2026 Derby, Wagering Strategy ($100 Budget)¶
Result: $85 ticket cashed for $520.06. WIN #19 Golden Tempo ($241.20) + Exacta 19-1 ($278.86). Net +$435 (6.1×). We missed a $5,625 trifecta because we never keyed #19 on top of a tri wheel, full lessons in
postmortem.md.
This is the companion to readout.md. The first page does the handicap. This page does the betting math: market structure, exacta overlays, and the actual $100 ticket.
The exacta math, briefly¶
For each (winner, placer) combo:
market_P = (1 - takeout) / probable_payout # CD exotic takeout ~22%
fair_P = p_i × p_j / (1 - p_i) # Harville model from win probs
overlay = fair_P / market_P
EV per $1 = fair_P × payout - 1
The Harville model assumes placement probabilities scale proportionally after the winner is removed. It's a strong assumption, it doesn't account for running-style × pace-fit interactions on placement. We'll come back to this.
Source code: src/exacta.py. Probable grid: data/races/2026-kentucky-derby/exacta_probables.txt. Output: data/races/2026-kentucky-derby/exacta_overlays.csv.
Where the public is wrong¶
Pool: $10.7M as of ~2.5h to post. Top exacta overlays by EV per $1 bet:
| Rank | Combo | Pays $1 | Market P | Our P | Overlay | EV/$1 |
|---|---|---|---|---|---|---|
| 1 | #4 Litmus Test → #18 Further Ado | $588 | 0.13% | 0.83% | 6.30x | +$3.91 |
| 2 | #18 Further Ado → #4 Litmus Test | $483 | 0.16% | 0.94% | 5.79x | +$3.52 |
| 3 | #1 Renegade → #4 Litmus Test | $219 | 0.36% | 2.03% | 5.71x | +$3.45 |
| 4 | #4 Litmus Test → #1 Renegade | $254 | 0.31% | 1.50% | 4.87x | +$2.80 |
| 5 | #1 Renegade → #3 Intrepido | $346 | 0.23% | 0.95% | 4.21x | +$2.28 |
| 6 | #1 Renegade → #18 Further Ado | $35 | 2.23% | 5.01% | 2.25x | +$0.75 |
| 7 | #18 Further Ado → #19 Golden Tempo | $192 | 0.41% | 0.77% | 1.90x | +$0.48 |
What the public is hammering (avoid): - #6 Commandment → #1 Renegade ($23.05), chalk-chalk, fair - #1 Renegade → #6 Commandment ($23.03), chalk-chalk, fair-ish - #18 Further Ado → #6 Commandment ($26.95), negative EV (-$0.42/$1) - #18 Further Ado → #12 Chief Wallabee ($39.09), also negative (-$0.62/$1)
The pattern: the public is loaded on the favorites finishing 1-2 with each other. Combos involving Litmus Test underneath, or Intrepido or Albus or Potente in the place spot, are underbet.
Two big caveats before sizing the ticket¶
1. Post 1 is a rail death historically¶
Renegade drew the rail. Since the field expanded to 20 in 1975, post 1 has produced exactly one Derby winner: Ferdinand in 1986. That's 1 in 50 modern Derbies, a strike rate of 2% vs. the 5% random expectation. Post 1 underperforms by ~50-60%.
Why: at Churchill the first turn comes ~3/16 mile out, the rail can be dead by Derby Day from a meet's worth of training, and 18 horses fanning right while you're trapped inside is a lose-lose decision tree.
The ML→live drift on Renegade (4-1 → 6-1) is partially this fear, and the fear is justified. Our model penalizes post 1 by ~50% (40 vs 90 elsewhere). That may be light. If we doubled the penalty, Renegade's overlay shrinks from 1.58x to ~1.20x, still a bet, but thinner. This argues for diversifying off Renegade rather than going all-in.
2. Harville inflates Litmus-Test-underneath overlays¶
Litmus Test is a confirmed front-runner. With 4 confirmed E's in a 19-horse Derby, he likely doesn't get the lead. Without the lead, his form line says he flattens. His true place probability is probably lower than Harville's proportional assumption, maybe 30% lower.
Even at the discount, the Litmus-Test-underneath combos remain positive EV. But a $588 payout we estimate at $400 is still good, just smaller than the headline overlay number suggests.
