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# Mathematics and the Lottery

652 replies. Last post 1 day ago by Catpickednumber.

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Can a winning lottery system be created with existing math formulas?

 Yes-It's all in the math books. [ 228 ] [43.02%] No-Anew math for will have to be created. [ 78 ] [14.72%] Math won't beat the lottery regularly. [ 224 ] [42.26%] Total Valid Votes [ 530 ] Discarded Votes [ 54 ]

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Kentucky
United States
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February 14, 2006
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 Posted: September 8, 2013, 3:52 pm - IP Logged

With retailers getting 5% of sales for selling and cashing in tickets, vendors probably getting 5% for supplying terminals and software and a staff of managers, security and maintenance people getting 10%, players would have to be giving up cashing in 40% of their prize money.  Do you really feel that many winning tickets go unclaimed?

Who knows, there might be enough unclaimed tickets to make up the 5%, but money the lotteries give to the state is in the 30% range of what they collect in profits. The stores are the ones booking the bets and the money they pay out to yesterday's winners is the money they collected from today's ticket sales. The 50% pick-3 edge is an average based over time so it's not accurate to say the winners are paid out of that "pot" because part of that "pot" was paid out to past winners.

From the store's point of view, they are booking the bets for the lottery and that is who is responsible for the payoffs. That's why many stores are reluctant to pay off winning bets before they collect enough in sales to cover it. The store lottery books are probably balanced every day and the store is given a 5% credit. The settlement might by bi-weekly or once a month. If a store pays out more than they collected plus the 5%, the lottery will send them a check or if there is a debit, the stores sends the lottery a check.

Most lotteries pay commissions to cashing agents for cashing tickets from \$601 to \$5000 and that too is added to the other expenses. When all the expenses are added up, if a state is paying out about 50% all the pick-3 sales in prizes, the actual profits might be lower than 30%.

Happyland
United States
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September 1, 2013
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 Posted: September 8, 2013, 4:28 pm - IP Logged

Who knows, there might be enough unclaimed tickets to make up the 5%, but money the lotteries give to the state is in the 30% range of what they collect in profits. The stores are the ones booking the bets and the money they pay out to yesterday's winners is the money they collected from today's ticket sales. The 50% pick-3 edge is an average based over time so it's not accurate to say the winners are paid out of that "pot" because part of that "pot" was paid out to past winners.

From the store's point of view, they are booking the bets for the lottery and that is who is responsible for the payoffs. That's why many stores are reluctant to pay off winning bets before they collect enough in sales to cover it. The store lottery books are probably balanced every day and the store is given a 5% credit. The settlement might by bi-weekly or once a month. If a store pays out more than they collected plus the 5%, the lottery will send them a check or if there is a debit, the stores sends the lottery a check.

Most lotteries pay commissions to cashing agents for cashing tickets from \$601 to \$5000 and that too is added to the other expenses. When all the expenses are added up, if a state is paying out about 50% all the pick-3 sales in prizes, the actual profits might be lower than 30%.

According to my state, 26.3% goes to the main fund ('profit'), 1.4% goes to secondary programs (unclaimed prizes), 5% goes to retailer commissions, 4.4% goes to lottery administration, and 62.9% goes to players in the form of prizes. But obviously that is overall, not for Pick 3.

I have never encountered a store reluctant to pay any amount. They are not even charged for packs of scratch-offs until at least 70% of the pack has been sold, or 45 days has passed after activating it. To my knowledge our lottery does not send checks to retailers, they perform ACH / direct debits and credits.

In the case of Pick 3, to say the lottery 'profits 50%' is a misnomer indeed, so a better interpretation would be that the 'lottery system gets 50%'. In FY 2012, my lottery had Pick 3 sales of \$279.41 million and player payouts of \$139.11 million. Guess what? That rounds off to 50%.

If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

2016: -48.28% (13 tickets) ||
P&L % = Total Win(\$)/Total Wager(\$) - 1

Kentucky
United States
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February 14, 2006
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 Posted: September 8, 2013, 5:08 pm - IP Logged

50 (lottery) + 50 (players) = 100.

It's simple wealth redistribution. If 1000 people give me a dollar each and I randomly pick 1 and give him/her \$500, then he/she gets 50% of the fund and I get the other 50%. The lottery does this on a large scale. People play for the minut chance of winning more than they put in. But if they keep playing over time they will have received/lost their expected value based on the odds and prizes (Law of Large Numbers).

