Lotto is five different minigames using the same room currency. The right ticket depends on whether you need safer wins, bigger best-win spikes, jackpot attempts, or Abacus EXP.
Use Green when extra lives and block upgrades make monster damage manageable.
Use Purple for higher risk gem spikes after you have extra lives and detection protection.
Use Blue when instant-win and prize upgrades are unlocked. The June 3 PDT hotfix lowered Unlock Blue Ticket from 3.5M to 150K Money, so it is no longer as delayed as launch-day pricing suggested.
Use Grey later, once your Lotto economy can afford the large board and symbol upgrades.