Penalty shootout games: how the multiplier ladder and scoring odds work

How does a penalty shootout game work?

1. Set a stake (0.12 to 200.00 in play money in Penalty Unlimited) and a difficulty: Easy, Medium or Hard.
2. Shoot at one of the 15 spots on the goal, 5 across and 3 high.
3. Score and the multiplier climbs one step up the ladder. The stake is placed once, on the first kick.
4. Cash out to bank the stake times the current multiplier, or shoot again.
5. If the keeper saves, the round ends and the stake is lost.

The game is a ladder of decisions. After every goal you choose between a sure amount now and a bigger, less likely amount later.

What is the multiplier ladder?

The ladder is the list of multipliers you reach goal by goal. Harder difficulties climb much faster, because each goal is less likely.

Scoring the last kick on the ladder cashes out by itself. So does any goal that reaches the 20,000.00 max-win cap.

What are the odds of scoring each kick?

In Penalty Unlimited, the chance of scoring the first k kicks in a row is 96% of the stake divided by the cash-out after k goals. That rule makes every cash-out point worth the same 96% on average.

Cash-outs are cut to the cent and capped, so the exact chances depend a little on the stake. The table uses the default stake, 0.20.

Take Medium. The first goal pays 1.8×, so a 0.20 stake cashes out 0.36. The chance of scoring it is 96% × 0.20 / 0.36 = 53.3%.

At 0.20, the cap ends Hard after 11 goals, before the top of the ladder. At bigger stakes it comes even sooner.

Does where you aim matter?

No. In Penalty Unlimited, whether and when the keeper saves is fixed the moment the stake is placed. The spot you pick only decides how the shot and the dive look.

The saved kick is computed from the seeds, the stake and the difficulty when the stake is placed, before you pick a spot, so your aim never feeds into it. Aim wherever you like.

When should you cash out?

Every cash-out point returns 96% on average, so there is no best kick to stop on. The choice is about how you want your results to look.

• Cash out after one goal on Easy: you win 73.8% of rounds, each at 1.3×.
• Cash out after five goals on Medium: you win 4.32% of rounds, each at 22.24×.
• Go for five on Hard: you win 0.41% of rounds, each at 233.28×.

All three cost the same over a long session. The first is calm. The last is long losing runs with the odd huge win. Chasing a loss with a bigger stake changes the swings, not the average.

Is Penalty Unlimited fair?

Penalty Unlimited is provably fair. The kick the keeper saves comes from HMAC-SHA256 of a server seed, your client seed and a round counter. You see the server seed's SHA-256 hash before the round, and My bet history reveals the seed afterwards and replays the round from it.

The provably fair guide shows the full check, and the RTP and house edge guide uses Penalty Unlimited's first kick as its worked example.