Please correct me if I'm wrong, but I thought an infinite combo that doesn't require user at interaction results in a draw. So your first example would be this, but the tapping one isn't. It's been years since i played however.
Infinite combos that not optional but win you the game instantly, like the sanguine bond + exquisite blood combo I mentioned earlier, means you just win.
Infinite combos that are not optional but do not win you the game result in a draw.
There's the 'donate an unsacrificable islandhome creature to an opponent who has no islands'.
Infinite amount of state based checks happen that are unavoidable, and cause the game to draw.
In paper once a player has demonstrated a loop they must choose a number of times to repeat the loop and then the game is fast forwarded to the chosen end state. For example, a player might execute a loop that could gain them infinite life, but really they must choose a point to stop. Usually that player will choose 1,000,000,000,000 or another “essentially infinite” value and the game moves on.
There are infinite loops that can draw the game, but in a tournament game if one player can take an action that would end the loop, say by destroying one of the loop pieces, that player must take that action. Only if no player can end the loop does the game end in draw.
“Some loops are sustained by choices rather than actions. In these cases, the rules above may be applied, with the player making a different choice rather than ceasing to take an action. The game moves to the point where the player makes that choice. If the choice involves hidden information, a judge may be needed to determine whether any choice is available that will not continue the loop.”
Basically if a player has open information, like an activated ability, that could end the loop that player is not allowed to not use it to keep the loop going indefinitely. If that player instead has hidden information, i.e. a card in hand, that could end the loop any player can call a judge to confirm that and force the player to end the loop.
Note this doesn’t extend past cards in hand, though. If a player has some way to search their deck for a card that could end the loop, they are not forced to search and then play that card. At that level it moves from a player intentionally delaying the game with the resources at hand or in play to a judge dictating a player’s actions.
In your games with your friends feel free to ignore this rule. If you made a deck that managed to pull it off I would think it was cool.
719.5. No player can be forced to perform an action that would end a loop other than actions called for by objects involved in the loop.
The rule about choices in mandatory action comes into play for cases like an Oblivion Ring loop. If there is another valid target for the oblivion ring, you must choose it instead of forcing a draw. You can't say that you always choose the opponents Oblivion ring.
I’m still not convinced uncontrollable loops should be forcibly avoided. That seems unnatural and I’m not really against draws per se. I guess I’d just feel very angry in chess if I were forced to play a worse move and lose when a repetition leading to a draw was available.