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Tucker Black

Colorado
United States
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February 25, 2016
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Aug 29, 2025, 3:09 pm

I was curious as to the improved probability of winning a large prize when you re-play small wins, so I wrote a computer program to calculate it, running 200 million simulations.

Naturally, this depends on the prize structure and what is your cutoff point for "large prize". I selected Colorado's $5 scratcher $100,000 Super Bonus. The odds are:

$100,000 = 1 in 960,000

$20,000 = 1 in 480,000

$5,000 = 1 in 480,000

$1,000 = 1 in 480,000

$500 = 1 in 2,500

$100 = 1 in 194

Starting with one ticket, if you win $1,000 or more and stop playing, and re-play any win of $500 or less, the average number of tickets played is 2.9. Your chances of winning the larger prizes with your original bankroll of one ticket become:

$100,000 = 1 in 344,000

$20,000 = 1 in 167,000

$5,000 = 1 in 167,000

$1,000 = 1 in 167,000

The probability you win $1,000 or more is about 3 times better than it was with your original one ticket where you keep any win. Of course, the downside of doing this is that if you win something and use the winnings, $5 up to $500, to buy more tickets, you could lose. The improved probability of winning a large prize is not "free".

Now, let's see if what happens if we lower our stop point to $500. We will buy more tickets with a win of $100 or less but stop playing if we win $500 or more.

$100,000 = 1 in 384,000

$20,000 = 1 in 186,000

$5,000 = 1 in 186,000

$1,000 = 1 in 186,000

$500 = 1 in 970

Average number of tickets played drops to 2.6. The probability of getting a big win is 2.5x, a bit less than the 3x improvement with a $1,000 stop point since we've included $500 as a stop point. The upside is that if we win $500, we don't blow it on 100 losing tickets. The downside is that if we win $500, we miss out on a big win in the next 100 tickets we don't want.

Finally, let's see what happens if we raise our stop point to $5,000. Winning $1,000 means buying 200 more tickets.

$100,000 = 1 in 343,000

$20,000 = 1 in 166,000

$5,000 = 1 in 166,000

Average number of tickets played is 2.9. Comparing this to the figures for a stop point of $1,000, the results are virtually identical. The improved probability of winning $5,000 or more is so slight, it is definitely not worth risking $1,000. Just keep it!

I ran these calculations again starting with a bankroll of two tickets, ten tickets, and 20 tickets. All the probabilities and average number of tickets played increase by the number of tickets purchased originally.
Stat$talker

700 light yrs West of Milky Way Galaxy's Center
United States
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September 1, 2019
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Aug 29, 2025, 4:20 pm

Quote: Originally posted by Tucker Black on Aug 29, 2025
I was curious as to the improved probability of winning a large prize when you re-play small wins, so I wrote a computer program to calculate it, running 200 million simulations.

Naturally, this depends on the prize structure and what is your cutoff point for "large prize". I selected Colorado's $5 scratcher $100,000 Super Bonus. The odds are:

$100,000 = 1 in 960,000

$20,000 = 1 in 480,000

$5,000 = 1 in 480,000

$1,000 = 1 in 480,000

$500 = 1 in 2,500

$100 = 1 in 194

Starting with one ticket, if you win $1,000 or more and stop playing, and re-play any win of $500 or less, the average number of tickets played is 2.9. Your chances of winning the larger prizes with your original bankroll of one ticket become:

$100,000 = 1 in 344,000

$20,000 = 1 in 167,000

$5,000 = 1 in 167,000

$1,000 = 1 in 167,000

The probability you win $1,000 or more is about 3 times better than it was with your original one ticket where you keep any win. Of course, the downside of doing this is that if you win something and use the winnings, $5 up to $500, to buy more tickets, you could lose. The improved probability of winning a large prize is not "free".

Now, let's see if what happens if we lower our stop point to $500. We will buy more tickets with a win of $100 or less but stop playing if we win $500 or more.

$100,000 = 1 in 384,000

$20,000 = 1 in 186,000

$5,000 = 1 in 186,000

$1,000 = 1 in 186,000

$500 = 1 in 970

Average number of tickets played drops to 2.6. The probability of getting a big win is 2.5x, a bit less than the 3x improvement with a $1,000 stop point since we've included $500 as a stop point. The upside is that if we win $500, we don't blow it on 100 losing tickets. The downside is that if we win $500, we miss out on a big win in the next 100 tickets we don't want.

