Mario Party Superstars Notes With Some Math

avatar

Hi there. In this post, I cover some mathematics and probability cases from the Mario Party Superstars video game on the Nintendo switch.

I do warn that this post is very long.


Pixabay Image Source

 

Topics


  • Thoughts On Mario Party Superstars
  • Simple Math Cases
  • Math & Probability In Some Mini Games
  • Items & Simple Probabilities
  • Probabilities With One Die
  • Sum of Two Dice Probabilities
  • Sum of Three Dice Probabilities With Python Code
  • Other Math/Probability Cases

 

Thoughts On Mario Party Superstars


Mario Party Superstars is a Nintendo game released on the Nintendo Switch on October 29, 2021. This is the second Mario Party game after Super Mario Party for the Switch. The game features 5 classic Nintendo 64 Mario Party boards with a large selection of minigames from previous Mario Party games.

Game modes include same-system, local wireless and online play. Players can collect points for unlocking items and there are achievements to be earned.

The goal of Mario Party is to collect the most stars at the end of the game on the board. Stars can be purchased with the in-game currency of coins. If there is a tie in stars, the player with the most coins wins. Items can be used to advance faster on the board, cause havoc on rivals, steal coins, steal items, unlock hidden paths, move Toadette star locations and more. Items can be purchased from an item shop or earned from Lucky Spaces, item mini games or sometimes the big enemy Bowser. Minigames at the end of each turn and from VS Spaces are for earning more coins.


Pixabay Image Source

 

Variations On Some Minigames

I come from mostly Mario Party 2 and a little bit from Mario Party 3. Some of the minigames have been altered a little bit. It is not just graphics that have been changed. Some of the minigames have different objectives or win conditions.

You can win a few coins if you come in second or sometimes third in a four player minigame.

In Mario Party 2, the mini-game Dizzy Dancing used to be whoever can navigate the random controls and touch the music note first wins. With Mario Party Superstars, the Dizzy Dancing minigame win condition is to collect as many music notes as you can.

Hot Rope Jump seems easier on Superstars than in Mario Party 2. If 2 or more players make it to 99 jumps the game ends and surviving players win. There is an endless mode for those who want to get 9999 jumps.

The 3 v 1 game of Archer-ival has a different animation when the three-player team wins. Surviving players behind the wall celebrate with their panels.

Item mini games are back. The barrels item mini game is in some room instead of the outdoor Pirate theme from Pirate Land in Mario Party 2. The Hammer slammer item mini game no longer has a space theme.

Gameplay footage of me and brother on Hot Rope Jumps max 99 jumps.

 

Only 5 Mario Party Boards

This game has made a large amount of minigames available but they give just 5 boards. I wish they had more boards from the older Mario Party games. Here are the boards.

  • Yoshi's Tropical Island (Mario Party)
  • Peach's Birthday Cake (Mario Party)
  • Space Land (Mario Party 2)
  • Horror Land (Mario Party 2)
  • Woody Woods (Mario Party 3)

 

Regardless of board, the minigame after every fifth turn has double coins. In general, it seems easier to collect coins and to keep coins. Items are cheaper to buy than in Mario Party 2.

Space Land

Space Land in my opinion is a little bit better as there are less happening spaces. When you land on a happening space, your character moves back several spaces as it is being chased by a Whomp in a space hovercraft thing. It is a little bit better to move around the board in Space Land versus the one in Mario Party 2.

 

Horror Land

Horror Land used to have one item shop back in Mario Party 2. There are now 3 item shops in Horror land along with more Koopa Banks. Koopa banks ask for a 3 coin deposit (before last 5 turns) when you pass by instead of 5 coins back in Mario Party 2. The prices for Mr. I are cheaper. It is now 6 coins to "warp" in the day and 3 coins for the night. The Magikoopa for turning day into night has a price of 3 coins now (I believe).

There is still the daytime Boo at the bottom left with the skeleton key door. It is now King Boo instead of Big Boo at the top right. For the King Boo at night, stealing coins from all opponents is free of charge but stealing stars is stealing one star from each opponent instead of stealing all stars at a price of 150 coins. It is no longer stealing all coins or stars.

 

Bad AI Cases

badAI.PNG

Screenshot image of gameplay

The computers can be stupid. Consider a scenario where the star is eight spaces away and the CPU has a custom dice block. You would think that the CPU would use the custom dice block and select a 8, 9 or 10. Nope, the CPU would roll something stupid like a 4, 5 or even a 1 and land on a Lucky Space that is located in front of Toadette and the star.

Sometimes the CPU would go in a direction away from the star even if they are nearby and have enough coins.

There are cases where the CPU has more than 50 coins and would use Boo to steal coins instead of steal a star at a price of 50 coins.

The CPUs can make some irrational decisions on the Hard mode or Master computer difficulty.

Here is an example of bad CPU AI on the Horror Land video. I play as Mario and a family member plays as Yoshi. We spam Whaaat?!! stickers as the CPU makes a bad decision. It is like as if the CPU does not try to win.

