A game of GoFish is played with a deck of 52 cards (4 suits, 13 ranks in each suit).

2 to 6 players play. With 2 players each player is dealt 7 cards. With 3 or more players each player is dealt 5 cards.

Players take turns asking each other for a rank. If the asked player has cards of that rank they give them all to the asking player. If not, the asking player draws a single card from the deck.

Whenever a player has 4 cards of the same rank, those cards are discarded.

The turn proceeds to the next player in clockwise order. The game ends when one a players hand is empty or the deck is depleted.

For simplicity purposes you could just assume a single player, drawing from the deck one at a time, whenever getting 4 cards of the same rank, discarding them.

Given either the normal rules or the simple version, what are the odds of having X number of cards in your hand?

For example what are the odds of reaching a hand of 30 cards? 31 cards? 32 cards?