Same Pack vs Multiple Packs: Should You Buy 5 Scratch-Offs From One Vending Machine?

We previously settled the one store vs. five stores debate. The data answer was: where you buy matters more than how many places you buy from.

This post answers the within-store version of that question. Walk into a typical NY convenience store and you will see something like this: a counter rack behind the register, plus one or two free-standing vending machines along the wall. Each of those is dispensing from a different active pack, even when they are selling the same $10 game.

So here is the real question: at a store with three active packs of $200,000,000 Cashword, should you buy all 5 of your tickets from the same vending machine, or pull one from each source?

What is actually inside a pack

NY Lottery packs are sized by price tier. Lower-price tiers get larger packs so that retailers receive a manageable inventory unit; from $5 up, every pack holds exactly 50 tickets, so the face value scales directly with the price.

The number of winners per pack is approximately fixed by the game's prize structure. The order of winners and losers inside the pack is randomized, but the contents are predetermined when the pack is printed.

That single fact — predetermined contents, randomized order — is what separates the same-pack and multiple-pack strategies mathematically.

Same pack: hypergeometric (slightly tighter)

When you buy 5 consecutive tickets from one pack, you are sampling without replacement. The pack has a fixed number of winners, so each ticket you remove changes the probability for the next one. This is the hypergeometric distribution.

For a $10 pack with 50 tickets and ~16 winners, the variance of "how many winners do I get in 5 tickets" works out to:

Var(same pack) = n · (K/N) · (1 − K/N) · (N − n) / (N − 1) = 5 · 0.32 · 0.68 · 45/49 ≈ 1.000

Compared to drawing 5 tickets from independent packs, where each draw is fresh:

Var(independent) = n · p · (1 − p) = 5 · 0.32 · 0.68 ≈ 1.088

So same-pack draws have about 8% lower variance on win count. Statistically real, practically tiny on a 5-ticket buy. Same expected number of winners either way, just slightly less swing.

Multiple packs: more shots at the rare big winner

The win-count variance is a sideshow. The interesting variance is in the tail: who has a shot at the unclaimed top prize?

Most NY scratch-off games print on the order of 10–30 million tickets and have somewhere between 4 and 15 top-prize winners across the entire print. Top prizes are therefore in roughly 1 out of every 1–5 million tickets, which means they live in roughly 1 out of every 20,000–100,000 packs.

Once a pack has been activated and partially sold, two things are true:

1. If a top prize was inside that pack, it's either already been claimed (someone got it) or it's still in the unsold portion.
2. You as a buyer don't know which case you're in.

Buying 5 tickets from one pack means your shot at a top prize is entirely tied to whether that single pack ever contained one. Buying 5 tickets across three different active packs at the same store gives you three independent rolls of that very rare die.

The store layout matters

A typical NY retailer has more than one ticket source for the same game running simultaneously:

• Counter rack — one active pack per game, sold by the clerk on request. Tends to turn fastest because every walk-in customer touches it.
• Vending machine A — one active pack per bin per game. Self-service. Often loaded later in the day or when a bin runs dry.
• Vending machine B — a second machine if the store is bigger. Independent inventory cycle from machine A.

For a popular $10 game, that is up to three concurrent active packs at the same retailer. They were activated at different times, are at different points in their burn-down, and have completely independent prize layouts.

The simulation

We modeled three within-store strategies on a $10 game, $50 spend (5 tickets), 100,000 trials each. Each pack draws its own top-prize-present indicator from the game-level rate, then independently draws each ticket's outcome from the pack contents.

The expected value is identical to the penny

$31.04 vs $31.05 vs $31.05. As with the cross-store version, no allocation strategy can move expected value, because the average payout per ticket is fixed by the game.

Same-pack is smoother on small outcomes

One pack gives you the lowest win-count variance and the slightly higher chance that some ticket pays back something. If you buy 5 from one machine, you are marginally more likely to walk out with at least a small win.

Multiple packs is the only way to expand top-prize coverage

This is the part nobody talks about. Spreading across two packs doubles your chance of ever touching a pack that contains an unclaimed top prize. Three packs triples it. The probability of any individual win is still microscopic, but the only lever you control as a buyer is how many independent packs you have inventory in.

What about pack age? Counter vs vending

Counter packs typically turn over faster than vending packs because every walk-in customer interacts with the clerk, while only self-service buyers touch the machines. As a rough rule:

• Counter pack age: ~1–3 days for high-volume stores
• Vending pack age: ~3–10 days, depending on the game's popularity

This matters for our hazard model. We separately track how close each game is to having all top prizes claimed. Older active packs in low-velocity vending bins are more likely to belong to games that have already had top winners claimed elsewhere, simply because the pack has been sitting longer in a market where the broader top-prize pool may have shrunk in the meantime.

If you're targeting a game we've flagged as fresh and unclaimed, both counter and vending packs are equally good prospects. If you're playing an older game whose remaining top prizes are scarce, the freshly-restocked counter pack is structurally a better bet because it represents one new, randomly-chosen pack out of the small remaining pool.

Practical playbook

Important caveats

1. None of this changes expected value. The statewide payout rate for $10 NY scratch-offs is around 70–72%. You still lose ~28–30 cents per dollar long-term, regardless of how you split the buy.
2. Pack coverage only matters for tail outcomes. Most plays result in small wins or losses; the difference shows up only across thousands of buys, when the rare top-prize trial actually fires.
3. You can't see pack age. The clerk doesn't know which machine has the freshest pack. Our Store Finder incorporates a fresh-inventory factor based on settlement-data jumps, but at the within-store level it's a black box.
4. Vending machine bin assignment is random. A game can be in machine A this week and machine B next week, depending on what the clerk loads. Don't try to "remember" which bin won — the bin doesn't have memory, the pack does, and the pack rotates.

Bottom line

Same pack vs multiple packs is not a debate about expected value — it's a debate about pack coverage. Concentrating in one pack smooths your small-win outcomes by a few percent. Spreading across packs at the same store is the only way to multiply your shot at being on an unclaimed top-prize pack.

If your store has a counter and two vending machines, treat them as three independent shots, not one. Same store, same trip, three packs. That is the cheapest free upgrade available in this entire game.

Related articles

• Should You Buy 5 Scratch-Offs at One Store or Spread Across 5 Stores?
• Which NY Scratch-Offs Are Running Out of Top Prizes Today
• How Many Scratch-Off Tickets Are in a Roll?
• NY Scratch-Off Delivery Schedule
• 5 Scratch-Off Strategies That Actually Work

Pack sizes from official NY Lottery retailer documentation. Prize structures from nylottery.ny.gov. For entertainment and informational purposes only. Please play responsibly.