Variance: Duel PlinkoEducation

Independent research
Reproducible from revealed seeds

UNDERSTANDING VARIANCE

A fair game can still
wipe out your bankroll.

Michael SmargiassiAuthor · ProvablyFair.org

We replayed 100 players from Duel’s revealed seeds. Same verified game, same starting bankroll, very different outcomes. Here’s what variance looks like.

1009

1009

0.2

ONE GAME. MANY POSSIBLE PATHS.

ILLUSTRATIVE

BALL PATH

PLINKO

16 ROWS · HIGH RISK

VERIFIED RTP

99.9%

100 PLAYERS

$1,000 each · $5 bets

78

Wiped out

22

Reached 10,000 bets

99.9% verified RTP. No identical journey.

PLINKO

99.9%

Verified RTP

100 PLAYERS

78

Wiped out

22

Reached 10,000

bets

Independent players100

Real revealed seeds. The same $1,000 starting bankroll.

Wiped out78

At $5 per bet, 78 players ran out before 10,000 bets.

Biggest final bankroll$8,362

Player 83’s outcome from the same verified game.

You lost your bankroll. Everyone on your feed seems to be winning. A losing streak feels like the house cheating, even when nothing is wrong, because variance is wildly unintuitive. So we replayed 100 deterministic sessions from the casino’s own revealed seeds, treating each as one player, to show how variance actually works. The game: Duel’s Plinko, ProvablyFair.org-certified, with a verified 99.9% RTP.*

*99.9% is the verified game math. Duel’s advertised 0.1% instant rakeback sits on top of it, outside the game code and this audit’s scope.

01Fair doesn’t mean smooth

On Duel’s Plinko at 16 rows, High risk, 79% of bets pay back 0.20x. Long losing runs are not evidence something is wrong; they are the published design. Nearly all of the payback sits in rare hits at the edges of the board. That is the appeal: this mode exists for the shot at the big multiplier.

Until one of those hits lands for you, a fair game and a rigged one feel identical from inside a session. The gap between what the math guarantees over millions of rounds and what it does to one bankroll is variance.

100 bets. Mostly small losses.

79 SMALL LOSSES20 OTHER WINS1 OUTSIZED HIT

Tap a bet to inspect its exact payout.

Bets 21–40 of 100

Grey: 0.2× · Blue: wins · Orange: outsized hit

Selected bet
Bet 25
Exact payout
131.21304367×
Net at a $5 stake
+$651.07
ALL 100 BETS+$614

Net result at $5 per bet

WITHOUT THE SINGLE 131× HIT−$37

Net result of the remaining 99 bets

100 consecutive real bets — seed pair #00 from our audit capture, bets 1–100. Hover or select a square for its exact payout. 79 paid 0.2×. A single 131× turned the window positive (+$614 at $5 bets). Remove that one bet and the remaining 99 net −$37.

79%of bets pay 0.20×
1 in 1,928bets hits ≥131×
1 in 32,768bets hits the 1009× corner
97%chance of zero 1009× in 1,000 bets

02100 simulated players, one real seed pair each

Our audit of Duel’s Plinko captured 8,100 live bets through ordinary, anonymous accounts and verified 162 revealed seed pairs: every seed matched its pre-committed hash, every bet reproduced exactly against our independent rebuild. Because each outcome is a deterministic function of the server seed, client seed and nonce, a revealed pair can be rolled forward past the captured bets.

To illustrate how variance works, we selected 100 of those pairs, in capture order. Each pair is one deterministic betting sequence: think of it as one player, replayed forward as though they kept betting. These are not live bets we placed: they are exactly what the live game would have produced on those seeds, and anyone can recompute every line.

One game. 100 independent players.

DUEL PLINKO / 16 ROWS / HIGH RISK / VERIFIED RTP 99.9%

Starting bankroll
$1,000

Per player

Fixed bet size
$5

Per bet, flat

Session limit
10,000

Bets, or until the bankroll cannot cover a bet

100 of 162 revealed seed pairs · Chronological sample

Each outcome is recomputed per nonce using the independently verified algorithm (audit Pass 2 reconstruction).

Inspect the published reconstruction and evidence ↗
All 100 revealed seed pairs

100 of 162 revealed seed pairs, in capture order. These are the published inputs behind the replay above.

PlayerServer seed hash (committed)Server seed (revealed)Client seed
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Scroll to inspect all 100 records. Each committed hash matches its revealed seed.

Replay method and seed selection ↑
5busted by bet 1,000
44busted by bet 3,000
62busted by bet 5,000
78busted by bet 10,000
78wiped out
22reached 10,000 bets

100 players. Find their story.

Choose an outcome, then hover or select a player to inspect their session.

