Modern Horizons 2
Chase card spotlight
Esper Sentinel
Showcase
- Single price
- $53.99
- Share of box EV
- 5.9%
- Pull any copy
- 1 in 3 (33.4% / box)
- Coin-flip chase
- 2 boxes ($1,076)
Chasing Esper Sentinel by cracking boxes means spending about $1,076for a 50/50 shot — vs $53.99 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 | 127.71 cards | 100.0% | Every time |
| Showcase | 31.10 cards | 100.0% | Every time |
| Extended art | 15.70 cards | 100.0% | 1 in 2 |
| Borderless | 5.49 cards | 99.6% | 1 in 2 |
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
- −31%
- Net EV per box
- −$166
- Chance to break even
- 6%
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%)
- $247
- Typical
- $365
- Average (EV)
- $372
- Lucky (90%)
- $505
The average box ($372) is $6.80 above a typical box ($365) — 2%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
- $538
- Standalone pack listing
- $60.00
- Implied pack (box / packs)
- $44.83
- EV per pack
- $30.97
- $372 / box
- Return opening box
- −31%
- Return buying packs at listing
- −48%
The box is the better deal per pack ($44.83 vs $60.00 listing). Still a losing bet on average at −31% 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 | $372 | $371(-$0.38) |
| Variance | 10387 | 10275(-1.1%) |
| Std deviation | $102 | $101 |
Buy the single instead?
Compare chasing a card by opening boxes vs buying it outright at today's price.
- Single price
- $53.99
- Pull any copy
- 1 in 3 (33.4% / box)
- Boxes for 50% chance
- 2
- Cost of those boxes
- $1,076
- Boxes for 95% chance
- 6
- Cost at 95%
- $3,228
You'd spend about $1,076 opening boxes for a coin-flip at Esper Sentinel, vs $53.99 to buy it now.
Box value distribution
25,000 simulated boxesDistribution of total card value per box across 18-bucket Monte Carlo simulation. Bars right of the box price are profitable openings.
The odds
- P(box ≥ box price)
- 5.9%
- P(box ≥ expected value)
- 47.2%
- Typical box (median)
- $365
- Average box (EV)
- $371
- Unlucky box (10th pct)
- $247
- Lucky box (90th pct)
- $505
- God box (99th pct)
- $634
Roughly 6% of boxes return more than the $538 you paid. You'd need to open about 50 boxes (~$26,900) for a 95% chance that even one of them breaks even. A typical box (median $365) is $6.80 below the $372 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 $372 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 $372 expected box value (pull rate times current price).
| Card | Treatment | Price | Pulls/box | EV share | $/box |
|---|---|---|---|---|---|
| Esper Sentinel#328 | Showcase | $53.99 | 0.407 | 5.9% | $21.95 |
| Misty Rainforest#438 | — | $63.27 | 0.315 | 5.4% | $19.93 |
| Scalding Tarn#439 | — | $52.50 | 0.315 | 4.4% | $16.54 |
| Urza's Saga#380 | Showcase | $37.88 | 0.407 | 4.1% | $15.40 |
| Scalding Tarn#478 | Extended art | $36.00 | 0.403 | 3.9% | $14.49 |
| Misty Rainforest#477 | Extended art | $34.99 | 0.403 | 3.8% | $14.09 |
| Arid Mesa#475 | Extended art | $34.00 | 0.403 | 3.7% | $13.69 |
| Arid Mesa#436 | — | $43.00 | 0.315 | 3.6% | $13.55 |
| Verdant Catacombs#440 | — | $41.26 | 0.315 | 3.5% | $13.00 |
| Marsh Flats#476 | Extended art | $31.50 | 0.403 | 3.4% | $12.68 |
| Verdant Catacombs#479 | Extended art | $31.00 | 0.403 | 3.4% | $12.48 |
| Marsh Flats#437 | — | $38.99 | 0.315 | 3.3% | $12.28 |
| Ragavan, Nimble Pilferer#315 | Borderless | $55.59 | 0.203 | 3.0% | $11.30 |
| Force of Negation#9 | — | $110 | 0.095 | 2.8% | $10.41 |
| Solitude#307 | Borderless | $39.27 | 0.203 | 2.1% | $7.98 |
| Yavimaya, Cradle of Growth#480 | Extended art | $18.00 | 0.403 | 1.9% | $7.25 |
| Cabal Coffers#325 | Borderless | $35.00 | 0.203 | 1.9% | $7.11 |
| Yavimaya, Cradle of Growth#441 | — | $19.11 | 0.315 | 1.6% | $6.02 |
| Prismatic Vista#40 | — | $63.09 | 0.095 | 1.6% | $5.98 |
| Sword of Hearth and Home#324 | Borderless | $17.77 | 0.203 | 1.0% | $3.61 |
| Cabal Coffers#301 | — | $32.53 | 0.110 | 1.0% | $3.58 |
| Chatterfang, Squirrel General#316 | Borderless | $17.00 | 0.203 | 0.9% | $3.46 |
| Subtlety#309 | Borderless | $15.00 | 0.203 | 0.8% | $3.05 |
| Imperial Recruiter#314 | Borderless | $15.00 | 0.203 | 0.8% | $3.05 |
| Ranger-Captain of Eos#5 | — | $63.00 | 0.047 | 0.8% | $2.99 |
| Dauthi Voidwalker#397 | — | $9.00 | 0.315 | 0.8% | $2.84 |
| Sword of Hearth and Home#433 | — | $17.82 | 0.158 | 0.8% | $2.81 |
| Academy Manufactor#469 | Extended art | $6.00 | 0.403 | 0.6% | $2.42 |
| Chatterfang, Squirrel General#410 | — | $15.02 | 0.158 | 0.6% | $2.37 |
| Ephemerate#1 | — | $9.00 | 0.255 | 0.6% | $2.30 |
| Goblin Engineer#16 | — | $20.96 | 0.095 | 0.5% | $1.99 |
| Dauthi Voidwalker#450 | Extended art | $4.93 | 0.403 | 0.5% | $1.98 |
| Imperial Recruiter#281 | — | $17.91 | 0.110 | 0.5% | $1.97 |
| Force of Vigor#21 | — | $19.94 | 0.095 | 0.5% | $1.89 |
| Mirari's Wake#320 | Borderless | $9.00 | 0.203 | 0.5% | $1.83 |