I've been playing A LOT of Plinko over the past few weeks.
If you haven't seen it before, Plinko is a popular game on Stake.us that resembles the famous Price is Right game with the same name.
There are two major differences between the Price is Right version and the one you can play on Stake.
The first difference is that the biggest prize slots are located on the outer edges on Stake. This means that you don't want your balls to fall according to the patterns found on a bell curve. You want your balls to land on the extreme edges of the board, so that you win the biggest prizes.
The second difference is that all balls are dropped from the same position, the middle position. This means that your overall results will most likely resemble a bell curve if you launch a flurry of balls at once.
Game Configurations
Even though you don't have any decisions to make regarding where the ball is dropped or where the ball lands, you still have a hand in deciding your fate. There are two settings for the game that you can change to suit to your liking: The number of Rows, and the level of Risk.
Rows
The Number of Rows is the number of horizontal rows of pegs the ball must drop through. This does NOT correspond to the number of prize slots that are available.
The more rows you choose, the larger the field of possible results. There is always one more slot than there are rows selected. So for the 8 row config, there are 9 possible slots. For the 16 row config, there are 17 possible slots.
With more rows, you have a wider range of possible winning slots, which also means you have the ability to win a larger multiple of your original bet. With the 16 row configuration, it is possible to win up to 1000x your initial wager.
Risk
You can also choose between one of three levels of "Risk": Low, Medium, and High.
The lower levels offer a flatter payout structure, and the worst slots will pay out more. For example, all High risk will pay out only 20% of your initial bet on the worst payout slots. On the Low risk tier, some of the configurations will still pay out 70% on even the WORST outcomes.
Not only do you have the potential to lose more money (e.g. losing 80% versus losing 30% in the extreme case), but there are often more slots where you lose (e.g. 5 losing slots versus 1 losing slot).
And with that higher risk, you gain the possibility of a higher reward. For all the High risk tiers, the top prize slots are much much higher than the extremes on the Low tiers.
Configuration
For the purposes of this blog post, the combination of Number of Rows and the Risk level selected is considered a "Configuration". So one configuration might be "16 Rows/High Risk". Another configuration might be "10 Rows/Medium Risk".
House Edge
Winning Slot Probabilities
So, how do each of these configurations affect the overall house edge?
The distribution of results is going to vary based on the probability of hitting each of the prize slots. The probability of hitting each of the slots is meant to represent a bell curve, but it's difficult to say whether the probabilities assigned are meant to mimic any kind of real-world simulation results for balls dropped in a hypothetical Plinko aparatus.
If you hover your mouse over each of the prize slots, it will show you the probability of hitting that slot.
I haven't done any sampling to see how accurate these probabilities are. Since the probability of hitting the most REMOTE slot on the 16 row configurations is 0.0015%, that means you will expect to hit it once ever 66,667 trials. Trying to see whether Stake's advertised probabilities fall in line with sample trials would require MILLIONS of trials.
I really don't have reason to believe that Stake would cheat, so I'm just going to accept them at their word.
Calculating the House Edge
Since we know the probabilities of hitting each slot and we know how much each slot pays, we can calculate the house edge for every configuration. So that's what I did! There are 9 different row values to choose from and there are 3 risk levels. That means there is a total of 27 different configurations.
Lowest House Edge
So which config is the best one for the player? Which config results in the lowest house edge?
Selecting 11 Rows with High risk results in the lowest house edge. Your expected result for a $1 wager is $0.991526, which is a house edge of only 0.8474%. With this configuration, you still have the possibility of winning 120x, which will happen 0.0488% of the time, or once in every 2049 balls.
WORST House Edge
And which configuration is the worst?
The Highest House Edge happens with the 8 Row/Medium Risk configuration. This config has a 1.0944% house edge.
Additional Resources
Out of the 27 different configurations, there is just a 0.2470% difference between the best and worst house edges. For most intents and purposes, you can just assume the overall house edge is just 1% for Plinko (at least at the time of this writing).
And you can see my findings for all 27 configurations here. This page also includes the graphs for all 9 row settings such as the graph below. This graph displays the distribution of value for each of the slots for the three risk levels: High (red), Medium (yellow), and Low (green).
Looking at the graph above, you can see that for the High risk level, most of the value is given to the outside slots, where you earn up to 1000x your wager. For the High risk level, you lose a lot of value in the middle slots. And for all three risk levels, there are inflection points on the 6th and 12th slots. At these points, the distribution of value crosses over for all three risk levels.
And you'll see similar characteristics for the other Row settings. The High risk levels will all have higher value on the outer slots, and these get inverted in the middle slots.
For the full set of stats and graphs, check out my Plinko page.
Play Plinko on Stake.us!
Read more about Stake and how to register here. You can sign up using the Welcome Code JACKACE to be eligible for rakeback, which gives you funds back every time you play.
