When you play with 1.1 ether, then the Difficulty is 118'181'817. Thats mean you have 1:118.181817 to win.
This is simple Math
no it's false. You assume you can divide both sides of the modulo and preserve the chances, it does not work like that.
the bignumber*1million should be a multiple of 118'181'817 for your contract to trigger the transaction.
that's 1 chance over 118'181'817
it's not the same as bigNumber divisable by 118 which is a chance over 118.
Btw you should know that there are no float (real) numbers in solidity so your 118.18 makes no sense.