So, as some of you know, I am an avid scratch player, and rather than quit playing as I was originally planning, I've simply stopped spending more than I can reasonably afford. Anyways, that's not the topic of this thread. I am trying to calculate what would be the most efficient manner of buying scratch tickets in terms of the ratio of $20, $10 and $5 tickets, or if there should even be a representation of all those three. This gets extremely complicated and elaborate, and I'm just not sure what the ultimate combination is. I used to buy these 'rounds' that consisted of a $20 ticket, two $10s and four $5s.... so essentially, $20 of each type of ticket. But then I realized that one $20 ticket has a 1:25 chance of winning $100, whereas four $5 tickets collectively have only a 1:248 chance of winning $100. So if I were to replace the four $5 tickets with a second $20, I'd have much greater odds of winning $100 than if I have the $20 and four $5s. However, a $20 ticket has a 1:3.51 chance of winning any prize. So with a $20 ticket there's a 71.5% chance that you lose all your money in one blow. Whereas with four $5 tickets, the odds that you don't get any of your money back are actually quite low. An average $5 ticket has a 1:3.76 chance of winning any prize, so between four tickets you have a 106% likelihood of hitting at least one prize. So, $20 ticket gives you much better odds of hitting something big, but also higher odds of losing all your money at once. And $10 tickets lie somewhere in between. Between two of them you have the same odds of winning $100 as you do on one $20 ticket, but you don't have nearly the odds of winning $200 that you do with a $20 ticket. But again, with two tickets your odds of winning Something are greater than your odds on a $20 ticket, so the game lasts longer, assuming you're not hitting a big prize either way. Of course, $5 can only get you $50,000, whereas $10 gets you up to $200,000 and $20 up to $1,000,000. So those of you who are math geeks, what would you do? In what ratios would you purchase the various tickets? One $5 for every $10 for every $20? Or four $5s for every two $10s for every one $20? Or would you only buy $5 tickets? Or only buy $20 tickets? Assuming you were going to establish a concept of a 'round' like I did, and always buy a fixed ratio of tickets in batches, how many $10s and $5s would you get for each $20 that you get?