If you select any Level 12 monster for the effect of this card, your opponent cannot select a monster of a higher level because there are no monsters level 13 or higher. In other words, if you select "Yubel - The Ultimate Nightmare" for example, you will always "win" the Ante and force your opponent to lose his/her card.
This card has two purposes: to get your opponent to reveal the strongest monster in their hand, and to then make them lose it and take damage. Naturally you should only play Ante if you have a very high-Level monster in your hand (Level 8 will typically do, as monsters that go higher in the hand are quite rare).
A canny opponent might deliberately choose a low-level or non-monster card so that they won't risk losing their top-level card, but they will still take damage. You can choose to do this as well, if you think that taking 1000 points of damage is worth seeing the opponent's card--you can then force them to discard it anyway using something like "Mind Crush".
This card works well in a Dragon deck which consist of high level dragons. So even if you lose it from your hand, it can be used as fusion fodder for fusion summons using "Dragon's Mirror" to call out even stronger dragons, or revive those high level Dragons with the effect of "Red-Eyes Darkness Metal Dragon".
This card can prevent dead draw monsters from being useless if you have no way to return them to the deck.
This card works well in an Earthbound Immortal deck, as each of the Earthbound Immortals is level 10.
This card works well in a Malefic deck, as most monsters are very high leveled. Especially "Malefic Truth Dragon", you will always "win" the Ante and force your opponent to lose his/her card.
Use cards that reveal your opponent's hand, like "Ceremonial Bell" or "Respect Play" to check if he/she has a monster with higher level than yours.
You can use this card with cards like "Rainbow Life" to intentionally "take damage", while you will instead gain that amount of life points. It can also be used as a prevention - if you have the higher-leveled monster you inflict 1000 points of damage, and if not, you gain 1000 life points.
This card is very powerful in a dedicated "Yubel" sequence deck, which typically runs at least 5 level 10+ monsters.
"Trap Dustshoot" can work well with this card, because you can not only check your opponent's hand, but also make him/her return a monster to the deck. You can choose the monster with the highest level to be returned and then activate this card.