The Game Corner has been an essential part of all Pokemon games, the exception being with Pokemon Black and White versions, in which it was mysteriously omitted. Normally, the game has tended to stay constant with slots which had designs that would change each game. Starting with HeartGold and SoulSilver, the slots were replaced by a game known as Voltorb Flip. This game was did not replace the slots in Japan, though; I think of it like an exclusive reward or something for living in a place where all Pokemon merchandise comes out the earliest.
For both games, the object of the game is to get as much coins as you can, and trade them in for prizes. Voltorb Flip works in a similar way, except for the fact that you do not need coins to play the game. Let’s explain Voltorb Flip. It is a relatively simple game that involves flipping cards to reveal coin amounts while avoiding the Voltorb cards. To help you flip all these cards over, there are signs on the side with two amounts. The first one, on the top, tells you the value of all the coin cards combined, while the second one on the bottom tells you how many Voltorbs there are in that row. You also have a memo pad to mark what you think are Voltorb or coins. You can stop at any moment and cash in, but if you beat levels by flipping all the non-Voltorb cards over, you can increase the multiplier (level) and play for more coins.
For slots, the game is much easier and requires less thinking. The object of slots is to match three icons, which will award you with coins. This game requires coins to play, which can be bought from the clerks at the counters. A minimum of one coin is required; it is optional to put in up to two more coins in case there are matches diagonally or on other rows. Once you put in the coins, you can press A to stop the slots and try to get a match. The icons that give the most are the 7 or the R/Poke Ball, and its values have changed over the years. After you’ve saved up enough coins in your Coin Case, you can proceed to the Prize Corner, where you can exchange coins for prizes such as TMs (which can’t be used multiple times like Generation V), hold items, or certain Pokemon.
Some Pokemon that have stayed as prizes include Mr. Mime, Eevee, and Porygon, which each cost multiples of 3333 coins. Version differences are also in effect (at least for HeartGold/SoulSilver), so the three Pokemon can purchase may be slightly different from another version. Regardless, both games are very fun and addicting, but require some time to master. Try to take a load off from being a Trainer, and relax in the Game Corner, where you can have fun without really losing anything in real life.