So let's say the person I randomly picked keeps playing. He/she only has to play 500 more times to lose all their winnings. With odds of 1:1000 it is pretty likely he/she will go broke before winning again.

Another example is a raffle. If the charity takes 50% of all money and gives 50% to the winner, it doesn't matter how many/few tickets they sell- your expected value on a bet would be -50%.

That still doesn't answer the question of who is collecting the 50% prize share that will exist in all future drawings if nobody can win playing pick-3 games.

"People play for the minut chance of winning more than they put in."

The percentage of wins they need to show a profit is minute too; it's less than 1% at 0.21%. Granted, they have to beat long odds, but they don't need to win even 1% of the drawings to beat the odds. If someone offered a pick-3 system that won in 0.4% of all pick-3 drawings, they would probably be laughed out of forum, but that adds up to \$1000 in profits betting \$1 straight every drawing for 1000 drawings.

"So let's say the person I randomly picked keeps playing. He/she only has to play 500 more times to lose all their winnings. With odds of 1:1000 it is pretty likely he/she will go broke before winning again."

That was my criticism when someone ran a simulation showing the results of 25,000 players each getting five \$1 straight QPs every day for five years. Each day they continued to bet \$5 to win \$500 regardless of how much they had already lost. Even with that unlikely scenario, a few of the player still managed to show a small profit after five years because of probability.

Because the simulated lottery was based on probability, the results are similar to what should be expected of a state lottery averaging \$125,000 per day in pick-3 wagers over five years. The average in winning tickets should be 0.1% times \$500 and based on probability, a few players to show a profit.

Happyland
United States
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 Posted: September 8, 2013, 5:27 pm - IP Logged

That still doesn't answer the question of who is collecting the 50% prize share that will exist in all future drawings if nobody can win playing pick-3 games.

"People play for the minut chance of winning more than they put in."

The percentage of wins they need to show a profit is minute too; it's less than 1% at 0.21%. Granted, they have to beat long odds, but they don't need to win even 1% of the drawings to beat the odds. If someone offered a pick-3 system that won in 0.4% of all pick-3 drawings, they would probably be laughed out of forum, but that adds up to \$1000 in profits betting \$1 straight every drawing for 1000 drawings.

"So let's say the person I randomly picked keeps playing. He/she only has to play 500 more times to lose all their winnings. With odds of 1:1000 it is pretty likely he/she will go broke before winning again."

That was my criticism when someone ran a simulation showing the results of 25,000 players each getting five \$1 straight QPs every day for five years. Each day they continued to bet \$5 to win \$500 regardless of how much they had already lost. Even with that unlikely scenario, a few of the player still managed to show a small profit after five years because of probability.

Because the simulated lottery was based on probability, the results are similar to what should be expected of a state lottery averaging \$125,000 per day in pick-3 wagers over five years. The average in winning tickets should be 0.1% times \$500 and based on probability, a few players to show a profit.

Whoever said "nobody" can win Pick 3?? They might profit in the short run, but in the long run they will still lose. There shouldn't be a question of who is collecting the 50% prize share. Lottery runs continuously. New and old players come and go. Some win and some don't.

Take those few players who came out with a profit after 5 years. Now have them play another 5 years. How many are still showing a small profit? That is the problem of simulating a short time period. In blackjack you don't simulate a few thousand hands to see what your edge is. You simulate billions of hands to find the true expected value. It doesn't matter that you will never play a billion hands in your lifetime.

If you play 1000 drawings and win 2 of those that does not necessarily mean you have a system that "beats the odds." Odds of 1:1000 does not mean that after 1001 drawings you will have won, and odds of 1:500 does not mean that it is not possible to win after just 1 drawing. What you are describing is basically classic of people who do not understand probability and the concept of randomness. Same goes for your mentioning of the few players who do manage to show a profit. It does not necessarily mean they have a winning system. You see someone win the big jackpot, does that mean they are special or doing something special???? Nope.

If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

2016: -48.28% (13 tickets) ||
P&L % = Total Win(\$)/Total Wager(\$) - 1

mid-Ohio
United States
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March 24, 2001
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 Posted: September 8, 2013, 9:10 pm - IP Logged

That still doesn't answer the question of who is collecting the 50% prize share that will exist in all future drawings if nobody can win playing pick-3 games.

"People play for the minut chance of winning more than they put in."

