Ultimate Hero!

1. Ultimate Hero!

2. Ultimate Hero!: The Ultimate Board Game! Rules, Player Cards and the Math Behind The Game By: Nicholas Hart

3. How to Navigate this Manual Everything in this Slide Show is linked, so all you need to do is choose from the table of contents what you wish to read about and follow the links to navigate from there. When viewing a page use the mouse and click once to proceed one slide, or press backspace on the keyboard to go back one slide.

4. Table of Contents (click on the following link) • Rules (Pages 4-7) • Types of Spaces (Page 8) • Character cards (Pages 9-17) • Math Behind the Game (Page 18) • How probability was used (Pages 19-23) • How expected value was used (Pages 24-25) • Works Cited (Page 26)

5. Rules to Ultimate Duel • A minimum of two players is needed to play with a maximum of eight players. • Each player starts with 30 life. • Each character has a unique special move that can only be used once per game unless it gets recharged on the spot marked “Special”. Each special is described on the character’s card. • To start, each player takes a turn rolling two dice, and they proceed to move the number of spaces equal to the sum of the two dice. • As each player lands on a space they must do whatever the space indicates. The spaces are as followed; recover three life, lose three life, do double the damage on your attack (when you duel that round), take double damage (when you get attacked on that round), special (recharges your special attack) and lastly redirection spots mean follow the arrows and move the number of spaces they indicate. Return to Table of Contents

6. Rules Continued.. • Once each player has rolled and landed on their space, now the dueling takes place. The first to attack is the first player who rolled and going down in order from there until each player has had a chance to duel that can. Dueling happens if you are on a spot that is touching any spot with another player on it, you must duel with them and however many people are in the same radius. For example, if you land on space five you will duel with anyone on spaces four, five, six, seven, eight or nine. If you get to duel then you do not get to attack anyone and you are done for the round unless someone else attacks you. The only way to attack another player is if you have not had a chance to duel for that round before it would be your turn to commence a duel. If a player is not attacked and is not close enough to duel anyone else, then that player loses one life, and their turn is over. Return to Table of Contents

7. Rules Continued • The process of dueling is quite simple. All players who are in a duel must take turns rolling two dice. The winner is the player with the highest number rolled, and all other players take damage equal to the difference from the highest roller to their roll. If there is a tie for the highest roll, the tied players each roll two dice again until there is no longer a tie. Then all other players take damage equal to the difference of their roll to the original highest roll. For example, if two out of 4 players rolled a 12 (which is the highest) the two players who rolled a 12 would roll again, lets say one got 8 and the other got 10. Then the player who rolled a 10 would have the highest roll, and all players take damage equal to the difference of their roll to 12. Thus, some players may take zero damage if their roll was equal to the highest. • To use a special the player must proclaim that they wish to use their special attack prior to the start of the duel, except for Little Mac. Little Mac’s special can take place anytime his player rolls a four or less. Return to Table of Contents

8. Rules Continued • Once all the dueling has taken place, then each player returns to the start square and this process is repeated (the player who starts a new round, is always the person to the left of the initial roller of the previous round) until there is only one player left, meaning all other players have lost all their life. The surviving player will have earned the title as the Ultimate Dueler. Return to Table of Contents

9. Types of Spaces on the Board • Special = Recharge your special move. • Give/Take Double Damage = while on these spaces during a duel. • Hurt (-5 life)/Heal (+5 life) = instantly upon landing on space. • Move forward or backwards 2 = instantly upon landing on space. • Move to the right/left 1= instantly upon landing on space. • Free Space (Good Luck! and Ultimate Hero!) = Character receives no benefit from this space. Return to Table of Contents (Click on the space title to learn about it’s placement on the board.)

10. Bill Clinton Hulk Hogan Batman Green Goblin Superman Little Mac Harry Potter Darth Vader Character Card Return to Table of Contents

11. Bill Clinton • Color = Blue • Special = FBI Attack; does double the damage to each player. (take your attack roll, double it, and that is your new attacking number). • Read more about Bill Clinton here. Return to Table of Contents Return to Character Card Index

12. Hulk Hogan • Color = Yellow • Special = Back Breaker; does instant damage of 6 life to all players in the duel. (no roll is necessary for this attack in a duel). • See Hulk Hogan wrestle The Rock here. Return to Table of Contents Return to Character Card Index

13. Batman • Color = Purple • Special = Use Bat Mobile; escape a duel with no damage. And move to any space where you will not have to duel (excluding “special”), if none exist then stay where you are and receive no damage. • Learn more about Batman in this Video Return to Table of Contents Return to Character Card Index

14. Green Goblin • Color = Green • Special = Use hover craft; escape a duel with no damage and move to any space but “special”. • See the Green Goblin duel with Spiderman here. Return to Table of Contents Return to Character Card Index

15. Superman • Color = Red • Special = Laser Eyes; (damage each player in duel 4 life then fly away to nearest heal space). • Learn more about Superman in this Video Return to Table of Contents Return to Character Card Index

