Plinko is a popular casino slot game developed by Gaming Arts, Inc., based on the classic TV show "The Price is Right." The game was first introduced in 2006 and has since become one of the most iconic slots among players. Despite its simplicity, the math behind Plinko is intriguing and makes it an excellent subject for analysis.
Theme and Design
Plinko’s theme revolves around a board that resembles a series of pegs arranged in a grid-like https://game-plinko.co.uk/ pattern. The game features colorful balls rolling down this board, which players aim to guide into higher-paying pockets. Each pocket has its own value, ranging from 1x the bet up to 35x the bet. When a ball drops onto the board, it randomly selects one of the pegs and then rolls towards it. Players can choose between five different betting options: $0.50, $1, $5, $25, or $100.
Symbols
Unlike many other slots, Plinko does not feature traditional symbols like fruits or icons related to a particular theme. Instead, each pocket on the board has its unique value and color scheme. These values range from 3x up to 35x the bet and are divided into several colors: red (5-10x), green (8-25x), blue (15-50x), purple (20-60x), orange/yellow (22-90x), and two gold pockets worth 30 and 35 times the bet.
Payouts
Since Plinko’s payouts are directly tied to the balls’ final position on the board, we must analyze the overall probability of landing in each pocket. As mentioned earlier, there are five different betting options available for players, but this choice primarily impacts the potential maximum win rather than influencing the likelihood of hitting specific pockets.
To calculate the expected value (EV) of each bet size, let’s consider a simplified example using only the base values from the board:
- Red pockets: 3x to 10x
- Green pockets: 8x to 25x
- Blue pockets: 15x to 50x
In a typical game session, players aim for higher-paying pockets with increasing frequency as their bet increases. To keep things manageable and demonstrate the general principle behind Plinko’s payouts, we will assume all betting options have an equal chance of occurring.
Now, let’s examine how these values translate into EVs using basic probability calculations:
- Assume each bet has a 100% hit rate for simplicity.
- We’re focusing on base values only (i.e., excluding special bets).
- Each red pocket would pay out between $1.50 and $10; green pockets between $8 and $25, blue pockets between $15 to $50.
Here is the calculation of EVs per bet size:
Bet Expected Value (Base Only) $0.50 – $2.65 (yes, a negative value since the house edge applies) $1 – $3.31 $5 -$16.58 $25 – $48.59
As we calculate further along with higher bets up to $100 and including potential bonuses: $0.50 bet yields an expected return of: (10% ($1,000 – $3)) / 50 = -6,300 $5 bet yields an expected return of: (22.22% $15) + (2.44% * -$45) + … > 4,700
To accurately determine EVs for each pocket value across multiple betting options, one would have to incorporate the real chances associated with winning at Plinko. Based on standard assumptions about a house edge in games similar to this type of slot machine:
- Red pockets (1-10): ~21% total hit rate (~2x 3x+ 9x +0)
- Green pockets: ~20,8% total hit rate
- Blue pockets: ~6.5%
With these probabilities in mind and our prior knowledge that we are dealing with slots which inherently favor the casino to some extent, consider how they influence overall results of expected gain/loss potential at each end (high-low values):
If every result follows this same basic structure:
1-10 = 30%, $15-$20 11-50x return = ~12%
We can see that higher amounts on boards contribute disproportionately greater numbers towards final revenue outputs.