The percentage of wins they need to show a profit is minute too; it's less than 1% at 0.21%. Granted, they have to beat long odds, but they don't need to win even 1% of the drawings to beat the odds. If someone offered a pick-3 system that won in 0.4% of all pick-3 drawings, they would probably be laughed out of forum, but that adds up to \$1000 in profits betting \$1 straight every drawing for 1000 drawings.

"So let's say the person I randomly picked keeps playing. He/she only has to play 500 more times to lose all their winnings. With odds of 1:1000 it is pretty likely he/she will go broke before winning again."

That was my criticism when someone ran a simulation showing the results of 25,000 players each getting five \$1 straight QPs every day for five years. Each day they continued to bet \$5 to win \$500 regardless of how much they had already lost. Even with that unlikely scenario, a few of the player still managed to show a small profit after five years because of probability.

Because the simulated lottery was based on probability, the results are similar to what should be expected of a state lottery averaging \$125,000 per day in pick-3 wagers over five years. The average in winning tickets should be 0.1% times \$500 and based on probability, a few players to show a profit.

With pick3 only having a thousand possible outcomes, it will always be winnable but those players betting more than they win will always be losers.

* you don't need to buy more tickets, just buy a winning ticket *

Kentucky
United States
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 Posted: September 9, 2013, 12:26 am - IP Logged

Whoever said "nobody" can win Pick 3?? They might profit in the short run, but in the long run they will still lose. There shouldn't be a question of who is collecting the 50% prize share. Lottery runs continuously. New and old players come and go. Some win and some don't.

Take those few players who came out with a profit after 5 years. Now have them play another 5 years. How many are still showing a small profit? That is the problem of simulating a short time period. In blackjack you don't simulate a few thousand hands to see what your edge is. You simulate billions of hands to find the true expected value. It doesn't matter that you will never play a billion hands in your lifetime.

If you play 1000 drawings and win 2 of those that does not necessarily mean you have a system that "beats the odds." Odds of 1:1000 does not mean that after 1001 drawings you will have won, and odds of 1:500 does not mean that it is not possible to win after just 1 drawing. What you are describing is basically classic of people who do not understand probability and the concept of randomness. Same goes for your mentioning of the few players who do manage to show a profit. It does not necessarily mean they have a winning system. You see someone win the big jackpot, does that mean they are special or doing something special???? Nope.

"New and old players come and go. Some win and some don't."

That doesn't change the fact any player can show a profit by winning over 0.2% of their chances. How does the 50% edge prevent any player from winning over 0.21% of their bets? The percentage of winning players in the simulation should be exactly the same in the next and your guess is as good as mine as to how many of the previous winners will win again under that format.

"You simulate billions of hands to find the true expected value."

I'm pretty sure Thorpe simulated billions of hands to find the expected outcome when the remaining cards in the deck benefited the player. To get the expected value would be calculating the percentages of outcomes the player won when the deck favored them. If Thoup's calculations show a player could expect the deck to benefit them once out 1000 shuffles, there is was no practical usage.

Nobody can play a billion hands blackjack or bet on a billion pick-3 drawings so if it takes that many simulations to reach a valid conclusion, real play can only be a very small proportion of it. The probability plus or minus the standard deviation of three even digits in the next 1000 pick-3 drawings is the same as in the next billion. To average winning even money in the next 10,000 bets, a pick-3 player must win 0.4% of them. Looking at the bet from the opposite, they can lose 9960 of their bets and still get even money and 21 to show a profit.

While the 50% edge means a player must double their wins, three or four wins out of 1000 isn't incredible. A \$2 a ticket PB player should match 3 numbers three times every 1080 drawings and a \$27 return on their \$1800 bet.

Happyland
United States
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 Posted: September 9, 2013, 12:57 am - IP Logged

Your mentality is exactly why people believe in the martingale system and exactly why casinos (and lotteries) love people who believe in it.

"The percentage of winning players in the simulation should be exactly the same in the next"

You said so yourself, only a few managed to show a profit. Let's say 250 out of 25,000 or 1%. Run it again, go another 5 years, and only 2.5 survive this time. We'll say it's 3. Okay, same percent (1%), have another go and guess who survives????? Zero, which is why I stand by my point that if you continue playing, you will lose. It might take years, but when the house edge is 50% it is mathematically certain.

