Modern Horizons 3
Chase card spotlight
Esper Sentinel
- Single price
- $89.34
- Share of box EV
- 8.0%
- Pull any copy
- 1 in 3 (33.9% / box)
- Coin-flip chase
- 2 boxes ($1,376)
Chasing Esper Sentinel by cracking boxes means spending about $1,376for a 50/50 shot — vs $89.34 to buy the single. Keep it sealed; buy the card.
Chase pull rates
Expected cards per box and the odds of pulling at least one, by Booster Fun treatment. “1 in N” is per box, not a percentage.
| Treatment | Expected / box | P(≥1 / box) | 1 in N boxes |
|---|---|---|---|
| Standard | 144.77 cards | 100.0% | Every time |
| Borderless | 19.37 cards | 100.0% | 1 in 2 |
| Extended art | 15.24 cards | 100.0% | 1 in 2 |
| Textured | 0.31 cards | 26.7% | 1 in 4 |
| Concept art | 0.31 cards | 26.7% | 1 in 4 |
Your store's price
TCGplayer low isn't what everyone pays. Plug in what your LGS or an online seller actually charges.
- Return if cracked
- −33%
- Net EV per box
- −$224
- Chance to break even
- 2%
What you actually get
Most boxes land well below the average. Chase cards pull the mean up — your typical box is the median, not the EV.
- Floor (10%)
- $339
- Typical
- $457
- Average (EV)
- $464
- Lucky (90%)
- $598
The average box ($464) is $6.37 above a typical box ($457) — 1%of the EV comes from above-median outcomes you probably won't see.
Pack vs box economics
Should you buy a sealed box or individual packs? EV per pack is the same either way; the question is what you pay per pack.
- Box price
- $688
- Standalone pack listing
- $70.75
- Implied pack (box / packs)
- $57.33
- EV per pack
- $38.63
- $464 / box
- Return opening box
- −33%
- Return buying packs at listing
- −45%
The box is the better deal per pack ($57.33 vs $70.75 listing). Still a losing bet on average at −33% return.
Theoretical vs simulated
Closed-form math from collation weights (zero sampling noise) compared to 25,000 Monte Carlo box openings.
| Statistic | Theoretical | Simulated |
|---|---|---|
| Expected value | $464 | $464(+$0.78) |
| Variance | 10347 | 10372(+0.2%) |
| Std deviation | $102 | $102 |
Buy the single instead?
Compare chasing a card by opening boxes vs buying it outright at today's price.
- Single price
- $89.34
- Pull any copy
- 1 in 3 (33.9% / box)
- Boxes for 50% chance
- 2
- Cost of those boxes
- $1,376
- Boxes for 95% chance
- 6
- Cost at 95%
- $4,128
You'd spend about $1,376 opening boxes for a coin-flip at Esper Sentinel, vs $89.34 to buy it now.
Box value distribution
25,000 simulated boxesDistribution of total card value per box across 23-bucket Monte Carlo simulation. Bars right of the box price are profitable openings.
The odds
- P(box ≥ box price)
- 2.3%
- P(box ≥ expected value)
- 47.5%
- Typical box (median)
- $457
- Average box (EV)
- $464
- Unlucky box (10th pct)
- $339
- Lucky box (90th pct)
- $598
- God box (99th pct)
- $731
Roughly 2% of boxes return more than the $688 you paid. You'd need to open about 131 boxes (~$90,127) for a 95% chance that even one of them breaks even. A typical box (median $457) is $6.37 below the $464 average - most of the EV lives in chase cards you probably won't pull.
Where a box's value comes from
Expected contribution of each booster slot to the $464 box EV. Cards valued under $0.25are treated as $0 bulk, since penny commons and foils can't realistically be sold at their listed price.
Top cards driving box EV
Individual card contributions to the $464 expected box value (pull rate times current price).
| Card | Treatment | Price | Pulls/box | EV share | $/box |
|---|---|---|---|---|---|
| Esper Sentinel#2 | — | $89.34 | 0.414 | 8.0% | $36.94 |
| Ruby Medallion#348 | Borderless | $46.97 | 0.414 | 4.2% | $19.42 |
| Ragavan, Nimble Pilferer#11 | — | $79.98 | 0.207 | 3.6% | $16.54 |
| Phyrexian Tower#355 | Borderless | $75.60 | 0.207 | 3.4% | $15.63 |
| Polluted Delta#438 | — | $112 | 0.138 | 3.3% | $15.47 |
| Ocelot Pride#322 | Borderless | $145 | 0.103 | 3.2% | $14.99 |
| Jet Medallion#346 | Borderless | $35.70 | 0.414 | 3.2% | $14.76 |
| Flooded Strand#436 | — | $107 | 0.138 | 3.2% | $14.74 |
| Orim's Chant#323 | Borderless | $35.00 | 0.414 | 3.1% | $14.47 |
| Arena of Glory#351 | Borderless | $32.50 | 0.414 | 2.9% | $13.44 |
| Pearl Medallion#347 | Borderless | $31.40 | 0.414 | 2.8% | $12.98 |
| Wooded Foothills#441 | — | $91.13 | 0.138 | 2.7% | $12.56 |
| Kaalia of the Vast#343 | Borderless | $121 | 0.103 | 2.7% | $12.48 |
| Shifting Woodland#357 | Borderless | $29.49 | 0.414 | 2.6% | $12.19 |
| Warren Soultrader#332 | Borderless | $55.99 | 0.207 | 2.5% | $11.58 |
| Solitude#3 | — | $55.00 | 0.207 | 2.5% | $11.37 |
| Ulamog, the Defiler#383 | Concept art | $110 | 0.103 | 2.4% | $11.34 |
| Polluted Delta#356 | Borderless | $78.99 | 0.138 | 2.3% | $10.89 |
| Flooded Strand#353 | Borderless | $78.41 | 0.138 | 2.3% | $10.81 |
| Wooded Foothills#361 | Borderless | $77.92 | 0.138 | 2.3% | $10.74 |
| Bloodstained Mire#435 | — | $75.38 | 0.138 | 2.2% | $10.39 |
| Bloodstained Mire#352 | Borderless | $72.95 | 0.138 | 2.2% | $10.06 |
| Windswept Heath#440 | — | $71.33 | 0.138 | 2.1% | $9.83 |
| Sapphire Medallion#349 | Borderless | $22.53 | 0.414 | 2.0% | $9.32 |
| Warren Soultrader#414 | — | $40.68 | 0.207 | 1.8% | $8.41 |
| Phelia, Exuberant Shepherd#364 | Borderless | $20.00 | 0.414 | 1.8% | $8.27 |
| Tamiyo, Inquisitive Student // Tamiyo, Seasoned Scholar#443 | Borderless | $40.00 | 0.207 | 1.8% | $8.27 |
| Psychic Frog#344 | Borderless | $38.00 | 0.207 | 1.7% | $7.86 |
| Windswept Heath#360 | Borderless | $57.00 | 0.138 | 1.7% | $7.86 |
| Flare of Fortitude#321 | Borderless | $36.08 | 0.207 | 1.6% | $7.46 |
| Flare of Denial#326 | Borderless | $36.00 | 0.207 | 1.6% | $7.44 |
| Ocelot Pride#394 | — | $71.91 | 0.103 | 1.6% | $7.43 |
| Ugin's Labyrinth#359 | Borderless | $34.00 | 0.207 | 1.5% | $7.03 |
| Flare of Duplication#333 | Borderless | $33.87 | 0.207 | 1.5% | $7.00 |
| Six#370 | Borderless | $33.19 | 0.207 | 1.5% | $6.86 |