Finally, let's see what happens if we raise our stop point to $5,000. Winning $1,000 means buying 200 more tickets.

$100,000 = 1 in 343,000

$20,000 = 1 in 166,000

$5,000 = 1 in 166,000

Average number of tickets played is 2.9. Comparing this to the figures for a stop point of $1,000, the results are virtually identical. The improved probability of winning $5,000 or more is so slight, it is definitely not worth risking $1,000. Just keep it!

I ran these calculations again starting with a bankroll of two tickets, ten tickets, and 20 tickets. All the probabilities and average number of tickets played increase by the number of tickets purchased originally.

The Green Hornet sed, You got Yo method outta dizz Book...

Did you consult Ole Texez 2 Stepper bout dat Aluminum foil?
JustMaybe

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Aug 29, 2025, 5:13 pm

I never replay small wins, at least not at the moment when I cash a ticket.

I always buy my tickets before I cash my winners.

I tell the store clerk "It's not everyday that I get to walk away with money" and they laugh 😂

So I could have a $4 winning PB ticket, but I will get $4 from my wallet, buy my tickets, get my receipt and then cash the winner.

Of course the next time when am buying lottery tickets, the money coming out of my wallet would be what I got paid last time.

However, in terms of return on investment, I always run out of money and have to make an ATM withdrawal. So far my lottery entertainment does not fund itself, unless I win some big jackpot then I can say am not using my "earned income"

I believe winning the lottery jackpot is a 💯 % factor of luck.

May Fortuna, goddess of chance or lot vindicate me.
Tucker Black

Colorado
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Member #173,294
February 25, 2016
1,134 Posts
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Aug 29, 2025, 8:25 pm

Quote: Originally posted by JustMaybe on Aug 29, 2025
I never replay small wins, at least not at the moment when I cash a ticket.

I always buy my tickets before I cash my winners.

I tell the store clerk "It's not everyday that I get to walk away with money" and they laugh 😂

So I could have a $4 winning PB ticket, but I will get $4 from my wallet, buy my tickets, get my receipt and then cash the winner.

Of course the next time when am buying lottery tickets, the money coming out of my wallet would be what I got paid last time.

However, in terms of return on investment, I always run out of money and have to make an ATM withdrawal. So far my lottery entertainment does not fund itself, unless I win some big jackpot then I can say am not using my "earned income"

I did my analysis on scratch-off tickets because most of the prize money goes towards lower prizes. With jackpot accumulation draw games such as Powerball, not much goes to lower prizes.

To summarize my first post, for the $5 Colorado scratch-off $100,000 Super Bonus, the average number of tickets played is 2.5x or 3x your original bankroll, depending on whether your stop point is $500 or $1,000. Not surprisingly, the improved odds of winning a large prize exactly correlate with the average number of tickets played.

For Powerball, where most of the prize money goes into the jackpot, if you buy more tickets using the winnings from small wins, the average number of tickets played is barely more than your original ticket bankroll.

If you re-play wins of $100 or less, average number of tickets played is only 1.09. It's slightly more if you win $7 and add a dollar to buy four more tickets, and slightly less if you keep the extra dollar and buy three more tickets.

A 10% increase in the overall odds of winning the jackpot is not much. Powerball is a game where you should just assume you are going to lose, and if you do win a small amount, $100 or less, it's a "consolation prize".
JustMaybe

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January 2, 2023
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Aug 29, 2025, 9:00 pm

"Powerball is a game where you should just assume you are going to lose, and if you do win a small amount, $100 or less, it's a "consolation prize".

If I won $100, I would go to Texas RoadHouse and spend $50 on a steak 🤣

I believe winning the lottery jackpot is a 💯 % factor of luck.

May Fortuna, goddess of chance or lot vindicate me.
Coin Toss

Zeta Reticuli Star System
United States
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January 17, 2006
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Aug 31, 2025, 5:41 pm

Just my two cents but I'm pretty sure the lotteries are very well aware that most small wins go right back into the lottery.

Those who run the lotteries love it when players look for consistency in something that's designed not to have any. So many systems, so many theories, so few jackpot winners.

There is one and only one 'proven' system, and that is to book the action. No matter the game, let the players pick their own losers.

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