Sometimes I ask my players to make a roll to see if something random happens (winning a game of chance, for instance, or a wilderness encounter). These rolls won't involve adding any modifiers, they'll almost always be straight up or down rolls.
In order to preserve some mystery, I won't tell them beforehand what they have to roll in order to achieve the outcome and I'll assign a random number or range of numbers to the outcome. Primarily this is to try and move away from the 20 = good and 1 = bad mentality that my players tend to have when rolling. It also means that if I make them roll a d20 when their characters are settling down to camp overnight, even though my players might have read the DMG, it won't actually be a roll of 17-20 that results in a random encounter, and instead it'll be a roll of 4-7 instead (for instance). Keeps them on their toes.
So what I've been doing is rolling a d20 in secret and then seeing if the player rolls a matching number. If I'm looking for a range I'll just add the size of the range to my rolled number and wrap around. E.g. I roll an 18. For an event with 25% chance of occurrence I'll look for the player to roll an 18, 19, 20, 1 or 2.
From a statistics perspective the odds of rolling any particular number on a d20 is 1/20. But to roll two of the same number in a row would be 1/400, which is much less likely.
So my question is: by expecting players to match the roll of my dice instead of picking a number at random (or sticking to the suggested ones in the DMG) am I inadvertently making it less likely for them to succeed?