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Bigbonk Studio

The maths room

How the games work, and what they really return

No mystery, no fudge. Every number here is calculated exactly from the same tables the games use, by counting every possible outcome. Nothing on this page is an estimate from a simulation.

Average return, in one paragraph

The average return of a game is the share of every coin staked that comes back, on average, over a very long run. A return of 93% means that across many rounds, 100 coins staked tend to bring back about 93. It says nothing about any one round: you can come out ahead or behind on any day. Every game on the set returns less than 100%, so over time the tin drains. That is true of all real gambling too.

All four scenes at a glance
GameAverage returnHow it was worked out
Wobble Drop93.69%Exact: all 4,096 paths through the pegs
Crown and Anchor92.13%Exact: all 216 rolls of three dice
Squish Reels94.07%Exact: all 10,648 reel combinations
Bonk Box93.33%Exact: all 84 ways to pick three holes

Where the randomness comes from

Each game draws its outcome in your browser using its built-in secure random number generator, with a rejection step so every outcome is exactly equally likely. The outcome is decided first; the animation then shows that decision. The ball follows the path that was drawn, the reels stop where they were told to, and the Bonk Box prizes are sealed in their holes before you pick.

Wobble Drop: a binomial pegboard

The ball meets twelve rows of pegs. At each row it goes left or right with probability ½, independently. The cup it reaches is the number of rights, from 0 to 12, so the number of paths into cup k is the binomial coefficient C(12, k), out of 212 = 4,096 paths in total.

Multipliers from the left edge to the middle are 50, 12, 4, 1.6, 1, 0.6 and 0.3, mirrored on the right. The weighted sum is 2 × (1×50 + 12×12 + 66×4 + 220×1.6 + 495×1 + 792×0.6) + 924×0.3 = 3,837.6, and 3,837.6 / 4,096 = 93.6914%. The two edge cups each come up about once in 4,096 drops; the middle cup about 22.6% of the time.

Crown and Anchor: three fair dice

Each die shows your symbol with probability 1/6. Over the 216 equally likely rolls, your symbol appears on no dice in 125, on one die in 75, on two dice in 15 and on all three in 1. A winning symbol returns its stake plus 1, 2 or 3 times the stake. For a 1-coin stake: 75×2 + 15×3 + 1×4 = 199 coins back across 216 rolls, so the return is 199/216 = 92.1296%. The house edge of 17/216, about 7.87%, is the same for every symbol and for any mix of bets.

Squish Reels: every stop counted

Each reel has 22 stops, and the line is made of one stop from each reel. The stops per symbol are:

Reel strips
SymbolReel 1Reel 2Reel 3Three of a kind pays
Crown22260×
Anchor33325×
Heart44415×
Diamond44410×
Spade4448×
Club5556×

If the line is not three of a kind, exactly two crowns pay 5× and exactly one crown pays 2×, wherever they sit. Going through all 10,648 combinations, a 1-coin stake on each would bring back 10,017 coins: 10,017 / 10,648 = 94.0740%. About 28.10% of pulls pay something.

Bonk Box: a shuffled table

The nine holes always hold the same nine prizes: 0×, 0×, 0.2×, 0.4×, 0.6×, 0.8×, 1.2×, 1.6× and 3.6×, each worth 10 coins times its multiplier. They add up to 8.4, or 84 coins. The prizes are shuffled at the start of the round, so any three holes you choose hold a random three of the nine. Each prize ends up among your three picks with probability 3/9, so the expected total is 84 × 3/9 = 28 coins for a 30-coin round: 93.3333%. Listing all 84 possible sets of three gives the same answer: 31 sets pay more than 30, 2 pay exactly 30 and 51 pay less.

Since the shuffle happens before you choose and you cannot see inside the holes, no strategy changes the odds. Bonk Box is a game of chance, not a skill game.

How we count a win

A round is a win only when more comes back than you staked. Getting exactly your stake back is shown as level. Getting part of it back, such as the 0.6× cups on Wobble Drop, is shown as a loss with the coins returned.

All coins are virtual and have no monetary value. These games are for adults aged 18 and over, for fun only. If the maths makes you want to try real-money gambling to “beat” it, please read safer play first: no strategy beats a return below 100%.

Before the cameras roll: are you 18 or over?

Bigbonk Studio is a free social casino for adults. Every game uses virtual coins that have no monetary value and can never be bought or withdrawn.

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