Values ending in .5 aren't always rounded the same way. Sometimes they round down, sometimes they round up. I tested a few cards/settings and came up with the following:

Sanctions Card: Sanction amount rounds down.
50% sanction on 5 income leaves the player with 3 income.

Reinforcement Card (value set to a percentage times # of turns passed): Rounds Down
Numbers ending in .5 round down, with one exception. Anything less than 1 army will round up (you don't get a reinforcement card of +0). For example, 50% per turn times 5 turns = 2.5, which rounds down to +2 armies.

Emergency Blockade/Blockade Card: Rounds Down
3.5 * 3 armies = 10.5, which rounds down to 10. This is why blockade cards are set to 351% in strategic games.

Bomb Card (halves armies on affected territory): Rounds down
Bombing 5 armies leaves 2 remaining (50% * 5 = 2.5, which rounds down).

Kill rates (offensive and defensive): Rounds up
These round up from .5. For example, with 5 defenders and 70% defensive kill rate, you will kill 4 attackers (5*.7 = 3.5, rounds up to 4). For the standard offensive kill rate, this is never an issue, but it works the same if it is modified to 70%.

Attack by percentage: Rounds down.
50% with 5 available attackers will move 2 armies. 50% * 5 = 2.5, rounds down to 2.

If you can think of others add them below and I'll update this post.

Edited 1/8/2017 01:42:57

useful post is useful!

nobody will ever understand the enigma that is Fizzer's thinking process

It's probably not the thinking process, just how these cards are programmed/how the data is stored/which values are actually rounded (e.g., the amount of troops remaining or the amount of troops lost).

Attack by percentage: Rounds down. 50% with 5 available attackers will move 2 armies. 50% * 5 = 2.5, rounds down to 2.

So that's why...! I'd include this information in your Attack By Percent knowledge bomb.

Once again, thank you so much for the share!

Edited 1/24/2017 03:37:21

Yeah I reckon knyte is right, like sanction cards, for a 5 income, 50% sanction, income=5*0.5=2.5 rounds up to 3. Maybe just depends on which value is being rounded in fizzers code.

i thought the same thing at first too

as in you could round two parts of the variable - either the number itself or the amount taken away from a number

but then... why would reinforcement cards round down? o_O

Edited 1/29/2017 06:54:31

If, for example, you wanted to set the card so that you get 1 reinforcement for every two territories, it would be odd if you got 2 for having three territories. Really any decimal should round down to follow that rule correctly. Did you check the rounding with decimals above .5 jz?

Edit: clarification

Edited 1/30/2017 00:32:30