The $100 ticket¶
Sensitivity scan (added late afternoon)¶
Before finalizing, ran 200 trials with each weight perturbed ±20% (random Gaussian, renormalized to sum to 1). The model with post-1 multiplier applied. Results:
| Horse | Bet % across 200 trials | Mean overlay | Range | Verdict |
|---|---|---|---|---|
| #18 Further Ado | 100% | 1.66x | 1.52–1.77x | ROCK SOLID |
| #19 Golden Tempo | 100% | 2.02x | 1.85–2.21x | ROCK SOLID |
| #14 Potente | 32% | 1.22x | 1.11–1.36x | Fragile |
| #1 Renegade | 0% | 1.14x | 1.01–1.25x | Cardinal says no |
| #4 Litmus Test | 0% | 1.27x | 1.18–1.39x | Marginal |
| #16 Pavlovian | 0% | 1.91x | 1.81–2.01x | Lottery (low fair P) |
The honest read: only Further Ado and Golden Tempo are robust cardinal overlays. Renegade is a rank-only play. Litmus Test is marginal but kept in exotics for asymmetric place upside.
WIN ($40)¶
| Stake | Horse | Live | If wins |
|---|---|---|---|
| $20 | #18 Further Ado | 6-1 | $140 |
| $10 | #1 Renegade | 6-1 | $70 |
| $10 | #19 Golden Tempo | 25-1 | $260 |
Further Ado is now the top win bet (rock-solid cardinal, Cox barn-pick signal). Renegade gets a smaller stake, rank says yes, cardinal-with-post-1-penalty says no, sensitivity says fragile. Golden Tempo is the rock-solid mid-priced overlay. Litmus Test dropped from the win pool (fair prob too low to clear 4% threshold reliably across perturbations) but kept in exotics where his Harville place upside is asymmetric.
EXACTAS ($54)¶
Key #18 Further Ado over (×$3 each = $9): - 18-4 ($483), 18-19 ($192), 18-1 ($34)
Key #1 Renegade over (×$2 each = $12): - 1-4 ($219), 1-3 ($346), 1-18 ($35), 1-19 ($118), 1-14 ($159), 1-8 ($47.78)
Key #19 Golden Tempo over (×$2 each = $4): - 19-1 ($133), 19-18 ($241)
Key #4 Litmus Test over (×$2 each = $8): - 4-1 ($253), 4-18 ($588), 4-6 ($335), 4-8 ($429)
Top-2 cardinal-overlay box (×$3 each = $6): 18-19, 19-18
Boosts on top three single-combo overlays (×$5 each = $15): - 1-4 (boost), 4-18 (boost), 18-4 (boost)
TRIFECTAS ($6)¶
Two part-wheels keying our overlay box (1, 4, 18, 19):
- 1 / 4-18-19 / 4-18-19, 6 combos × $0.50 = $3
- 4 / 1-18-19 / 1-18-19, 6 combos × $0.50 = $3
Summary¶
| Pool | Spend | Coverage |
|---|---|---|
| WIN | $40 | 3 horses (1, 4, 18) |
| EXACTA | $54 | 13 distinct combos, 3 boosted |
| TRIFECTA | $6 | 12 part-wheel combos |
| Total | $100 |
Outcome scenarios¶
| Outcome | Win pool | Best exacta | Trifecta |
|---|---|---|---|
| 1 wins, 4 places | $175 | $1758 (boosted 1-4) | $32 |
| 1 wins, 18 places | $175 | $280 (1-18) | $32 |
| 4 wins, 18 places | $270 | $4118 (boosted 4-18) | possible |
| 18 wins, 4 places | $35 | $3864 (boosted 18-4) | possible |
| 1 wins, 3 places | $175 | $1039 (1-3) | , |
| 4 wins, 1 places | $270 | $1521 (4-1) | possible |
| 18 wins, 19 places | $35 | $576 (18-19) | possible |
| 1 wins, anyone else covered | $175 | $0–$300 | $0–$32 |
| Renegade DOESN'T win | $0–$270 | $0–$4118 | $0 |
Best-case home runs: Litmus Test → Further Ado or vice versa (both pay $4K+ on the boosted ticket). Realistic base case: Renegade wins, decent exacta hit if any of {3, 4, 8, 14, 18, 19} places.
Pre-bet checklist¶
- Re-pull live odds within 30 min of post, they'll move
- Re-pull exacta probables (the ones above are from ~16:00, will shift)
- Track-bias check: has the rail been working today, or has speed been cooked?
- Confirm no late scratches
- Bet through TwinSpires or track windows