Youtube video of bad AI case. Brother & I gameplay.

 

Simple Math Cases


The simple math cases refer to scenarios where you are adding and subtracting coins.

  • Needing to win the minigame to get an extra 10 coins or more to have at least 20 coins to buy a star
  • Golden Pipe cost at 25 coins plus a star at 20 coins requires 45 coins.
  • Triple dice at 10 coins price plus star at 20 coins requires 30 coins.
  • Half price of a star from Lucky Space outcome is 10 coins for a star.
  • Buying a star and stealing a star would be 20 + 50 coins = 70 coins.

 

Items & Simple Probabilities


Items in Mario Party can give your character an edge over the opponents. A good handful of the items do involve some probabilities. I cover dice probabilities in the next sections.

This youtube video provides a nice overview of the items in Mario Party Superstars.

Cursed Item Block

If a character is cursed from the Cursed Item Block, the choices for the die is 1, 2 or 3. Each would be a 1 in 3 chance in terms of theoretical probability. Being cursed is good for limiting the number of spaces for an opponent from reaching the star or a destination. A cursed dice block can be good for increasing the chances of landing on a nearby space like a bank space, item space, Lucky space or maybe even Chance Time.

 

Warp Block

The Warp Block item allows the user to switch places with another player at random. As there are 3 opponents on a board, each opponent has a theoretical probability of 1/3 of being chosen. Warp blocks can be really good if 2 or all 3 opponents are near the star.

A better item than the Warp Block is the Super Warp Block which allows the user to choose who to switch spots with. This item is rare and I think it can only be obtained from an Item Bag through a Lucky Space spot.

 

Plunder's Chest

In Mario Party 2, the Plunder's Chest was an option from the item shop in all the boards. With Mario Party Superstars, the Plunder's Chest can only be purchased at the bottom left item shop in Woody Woods and can be obtained from the Item Bag through a Lucky Spot Space. This item is more rare now.

The Plunder's Chest allows the user to steal a random item from an opponent of the user's choice. If the chosen opponent has one item, the chest will steal that lone item. If the opponent has 2 or 3 items held, the Plunder's Chest chooses the item at random. The chosen item has a 1/2 chance or 1/3 chance of being chosen in this case.

A strategy against the Plunder's Chest is to avoid buying expensive items such as Custom Dice Blocks and Golden Pipes. The chest could be good when opponents obtain items from item mini-games, Lucky Spaces or from an item bag that could contain a rare item.

 

Hidden Block Card

The Hidden Block Card is an item that is only available in the Woody Woods board at the bottom left item shop. This can be purchased for 40 coins. A hidden block appears when this item is used. The reward from the hidden block is either more coins or a star. Probabilities are unknown for either outcome. (You cannot really assume half for either case.)

Getting a star from the hidden block card is somewhat cheaper than buying a Golden Pipe plus buying a star. The Golden Pipe and buying star costs 45 coins compared to the hidden block card price at 40 coins with no guarantee of a star.

 


Pixabay Image Source

Probabilities With One Die


Probabilities with one die is not too difficult. In Mario Party you have a ten sided die with the numbers from 1, 2, 3 all the way to 10. The chance of hitting a certain number is 1 out of 10 or 10 percent. In a lot of cases a high roll is good as your character can move many spaces in one turn. There are rare cases where a high roll can allow for a chance of buying 2 stars in one turn!

With a Cursed Dice Block, the die is restricted to the numbers of 1, 2 or 3. You can use this Cursed Dice Block on an opponent or on yourself to limit movement or increase the chance of an opponent or you landing a certain space nearby. The probability of choosing one of these 3 numbers is 1/3 or 33.3%.


Pixabay Image Source

 

Sum of Two Dice Probabilities


In Mario Party Superstars, it is cheaper to have access to double dice. It was 10 coins in the form of a mushroom in Mario Party 2. The price of a Double Dice item in Mario Party Superstars is 5 coins.

With double dice users can move from 2 spaces all the way to 20 spaces. The probabilities with a single dice is easy. With the sum of two dice, it is not as simple. You have to consider all the combinations that makes the sums from 2 to 20. It could be done by hand but it is better to code this in with a programming language like R or Python.

I provide some Excel screenshots on looking at probabilities of getting a certain sum of two dice. There are also probabilities of getting above or below a sum of two Mario Party dice. In Excel, I create a table with all the possible sums from two ten-sided dice. The user can select a sum from 2 to 20 from the dropdown menu at the top right. With the use of COUNTIF functions in Excel I compute the probability of getting the sum, the probability of getting above the sum and the probability of getting below the sum.

Knowing some of these probabilities can be helpful with decision making. You could ask yourself if using a double dice to get a star in a certain amount of steps is a high probability play. If the star is 20 spaces away, then using a double dice may not be good as it is a 1% success play with 10 plus 10.