This is why you simulate over large numbers. It's called the Law of Large Numbers for a reason. Your reasoning that it shouldn't take that many trials to arrive at an appropriate value couldn't be further from the truth. We simulate over a large number to be certain that the value we seek really is the mathematical truth. We look for an approximate constant, not a variable.

Expected value has nothing to do with the frequency of appearances. That would be like saying because I flipped 10 heads in a row I can expect to win/lose the next one.

All that aside, what is your point? I have already said that people win the lottery but this does not make them special. You seem to imply that if someone wins the lottery there is something they are doing differently than everyone else. You are clinging to the hope that just because 1% of people end up with a profit then you can be one of them too. Even in the event that somehow it was possible for a lottery player to win more than they lose, tell me HOW on earth is the lottery not taking notice, shutting down the game??? The lottery is the house, and the house never accepts losing.

Really the only way to "win" per se is as RJOh mentioned, stop when your winnings exceed your losses. But, I would wager that most lottery players won't stop after winning just once. It's also why you never see gamblers bet all on red once and then leave the casino, despite the fact that it is most mathematically optimal for winning.

Having read some of the earlier posts in this thread I can see that you are pretty much bent on your position, so I really have nothing else to say except that I recommend taking a university level course in statistics and probability.

If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

2016: -48.28% (13 tickets) ||
P&L % = Total Win(\$)/Total Wager(\$) - 1

Kentucky
United States
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February 14, 2006
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 Posted: September 9, 2013, 8:04 pm - IP Logged

Your mentality is exactly why people believe in the martingale system and exactly why casinos (and lotteries) love people who believe in it.

"The percentage of winning players in the simulation should be exactly the same in the next"

You said so yourself, only a few managed to show a profit. Let's say 250 out of 25,000 or 1%. Run it again, go another 5 years, and only 2.5 survive this time. We'll say it's 3. Okay, same percent (1%), have another go and guess who survives????? Zero, which is why I stand by my point that if you continue playing, you will lose. It might take years, but when the house edge is 50% it is mathematically certain.

This is why you simulate over large numbers. It's called the Law of Large Numbers for a reason. Your reasoning that it shouldn't take that many trials to arrive at an appropriate value couldn't be further from the truth. We simulate over a large number to be certain that the value we seek really is the mathematical truth. We look for an approximate constant, not a variable.

Expected value has nothing to do with the frequency of appearances. That would be like saying because I flipped 10 heads in a row I can expect to win/lose the next one.

All that aside, what is your point? I have already said that people win the lottery but this does not make them special. You seem to imply that if someone wins the lottery there is something they are doing differently than everyone else. You are clinging to the hope that just because 1% of people end up with a profit then you can be one of them too. Even in the event that somehow it was possible for a lottery player to win more than they lose, tell me HOW on earth is the lottery not taking notice, shutting down the game??? The lottery is the house, and the house never accepts losing.

Really the only way to "win" per se is as RJOh mentioned, stop when your winnings exceed your losses. But, I would wager that most lottery players won't stop after winning just once. It's also why you never see gamblers bet all on red once and then leave the casino, despite the fact that it is most mathematically optimal for winning.

Having read some of the earlier posts in this thread I can see that you are pretty much bent on your position, so I really have nothing else to say except that I recommend taking a university level course in statistics and probability.

"You said so yourself, only a few managed to show a profit. Let's say 250 out of 25,000 or 1%. Run it again, go another 5 years, and only 2.5 survive this time. We'll say it's 3."

A few is 0.1% of all wagers the lottery expects to lose. Had the winnings been equally distributed, each player lost 50% of their total bet. Because the rules of the simulation required each player to continue wagering \$5 to win \$500 regardless of how much they had lost, some players continued to lose and lost more than 50% of their total bets. And the same rules meant some players could increase their profits.

"All that aside, what is your point? I have already said that people win the lottery but this does not make them special. You seem to imply that if someone wins the lottery there is something they are doing differently than everyone else."

You gave an example of your state lottery averaging about 50% in gross profits and paying out 50% in prizes and doing the math shows on average each player lost 50% of their wagers. The lottery payoffs were not evenly distributed and not in the simulation either so a percentage of those players (at the least 50%) lost 100% of their \$500 wagers after the first 100 drawings. Their losses didn't increase their 0.5% chance of winning any of the next 100 drawings so a percentage of them will lose 100% of their \$1000 in wagers after 200 drawings. Those of the over 50% that managed to win once in the next 100 drawings still lost 50% of their total wagers and that amount will increase until their next win. The lottery still gets their 50% while the winners are sharing the losses.

