I'm going to assume that your coin only affects ability checks because it doesn't seem to be the sort of thing that, thematically, you could whip out in the middle of combat or when you trigger a trap. It makes no difference if applied to saving throws but if applied to attacks the possibility of critical hits and automatic misses makes things more complex and requires consideration of damage dice and modifiers for completeness.
Let's assume that your target number to pass the ability check is \$t\$ (with \$1 \le t \le 20\$); which is calculated by subtracting the PC's bonuses (ability, proficiency etc.) from the DC. Ignoring the coin for the moment, they have the following chances to succeed:
If you use this coin, the chances of success are:
So, we can determine when it is better to use the coin and when it isn't and when it makes no difference.
It's obvious that if you have neither (or both) advantage or disadvantage using the coin makes no difference because the probabilities are the same either way.
For advantage, you should never toss the coin because for all values of \$t\$ not tossing has a higher chance of success.
For disadvantage, you should always toss the coin because for all values of \$t\$ tossing has a higher chance of success.
So, this method gives the player no interesting choices to make because it's completely irrelevant.
One tiny edge case is if the target is 21 to 23 - then the coin has a 50% chance of making the impossible possible but that is a sufficiently rare situation that it hardly seems relevant.
I will first point out that if the players have the time and inclination, they should always be able to find some method of getting advantage on an ability check - the Help action, for example.
Leaving that aside, there are 4 possible situations the player considering using this coin can be in:
- Advantage without disadvantage: never flip the coin; you can only make things worse.
- Disadvantage without advantage: always flip the coin; you can only make things better.
- Both advantage and disadvantage: doesn't matter; the coin can't change anything.
- Neither advantage nor disadvantage: doesn't matter; you can do the math yourself but a 50% chance of advantage or disadvantage gives you exactly the same chance as a normal roll.
This is a thematically cool and interesting magic item.
However, the mechanics just make it boring because the coin is either useless or obviously worth using or not. There is no significant choice to be made by the player here. Even the mathematically illiterate player will use this a few times and then just forget about it.
How to fix it
Do away with the negative on a fail and give it 3 charges/day with the usual 1 in 20 chance of losing its magic if you use the last charge.
I'd go with advantage on success but a +3 is OK too - its more powerful than a Bless spell but less powerful than Bardic inspiration. Or you could use those as a model and roll a die on success - possibly more in keeping with the luck feel of a coin toss.