#### Tonton-des-bois

##### Illusionist

You can get some nice buildings from the long events daily rewards, globaly better than the solo grand prizes...

But which Chest gives the best probability to get the more buildings ?

To calculate that, you must keep in mind the chances to get extra items that will give you more tries, so, this is what is called a "recursive"(*) function : you first calculate what your starting collected items will give you as buildings and extra items, then you must calculate what you'll get as buildings and extra items from the first extra items, then... this nested function only end when you can't do any more try.

Statistically, the 1st chest gives more chances to get buildings out of the same items amount BUT statistics are for huge numbers and you need

You can't compare your 10-15 tries with the statistics !

The statistics only say : averagely, all the people, all together, will get a higher

No matter how much item you have at the moment you do your tries, the winner is always the 1st chest as you can see below...there is an unsignificant advantage for chest 2 (half a percent of a building) if you have only between 90 and 139 items (nuts, bets, snowflakes, etc)

In the following tables I've tried differents amounts of items to show what changes or not.

The 1st "pass"(*) matches with what you receive from your starting items, the following passes are what you'll get from the extra items you've got from the previous ones...

Each recursive calculation ends when you can't afford one full try, after that, the values are greyed...

You got nuts

Chest 1 wins by default of opponent. No math required

Unsignificant advantage for chest 2 (less than half a percent of a building)

The winner is always 1st chest

A recursive function means (in this case) "an action that will have as result to do this action again... and again..."... We have nuts, they provide chests openings, those openings can give more nuts that will give more openings, etc... until you can't do one opening.

Each step provides less product for next step so you fast reach too few products for a single try.

It's like if you were doing tries using your first "pot" of nuts and putting the nuts you gain in a second pot, that's the first "pass", then you do a second pass with the second pot and fill a third one, etc

But which Chest gives the best probability to get the more buildings ?

To calculate that, you must keep in mind the chances to get extra items that will give you more tries, so, this is what is called a "recursive"(*) function : you first calculate what your starting collected items will give you as buildings and extra items, then you must calculate what you'll get as buildings and extra items from the first extra items, then... this nested function only end when you can't do any more try.

**REMARK**Statistically, the 1st chest gives more chances to get buildings out of the same items amount BUT statistics are for huge numbers and you need

**thousands**tries for the random results to approach the statistical numbers...You can't compare your 10-15 tries with the statistics !

The statistics only say : averagely, all the people, all together, will get a higher

**probabilty**with the 1st chest, not that**you**will get them...No matter how much item you have at the moment you do your tries, the winner is always the 1st chest as you can see below...there is an unsignificant advantage for chest 2 (half a percent of a building) if you have only between 90 and 139 items (nuts, bets, snowflakes, etc)

In the following tables I've tried differents amounts of items to show what changes or not.

The 1st "pass"(*) matches with what you receive from your starting items, the following passes are what you'll get from the extra items you've got from the previous ones...

Each recursive calculation ends when you can't afford one full try, after that, the values are greyed...

**Less than 50 items**You got nuts

**50 to 89 items**Chest 1 wins by default of opponent. No math required

**90 to 139 items**Unsignificant advantage for chest 2 (less than half a percent of a building)

**140 items and over**The winner is always 1st chest

**(*) Recursivity and "passes"**A recursive function means (in this case) "an action that will have as result to do this action again... and again..."... We have nuts, they provide chests openings, those openings can give more nuts that will give more openings, etc... until you can't do one opening.

Each step provides less product for next step so you fast reach too few products for a single try.

It's like if you were doing tries using your first "pot" of nuts and putting the nuts you gain in a second pot, that's the first "pass", then you do a second pass with the second pot and fill a third one, etc

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