That special something different might be as simple as playing the date of the drawing (909) and winning 0.3% of the bets. I'm not saying it's easy to show a profit over time, just saying there is a possibility. I'd love to prove I could win 1% of pick-3 wagers, but it doesn't prove it's mathematically impossible.

"But, I would wager that most lottery players won't stop after winning just once. It's also why you never see gamblers bet all on red once and then leave the casino, despite the fact that it is most mathematically optimal for winning."

The first thought of anyone who wins \$500 on a \$1 bet within their first ten tries is to continue betting a \$1 hoping to increase their profits. After 250 straight losses will that player reevaluate their chances of increasing their profits and continue playing or will they take the remainder of their profits and try something else?

Betting all on red is not an optimal bet when the pill lands on a black number, 0, or 00. Buying 100% of the tickets in a "winner take all" raffle is not even an optimal bet because the gambler wins nothing. Is betting \$1000 to win \$1000 on one bet really more optimal than making 1000 \$1 bets when each bet has a chance to win \$500?

"Having read some of the earlier posts in this thread I can see that you are pretty much bent on your position, so I really have nothing else to say except that I recommend taking a university level course in statistics and probability."

If you read all my post, my position is all bets are conditional and exactly the same as betting all on red. If a pick-3 player believes because of a logical or an illogial reason they can win 0.3% of their bets, that is the condition they set. Some conditions are very unlikely of winning like the chance of one ticket winning a PB or MM jackpot, but the risk of losing \$1 or \$2 is outweighed by the multi-million dollar reward.

I don't need a refresher course in statistics and probability to calculate your optimal all on red bet only has a 47.3% chance of winning.

Kentucky
United States
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 Posted: September 9, 2013, 8:16 pm - IP Logged

With pick3 only having a thousand possible outcomes, it will always be winnable but those players betting more than they win will always be losers.

A Roulette game has 5.26% edge and more often you'll see players lose \$100 in five minutes. Using the same math, 94.74% of the losses are distributed by the winning bets so there is plenty enough for some roulette players to show a nice profit while the casino is steadily collecting their 5.26%.

The 50% pick-3 edge has no effect on the players who wager \$100 and lose it all. It will be distributed equally to the winning tickets and the lottery. If it's a fact all pick-3 players must lose in the long run, I missed the memo.

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Ukraine
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September 10, 2013
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Economy class
Belgium
Member #123700
February 27, 2012
4035 Posts
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 Posted: September 10, 2013, 2:49 pm - IP Logged

If I want to go random, I program that myself or I take a quick-pick. I don't need the Russians for this. Maybe the Syrians need the Russians now, I don't know.

bgonÃ§alves
Brasil
Member #92564
June 9, 2010
2126 Posts
Online
 Posted: September 10, 2013, 7:34 pm - IP Logged

Hello, sergem, enter Russian sites? Only two antivirus KASPERSKY, incidentally is the best antivirus around, is Russian! Ahhh! But on the subject of lotteries board, the Russians copy much of the West,

Economy class
Belgium
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February 27, 2012
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 Posted: September 17, 2013, 1:04 pm - IP Logged

Sorry but I don't know the Russian lottery, but heard about the roulette.

bgonÃ§alves
Brasil
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June 9, 2010
2126 Posts
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 Posted: September 21, 2013, 11:26 pm - IP Logged

small town USA
United States
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October 8, 2003
224 Posts
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 Posted: September 26, 2013, 11:43 am - IP Logged

I'm not too proficient at math so I try to use geography instead.

(To the tune of "I Was In The Right Place But It Musta Been The Wrong Time" by Dr Hook and the Medicine Show)

By being in the right place

And hoping it's the right time.

Buyin' me some Quick Picks

And standin in the right line

Smilin' at the cashier

Tellin' her she looks fine

Gettin' me some cold beer

Over by the beer sign

Askin' if she'd like one

Let 'er know that I'm buyin'

Meet 'er later out back

Let 'er know she's my kind

Get 'er in the pickup

Let 'er know that I'm tryin'

To win a big ol' jackpot

Bigger than a gold mine

Sittin' in the backwoods

Sippin' on some moonshine

Thinkin bout the powerball

Thinkin' that we'll do fine

She pulls out some Midol...

The End

Lucky is what I call it too!!

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