Progression systems in gambling, including flat betting, Martingale, Fibonacci, and Paroli, offer varying methods for managing bets and bankrolls. Flat betting maintains a consistent wager, promoting stability but potentially capping gains. The Martingale strategy doubles bets after losses to recover losses, but this can lead to significant risks and hitting betting limits. The Fibonacci system employs a sequence based on previous losses for a more balanced approach, while the Paroli system increases bets after wins to maximize gains during winning streaks.