Player 00 selected. ↑↑ Finished up big. Ending bankroll $5,188 after 10,000 bets.

Players 1–10 of 100
SELECTED PLAYER

Player 00

↑↑ Finished up big

Ending bankroll
$5,188
Highest bankroll
$6,168

Bankroll over the run · $5 bets

Player 00: bankroll starts at $1,000, peaks at $6,168, and finishes at $5,188 after 10,000 bets.

Hover or tap the chart to inspect the nearest recorded sample. Use arrow keys for adjacent samples, Page Up or Page Down for ten samples, Home or End for the first or last sample. Escape clears the selection.

Hover or tap the chart to inspect the session.

100 players, each starting with $1,000 and betting $5. Select a player to follow their session. The outcome is fixed by the revealed seeds; the game’s rules are the same for everyone.

Same starting point. Four outcomes.

OutcomePlayersWhat happenedSaw a ≥131×Saw the 1009×
78Median bust: bet 2,59941 of 780 of 78
2Finished $411 & $7782 of 20 of 2
5$1,224 – $2,3765 of 50 of 5
15$2,519 – $8,36215 of 1510 of 15

Read the last column carefully. All ten players who hit a 1009x finished in the top group, and none of the 78 who went bust ever saw one. 41 of the 78 caught a 131x and went bust anyway. The jackpot did not decide who was rescued; it decided who had a win worth posting. Tap a row to open that group below.

Same starting point. Four outcomes.

78 wiped out

Median bust: bet 2,599 · y-axis to $5,000

$0$2.5k$5k05k10kBets
Compare the four outcomes⌄
OutcomePlayersWhat happenedSaw a ≥131×Saw the 1009×
78Median bust: bet 2,59941 of 780 of 78
2Finished $411 & $7782 of 20 of 2
5$1,224 – $2,3765 of 50 of 5
15$2,519 – $8,36215 of 1510 of 15

All ten players who hit a 1009x finished in the top group, and none of the 78 who went bust ever saw one. 41 of the 78 caught a 131x and went bust anyway. The jackpot did not decide who was rescued; it decided who had a win worth posting. Use the outcome tabs to compare these groups.

These are the same players and the same starting bankroll. Each chart has its own vertical scale. A winning screenshot shows one path, not the experience of the whole group.

Follow a player’s session

Player 83: bankroll starts at $1,000, peaks at $8,717, and finishes at $8,362 after 10,000 bets.

Hover or tap the chart to inspect the nearest recorded sample. Use arrow keys for adjacent samples, Page Up or Page Down for ten samples, Home or End for the first or last sample. Escape clears the selection.

Hover or tap the chart to inspect the session.
Player 83: bankroll starts at $1,000, peaks at $8,717, and finishes at $8,362 after 10,000 bets.

Hover or tap the chart to inspect the nearest recorded sample. Use arrow keys for adjacent samples, Page Up or Page Down for ten samples, Home or End for the first or last sample. Escape clears the selection.

Hover or tap the chart to inspect the session.
Result
Survived all 10,000 bets
Final balance
$8,362
Biggest hit
1,009x
Hits of 26x or more
47
Longest losing streak
34 bets in a row
Peak bankroll
$8,717

Pair #83. A 131x at bet 468 keeps the session alive; a 1009x arrives at bet 2,131, and a second at 9,448. Final balance $8,362. The seeds behind this run were committed before the first bet — the same guarantee, and the same odds, as every other line on this page.

03Same seeds. Only the bet size changed.

Rerun the identical 100 seed pairs — the same bets, in the same order — and change only the stake. The outcomes don’t change. How long a bankroll survives them does:

Turn the bet-size dial

78 of 100busted within 10,000 bets
bet 2,599median bust point
22survivors

0%

25%

50%

75%

100%

0

2,000

4,000

6,000

8,000

10,000

Bets

$5 · 22

$10 · 13

$20 · 5

$5 per bet: 22 of 100 players reached 10,000 bets$10 per bet: 13 of 100 players reached 10,000 bets$20 per bet: 5 of 100 players reached 10,000 bets

0%

25%

50%

75%

100%

0

10,000

Bets

$5 · 22

$10 · 13

$20 · 5

2,000

4,000

6,000

8,000

$5 per bet: 22 of 100 players reached 10,000 bets$10 per bet: 13 of 100 players reached 10,000 bets$20 per bet: 5 of 100 players reached 10,000 bets
Bet 10,000$5: 22 remaining$10: 13 remaining$20: 5 remaining
StakeBusted by 1,000By 3,000By 5,000By 10,000Median bustSurvivors
$5 bets5446278 of 100Bet 2,59922
$10 bets47738087 of 100Bet 93713
$20 bets74869295 of 100Bet 3615

Same seeds, same outcomes. Doubling the stake more than halves the median time to bust. A smaller bet buys time to encounter rare wins; it does not change the game’s return or guarantee a profit.