 

Two Dice Being Seven Case

doubleDice_seven.PNG

The double dice adding up to seven has a probability of 6%. Getting higher than a seven on the double dice is at 79% which is highly likely. This 79% is much higher than getting either 8, 9 or 10 on a single die at 30%.

Two Dice Being Ten Case

doubleDice_ten.PNG

For the double dice being exactly 10, that is a 9% chance. You are better off rolling a single die if you want exactly a ten (assuming equal probabilities for 1 to 10).

Getting above a 10 on the double dice is 55%. This probability is good slightly better than a coin flip for moving more than 10 spaces.

 

Sum of Three Dice Probabilities With Python Code


Having triple dice is much better than double dice. You can move from 3 spaces all the way to 30 spaces with triple dice. The cost of triple dice is 10 coins compared 20 coins in the form of a golden mushroom from Mario Party 2.

In this section, I feature Python code in obtaining the probabilities for the sum of 3 ten sided dice. For those not interested in the code, you can consider a calculator from this link.

 

Python Code

To save space I do not want to go into details on the Python code. I want to share insights from the results.

import pandas as pd
import numpy as np

# Sum all possible combinations on Mario Party triple dice
sample_space = [a + b + c for a in np.arange(1, 11) for b in np.arange(1, 11) for c in np.arange(1, 11)]

# Convert into dataframe:
sums_df = pd.DataFrame(sample_space, columns = ["Sum"])

# Obtain counts:
sum_probs_df = pd.DataFrame(sums_df['Sum'].value_counts(normalize = True).sort_index())

# Rename column & Index
sum_probs_df = sum_probs_df.rename(columns = {'Sum': 'Probability'})
sum_probs_df.index.name = "Sum"

# Add cumulative probability, probability of getting sum less than the number (index):
# Shift of 1 needed as you cannot roll less than 3 on 3 MP dice:
sum_probs_df["Pr(Roll < Sum)"] = sum_probs_df["Probability"].shift(1).cumsum()

 

python_sum3Dice.PNG

From the screenshot table output above, we have a table for the probabilities of rolling a sum from the triple dice in Mario Party.

Rolling exactly a 3 is 1 out of 1000 of 0.1%. Rolling a 30 is also 1 out of 1000 as you need 10, 10, 10. This one tenth times one tenth times a tenth.

The most probable sums are 16 and 17 at 7.5% each. Rolling a 16 or a 17 on the triple dice would be 15%.

I found it important to add a new column for the probability of getting the sum being less than a number. From the table the probability of rolling less than a 10 on the triple dice is 0.084 or 8.4%. You can also say that rolling a 10 or higher is 0.916 or 91.6% (1 minus 0.084).

Rolling less than 17 is 50%. Alternatively rolling a 18 or higher is 50% as well.

Rolling less than 23 is 88%. Rolling a 24 or higher is 12%.

A triple dice roll less than 20 is 71.7%. Rolling a 20 or higher is 0.283 or 28.3%. For those who want to chase a star that is 20 spaces away, the chance of getting that star with a triple dice roll is not very likely.

In summary, a triple dice greatly increases the chance of rolling a 10 or higher. This is at the cost of 10 coins in Mario Party Superstars.


Pixabay Image Source

 

Other Math/Probability Cases


Bowser Revolution

Bowser Revolution is an event from the random selector after landing on a Bowser space. In this event Bowser takes (steals) all the coins from all 4 players and distributes them evenly to everyone. Those who had very few coins may find themselves with more coins and those with a lot of coins most likely will have less coins. Each player receives the average amount of the total coins.

Here is one example. Consider the table below with the characters and their coins.

CharacterNumber of Coins Before Bowser Revolution
Mario121
Luigi72
Rosalina10
Waluigi37

 

The average amount of coins here is 60. Bowser would take all these coins and gives 60 to everyone fairly.

CharacterCoins Before Bowser RevolutionCoins After Bowser RevolutionGain/Loss
Mario12160-61
Luigi7260-12
Rosalina1060+50
Waluigi3760+23

 

Mario's coins were way above the average so he loses the most. Rosalina's coins were low before the redistribution and she gained 50 coins from the Bowser Revolution.

 

Bowser Big Blast Mini Game

I was not thrilled when they brought this mini-game back. They always have to include some sort of luck mini-game in the mix. Bowser's Big Blast is a guessing game where players take turns pressing down on one pump that they believe is safe. The arrangement is like this.

A B C D E

 

Select the wrong pump and you get eliminated. Last person standing wins. The pumps get reset if the last pump available is the unsafe one.

Whenever a player gets eliminated there are fewer pump choices to choose from. If one player is eliminated there are 4 options to choose from instead of 5. The arrangement of ABCDE turns into BCDE with three players and then BCD with the last two comepeting players. When two players are eliminated, there are 3 choices to choose from.

 

Thank you for reading.

Posted with STEMGeeks



0
0
0.000
2 comments
avatar

Now, these are applicable info to school your family this holiday season.

0
0
0.000
avatar

And the online competition too. Button mashing though, I do not have tips for that.

0
0
0.000