Asia's 4 digit lottery system - expected value?
I am from Singapore and I wish to enquire the expected value of betting/purchasing the lottery tickets of the above.
You basically can choose 4-digits from 0-9 and come up with a number. Eg. 0-1-2-3 or 0-0-0-0 etc.
Purchase $1 in the (BIG) category for that number of your choice and it entitles you to the following payouts (every dollar) :
1st prize : $2,000
2nd prize : $1,000
3rd prize : $490
Starter prize (10 numbers) : $250
Consolation prize (10 numbers) : $60
Purchase $1 in the (SMALL) category :
1st prize : $3,000
2nd prize : $2,000
3rd prize : $800
I am very interested to know the expected value for the above two categories.
Thank you guys for chipping in!
please explain more.
Quote: BryanHuangPSHi,
I am from Singapore and I wish to enquire the expected value of betting/purchasing the lottery tickets of the above.
You basically can choose 4-digits from 0-9 and come up with a number. Eg. 0-1-2-3 or 0-0-0-0 etc.
Purchase $1 in the (BIG) category for that number of your choice and it entitles you to the following payouts (every dollar) :
1st prize : $2,000
2nd prize : $1,000
3rd prize : $490
Starter prize (10 numbers) : $250
Consolation prize (10 numbers) : $60
Purchase $1 in the (SMALL) category :
1st prize : $3,000
2nd prize : $2,000
3rd prize : $800
I am very interested to know the expected value for the above two categories.
Thank you guys for chipping in!
I don't understand the question because you don't specify how one goes about winning second or third prize in either case. In fact, I am only assuming that picking the correct four numbers, in order, results in first prize. I further don't understand the ten number starter/consolation prizes for 10 numbers because you are only picking four numbers.
Quote: BryanHuangPSHi,
I am from Singapore and I wish to enquire the expected value of betting/purchasing the lottery tickets of the above.
You basically can choose 4-digits from 0-9 and come up with a number. Eg. 0-1-2-3 or 0-0-0-0 etc.
Purchase $1 in the (BIG) category for that number of your choice and it entitles you to the following payouts (every dollar) :
1st prize : $2,000
2nd prize : $1,000
3rd prize : $490
Starter prize (10 numbers) : $250
Consolation prize (10 numbers) : $60
Purchase $1 in the (SMALL) category :
1st prize : $3,000
2nd prize : $2,000
3rd prize : $800
I am very interested to know the expected value for the above two categories.
Thank you guys for chipping in!
I looked up info about the Singapore 4D lottery, and it looks like there are 23 independent draws of 4 numbers per game and you get paid depending on which draw your numbers are hit:
1st draw: 1st prize
2nd draw: 2nd prize
3rd draw: 3rd prize
4th-13 draw: Starter prize
14th - 23rd draw: Consolation prize
So, the ev is really easy to calculate: (2000*1 + 1000*1 + 490*1 + 250*10 + 60*10)/1000 = 0.659 .
For the small bet, the ev is (3000*1 + 2000*1 + 800*1)/1000 = 0.58 .
People look for so called lucky combinations when playing this. I'm not sure how it's considered lucky but you will find a lot of people play the 4 digit license plate of a car which has just been involved in a serious accident.
In the 1950's my dad drove a cab and if a cab driver took somebody to a house and they were wearing a black armband for mourning, and the house was a 3 digit number, instead of betting your cab number , you would bet the CRAPE number.
Quote: CrystalMathI looked up info about the Singapore 4D lottery, and it looks like there are 23 independent draws of 4 numbers per game and you get paid depending on which draw your numbers are hit:
1st draw: 1st prize
2nd draw: 2nd prize
3rd draw: 3rd prize
4th-13 draw: Starter prize
14th - 23rd draw: Consolation prize
So, the ev is really easy to calculate: (2000*1 + 1000*1 + 490*1 + 250*10 + 60*10)/1000 = 0.659 .
For the small bet, the ev is (3000*1 + 2000*1 + 800*1)/1000 = 0.58 .
Sorry for the badly phrased question from before and thank you CM for looking up the 4D game rules n payouts.
Does your calculation take into consideration the possibility of your number hitting several prizes during the same draw? Eg. Possibility of the same number coming 1st , starter and consolation during the same draw?
Regards,
Bryan
Quote: BryanHuangPSSorry for the badly phrased question from before and thank you CM for looking up the 4D game rules n payouts.
Does your calculation take into consideration the possibility of your number hitting several prizes during the same draw? Eg. Possibility of the same number coming 1st , starter and consolation during the same draw?
Regards,
Bryan
Yes, the return stated assumes that the lottery draw the same set of numbers more than once, which would give the possibility of winning multiple times.
Rather than hit the exact number they are considering adding "Bonuses" on hitting the 1st 3 digits of the winning number.
Example:
1st Prize winning number is 1234.
The number I purchased was 1237. As a result I would win a prize of $25 for every dollar I buy.
What is the new EV here and how does it change now that the "bonus" prize is just the 1st 3 digits of the winning number?
Quote: buzzpaffOne of the biggest losing days when NY lottery was just starting was people betting on the number og a big jet that crashed and killed hundred of passengers. Several year later the lottery commission would stop taking action on numbers that got too much play.
In the 1950's my dad drove a cab and if a cab driver took somebody to a house and they were wearing a black armband for mourning, and the house was a 3 digit number, instead of betting your cab number , you would bet the CRAPE number.
The organization that runs this lottery (Singapore Pools) has a built in system to prevent such scenarios. All bets are basically covered because they set limits on every available 4 digit number. i.e. numbers can get "sold out" if they are very "popular". Since all bets are made at outlets linked to their central database, I believe the limits are dynamic and sold out bets can become available should the bets be covered by purchases of other numbers.
Quote: BryanHuangPSI think there are additional prizepayouts now that they are considering.
Rather than hit the exact number they are considering adding "Bonuses" on hitting the 1st 3 digits of the winning number.
Example:
1st Prize winning number is 1234.
The number I purchased was 1237. As a result I would win a prize of $25 for every dollar I buy.
What is the new EV here and how does it change now that the "bonus" prize is just the 1st 3 digits of the winning number?
Is this going to happen?