16. Little Mac • Color = White • Special = Upper Cut; triple damage on any attack of your choice that is less than or equal to 4. • Learn more about Little Mac in this Video Return to Table of Contents Return to Character Card Index

17. Harry Potter • Color = Orange • Special = Cast a protection spell; take no damage for current round and following round. • You can check out Harry Potter’s in this movie trailer. Return to Table of Contents Return to Character Card Index

18. Darth Vader • Color = Black • Special = Use the force; if player rolls doubles in a duel it takes half the life of all characters. • See Darth Vader duel here. Return to Table of Contents Return to Character Card Index

19. Math Behind The Game • Probability and Expected Value were both concepts used in determining how to construct this game. • The following Slides will describe how each of these concepts were used and why. • Here is a link to a site describing math concepts of another game, NBC’s “Deal or No Deal”. Return to Table of Contents

20. Probability • Since two dice are rolled in this game to determine how many spaces each player should move, caused me to make the game board 12 spaces long and a continuous loop. This is because I assigned each space a probability to represent the likelihood of landing the space. • The next slide is a table of all the probabilities and possible combinations to get each number. Return to Table of Contents

21. Table of Probabilities for 2 Dice Return to expected value slide Return to Table of Contents

22. How I chose what to put on each space on the board • Special Space was valued as the most beneficial space, so because 12 is tied with space 2 as the least likely spaces to land on and since 12 is farthest from the start I labeled space 12, Special. • Take Double Damage and Give Double Damage are the second most influential spaces so these were awarded 3 of the next 4 lowest probabilities, spaces 2,10, and 11. Also having them so close together can make the game a bit more exciting if a group of players all have to duel around those spaces. Return to Table of Contents Return to Types of Spaces

23. Space Choosing Continued • The third most influential spaces are the heal and hurt spaces where you gain or lose 3 life. These spaces were awarded to the spots that held the mid-range probabilities of all the possible lots. The lots chosen were 3,4,6 and 8. These are all spots that will be landed on frequently so they should have some form of immediate impact on the game. • The fourth most influential spaces are the move 2 forwards or backwards space along with the move 1 to the right/left space.The move two space was assigned lot 7 because it is the most likely number to rolled so the best way to make the game more interesting is to have space 7 move the player elsewhere, hopefully toward fellow duelers. Likewise move 1 to the right space was awarded lot 9, which will send the player to a “hurt” space. Return to Table of Contents Return to Types of Spaces

24. Space Choosing Continued.. • The final spaces to be chosen are the two empty spaces. They will be labeled, Good Luck!, and Ultimate Hero!. Ultimate Hero! was chosen to be on lot 1 because it is impossible to roll a 1 with two dice. Lot 5 was assigned Good Luck! because lot 5 is right in the middle of the board where a lot of the action will take place. It will not benefit the players much to land on it, so it will make the duels around it more meaningful. Return to Types of Spaces Return to Table of Contents

25. Use of Expected Value • Expected Value was used in the creation of this game to find what the expected sum of the dice to be rolled would be. By referring to the table we can easily compute the expected value for the sum of the two dice. • E(sum of two dice) = 2(1/36) + 3(2/36) + 4(3/36) + 5(4/36) + 6(5/36) + 7(6/36) + 8(5/36) + 9(4/36) + 10(3/36) + 11(2/36) + 12(1/36) = 7 Return to Table of Contents

26. Expected Value Use Continued • Knowing that the expected sum of the dice is going to be 7 I was able to decide how much life each player would start with. Knowing that the average would be seven, any given player could expect to lose/attack for around 5 life per turn. This was found by taking the max 12 - expected 7 = 5, and the expected 7 - min 2 = 5. • Prior to planning I figured the game should last about 10 turns to complete. So if a player wins half the duels in a two player game, then they would do about 5 damage to the other player half the time. I then took 5 (damage done)*5(half the turns causing damage during a duel) = 25. Thus the starting life for a player should be about 25. I decided to add 5 to it to take into consideration that the more players playing one would need more life, which is how I arrived at a starting life of 30. Return to Table of Contents

27. Works Cited • All Images and Videos were found through www.google.com (their URL’s appear in the link) • The URL’s are as followed as they appeared in the slide show. • http://xpower.knox.edu/theknoxparent/Images/clinton-bill.jpg • http://usversusthem.files.wordpress.com/2007/11/hulk-hogan-listen.jpg • http://www.berlinwallpaper.com/Murals/York_HP/BatmanAccent2.jpg • http://www.xmwallpapers.com/wallpaper/movies/spider-man/images/green%20goblin.jpg • http://www.watchingamerica.com/images/superman_pic.jpeg • http://ui28.gamespot.com/731/dsc00515_2.jpg • http://apologies.files.wordpress.com/2007/07/harry-potter-0036.jpg • http://sithsigma.files.wordpress.com/2007/06/darthvader.jpg Return to Table of Contents

28. Ultimate Duel! This has been a presentation created by Nicholas Hart, of the NYC game creators, made for the game development contest put on by Donald Trump. Return to Table of Contents