W2G forms are definitely something to think about when playing video poker at the larger bet amounts. Although you are obligated to pay taxes on your net win at the end of the year regardless of how many W2G forms you have, a payout of $1200 or more will necessitate a wait and obligate you to tip the person paying you. In less classy casinos a hand pay will also cause the tip vultures to start hovering around you. To avoid all of this sometimes the player should consider deviating from optimal strategy. For example with AAA88 in 10/7 double bonus the odds marginally favor keeping the aces only. However in a $2 to $10 game hitting four aces will pay over $1200, necessitating a W2G form, while a full house will stay under the limit. Considering the tax implications keeping the full house is the better play.
To answer your question I’ll assume a four of a kind pays 25 times the bet. Then a four of kind on the deal in a $0.20 50-play game will pay $0.20 * 5 * 50 * 25 = $1250. You will get a four of a kind on the deal once every 4165 hands, on average. If you were to drop the number of hands to 47 the win for a four of a kind on the deal would be 47 * $0.20 * 5 * 25 = $1175, staying under the W2G threshold.