Compare all three stakes⌄
StakeBusted by 1,000By 3,000By 5,000By 10,000Median bustSurvivors
$5 bets5446278 of 100Bet 2,59922
$10 bets47738087 of 100Bet 93713
$20 bets74869295 of 100Bet 3615

04What the advertised RTP actually refers to

If the RTP is 99.9%, why is your balance down? Because an advertised RTP is a statement about the game at scale: it is the average the math converges to over millions of rounds. It is not a description of a session, and at 10,000 bets it never had the chance to become one. The number on the label is real; it just lives at a volume only the casino ever plays.

This is the audit’s simulation pass: every one of the game’s 27 configurations, run for 1,000,000 rounds each (27,000,000 in total) on fresh seeds, using the independently verified algorithm. Every line below is one configuration finding its way to the advertised return.

Switch to the all-27 view and note where the orange line sits: it is the configuration on this page (16 rows, High risk), and after a full million rounds it still reads 100.74%; high-variance configurations are the slowest to settle. That is not the RTP being wrong: even after a million rounds this configuration is still fluctuating naturally around its theoretical return, and with more rounds it keeps converging toward 99.9%. The pooled result across all 27 lands at 99.92% against 99.90% theoretical, with zero chi-squared failures. Your 10,000-bet session lives in the first pixel of this chart.

Zoom out to a million rounds

ADVERTISED RTP99.9%

Reference for the dashed line

ALL 27 CONFIGURATIONS99.92%

27,000,000 rounds pooled

SIMULATED ROUNDS27M

27 configurations × 1M rounds

96%

98%

100%

102%

1k

10k

100k

1M

Simulated rounds per configuration (log scale)

Advertised RTP: 99.9%

Fair-game envelope (±3 SE)

96%

98%

100%

102%

1k

1M

Rounds per configuration · log

Advertised RTP: 99.9%

Fair-game envelope (±3 SE)

10k

100k

The pooled average of all 27 configurations: 27,000,000 rounds settling onto the advertised return, 99.92% observed against 99.90% theoretical. The shaded funnel is the envelope a fair 99.9% game stays inside (±3 standard errors, computed from the published paytables); the audited line never leaves it. Switch views to see how much a single configuration wobbles on the way there.

All 27 configurations
ConfigurationRoundsTheoreticalObservedΔ pts
1,000,00099.90%99.89%-0.01
1,000,00099.90%99.68%-0.22
1,000,00099.90%100.00%+0.10
1,000,00099.90%99.90%-0.00
1,000,00099.90%99.99%+0.09
1,000,00099.90%99.57%-0.33
1,000,00099.90%99.90%+0.00
1,000,00099.90%99.82%-0.08
1,000,00099.90%99.46%-0.44
1,000,00099.90%99.88%-0.02
1,000,00099.90%99.92%+0.02
1,000,00099.90%100.09%+0.19
1,000,00099.90%99.92%+0.02
1,000,00099.90%99.90%-0.00
1,000,00099.90%99.85%-0.05
1,000,00099.90%99.91%+0.01
1,000,00099.90%99.75%-0.15
1,000,00099.90%100.36%+0.46
1,000,00099.90%99.87%-0.03
1,000,00099.90%99.95%+0.05
1,000,00099.90%99.91%+0.01
1,000,00099.90%99.92%+0.02
1,000,00099.90%99.92%+0.02
1,000,00099.90%100.00%+0.10
1,000,00099.90%99.88%-0.02
1,000,00099.90%99.79%-0.11
1,000,00099.90%100.74%+0.84

05The audit verdictWhat this means for players

✓ VERIFIED162 / 162

Seed commitments matched

Every seed matched its committed hash. Outcomes could not be altered or swapped after the bet.

✓ VERIFIED8,100 / 8,100

Live bets reproduced exactly

Recomputed from seeds alone, with zero mismatches across every live bet in the capture.

✓ VERIFIED27 million

Simulated rounds checked

The distribution matches fair binomial math, with no chi-squared failures across the simulated rounds.

✓ VERIFIED162 epochs

Seed rotation tests passed

No seed cherry-picking: rotation-timing tests passed on all 162 real seed epochs.

THE TAKEAWAY

Fairness is verifiable.
Winning isn’t guaranteed.

Your loss verifies. Provably fair doesn’t promise you’ll win. It promises you’ll never have to wonder whether the casino changed the outcome after your bet.

Michael SmargiassiAuthor · ProvablyFair.org