## Tuesday, May 13, 2014

### Tiny Dice Dungeon Guide

How to calculate the chance of getting 1 result for multiple dice.

Example: You choose head over tail when playing the toss coin. However there is a catch, you will be given two times to toss the coin. If the first toss result is head, it is a win for you. But if the result is tail, you will be given another chance and if it is head for the second time around, it is still a win for you.

Playing toss coin have 50% chance for either head or tail. But how to calculate the new chance percentage if the condition is you have is to be able toss twice?

This is the formula for "Chance Stacking" when it comes to Tiny Dice Dungeon game.

Some dice when you roll it and you get 1, you will lose a turn.

New Chance for Losing a Turn = 1 - [(1- 1st Dice Chance for Losing a Turn) *  (1- 2nd Chance for Losing a Turn) * (1- 3rd Dice Chance for Losing a Turn) *  (1- 4th Dice Chance for Losing a Turn) *.....]

The formula can be extend when you roll another dice, just add (1- Dice Chance for Losing a Turn) and multiply inside the bracket.

Example for normal attack dice:

The chance of getting 1 out of 6 is 16.67% or 0.1667 in decimal.
Formula: [(1/6) * 100]

If you only roll the dice once

New Chance =  1  - [(1- 0.166667)]
New Chance = 1 - 0.833333
New Chance = 0.166667 in decimal
New Chance = 16.6667 in percentage

If you roll the dice twice

New Chance =  1  - [(1- 0.166667) * (1- 0.166667)]
New Chance = 1 - 0.694443
New Chance = 0.305556 in decimal
New Chance = 30.5556 in percentage

If you roll the dice three times

New Chance =  1  - [(1- 0.166667) * (1- 0.166667) * (1- 0.166667)]
New Chance = 1 - 0.5787030
New Chance = 0.421297 in decimal
New Chance = 42.1297 in percentage

If you roll the dice four times

New Chance =  1  - [(1- 0.166667) * (1- 0.166667) * (1- 0.166667) * (1- 0.166667)]
New Chance = 1 - 0.48225231
New Chance = 0.517747 in decimal
New Chance = 51.7747 in percentage

As you can see, when you roll the dice 4 times you will get almost 50% chance to lose a turn. It is lower compared to Quadruple 1st dice (16 x 4 = 64%) So why we need to calculate the stacking chances? The only reason why is when you dice, you will have the OPTION to dice again. If you dice again, the risk will increase but you will eventually increase your potential damage until you press the end turn.

We know that for every end turn, we receive attacks if the enemies are still alive.

How about more than 4 stack dice? You can also do 5, 8 or more dice but eventually the risk will be higher despite of high damage and low increase chance for the next dice.

I recommend that 4 stack dice is better because it has 51% chance and deal nice damage.

BUT there is ANOTHER FACTOR for deciding whether the 51% chance is enough .

It is your (attack damage vs monster HP Factor) and (monster attack damage).

Since your damage is based on chance, you should just estimate when to end turn.

I recommend that if your Monster's HP is Very High, just use the 4 stack dice 51% chance.
I also recommend that if your Hero or Allies has very low health, you can do the 51% chance or more depending on the monster's HP

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