probability assessments exceed these minimums (likely), returns will surpass calculated expectations.

LP Threshold Criticality

The LP threshold being consistently higher than the EV threshold demonstrates why stake sizing matters even for positive-EV bets. Excessive stakes can create negative geometric growth despite positive expected value - a critical insight for bankroll survival.

Real-World Application

South Africa's victory in the Rugby World Cup 2023 validated the safe allocation approach, while maintaining exposure to potential Black Swan events preserved optionality for extreme outsiders. The mathematical framework translated effectively to practical application.

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Note: The final draft of this post was sanity checked by Claude.

# https://vendire-ludorum.blogspot.com/

<#
.SYNOPSIS
    DMDA Probability Thresholds Calculator
    
.DESCRIPTION
    Calculates the probability thresholds for positive Expected Value (EV) and 
    positive Likely Profit (LP) based on the Dual-Metric Decision Algorithm (DMDA).
    
.PARAMETER DecimalOdds
    The decimal odds offered by the market (e.g., 1.25, 50.0)
    
.PARAMETER StakeFraction
    The fraction of bankroll being staked (e.g., 0.045 for 4.5%)
    
.EXAMPLE
    .\DMDA-Thresholds.ps1 -DecimalOdds 1.25 -StakeFraction 0.045
    
.EXAMPLE
    .\DMDA-Thresholds.ps1 -DecimalOdds 50.0 -StakeFraction 0.005
#>

param(
    [Parameter(Mandatory=$true)]
    [ValidateRange(1.01, [double]::MaxValue)]
    [double]$DecimalOdds,
    
    [Parameter(Mandatory=$true)]
    [ValidateRange(0.001, 0.999)]
    [double]$StakeFraction
)

# Calculate multipliers based on DMDA framework
$LossBalanceMultiplier = 1 - $StakeFraction
$WinBalanceMultiplier = 1 + $StakeFraction * ($DecimalOdds - 1)

# Calculate probability thresholds
$P_EV = 1 / $DecimalOdds
$P_LP = [Math]::Log(1 / $LossBalanceMultiplier) / [Math]::Log($WinBalanceMultiplier / $LossBalanceMultiplier)

# Output results
Write-Host ""
Write-Host "DMDA Probability Thresholds Calculator" -ForegroundColor Cyan
write-Host "(https://vendire-ludorum.blogspot.com/)" -ForegroundColor Cyan
Write-Host "======================================" -ForegroundColor Cyan
Write-Host ""
Write-Host "Input Parameters:" -ForegroundColor Yellow
Write-Host "  Decimal Odds (O): $DecimalOdds"
Write-Host "  Stake Fraction (F): $StakeFraction ($($StakeFraction * 100)%)"
Write-Host ""
Write-Host "Calculated Multipliers:" -ForegroundColor Yellow
Write-Host "  Loss-Balance Multiplier (LB): $($LossBalanceMultiplier.ToString('F6'))"
Write-Host "  Win-Balance Multiplier (WB): $($WinBalanceMultiplier.ToString('F6'))"
Write-Host ""
Write-Host "Probability Thresholds:" -ForegroundColor Green
Write-Host "  P(EV) = $($P_EV.ToString('F6')) ($($($P_EV * 100).ToString('F4'))%)"
Write-Host "  P(LP) = $($P_LP.ToString('F6')) ($($($P_LP * 100).ToString('F4'))%)"
Write-Host ""
Write-Host "Market Implied Probability: $($($P_EV * 100).ToString('F2'))%" -ForegroundColor Cyan
Write-Host "Positive Bankroll Growth Probability: $($($P_LP * 100).ToString('F2'))%" -ForegroundColor Cyan
Write-Host ""

# Validation check
if ($P_LP -gt $P_EV) {
    Write-Host "LP threshold exceeds EV threshold" -ForegroundColor Green
} else {
    Write-Host "Warning: LP threshold does not exceed EV threshold" -ForegroundColor Red
}

Write-Host ""
Write-Host "For a bet to be considered sustainable (bankroll growth), "
Write-Host "our estimated win probability should be greater than both P(EV) and P(LP)."
Write-Host "As shown, the P(LP) threshold is always stricter than the P(EV) threshold." -ForegroundColor Cyan
Write-Host ""


# Example usage:

<# 
.\DMDA_Probability_Thresholds.ps1 -DecimalOdds 1.9091 -StakeFraction 0.01

DMDA Probability Thresholds Calculator
(https://vendire-ludorum.blogspot.com/)
======================================

Input Parameters:
  Decimal Odds (O): 1.9091
  Stake Fraction (F): 0.01 (1%)

Calculated Multipliers:
  Loss-Balance Multiplier (LB): 0.990000
  Win-Balance Multiplier (WB): 1.009091

Probability Thresholds:
  P(EV) = 0.523807 (52.3807%)
  P(LP) = 0.526188 (52.6188%)

Market Implied Probability: 52.38%
Positive Bankroll Growth Probability: 52.62%

LP threshold exceeds EV threshold

For a bet to be considered sustainable (bankroll growth),
our estimated win probability should be greater than both P(EV) and P(LP).
As shown, the P(LP) threshold is always stricter than the P(EV) threshold.

#>