Pick 3 math lol ok:
TRIPLES: 000-999. There are only 10 of them. The most beautiful thing about that is that there are only 10 of them . You have a 10/1000 chance of hitting a triple. Or 1%.
SINGLES: The chances of getting a exact pick 3 hit is 1 out of 1000. How do we know this? There are only ten numbers. 0-9.
You have a 1 in 10 chance of getting the number of your choice. Say you want the number 7. There's a 1/10 chance of you getting the number 7. The next number you want is 1, that too is a 1/10 chance. The third and final number you want is 8. Yep, 1/10 chance.
All you do is multiple 1/10*1/10*1/10=1/1000. You have 1/1000 chance of getting 718 on any given day.
There are 120 six way combinations in pick 3. Combinated 718 would be:
718, 781, 871, 817, 178, 187. They count as ONE ANY hit and SIX EXACT hits. This means the chances of hitting the combination is 6/1000 but of getting 718 exactly...still 1/1000.
Let's say that you want 7 to be your first number, 1/10 chance. But The second number must be a number that is NOT 7...it could be any number except 7. This means there is a 1/9 chance of picking, say, 1. Then the last number can be any number BESIDES 7 or 1. You still have eight numbers to choose from. The chances of you picking an 8 is 1/8.
So we take (1/10)*(1/9)*(1/8) and multiply them together and we get....1/720. Which means that 718 is 1 out of 720 straight numbers that can be hit EXACT. There are 720 straight 6-way numbers that could come out. If you played all of them tonight you would have a 720/1000 chance of hitting. 72% chance of hitting is pretty good odds. But you would have spent MORE playing the number than you would be paid out!
If you're an ANY person then you would have to only buy 120 tickets to have that 72% chance. Because there are 120 combos for a 6-way number! 120*6=720.
We know that there is a 10/1000 chance of hitting a triple. 720/1000 chance of hitting a single. Added together there is a 730/1000 chance of NOT hitting a double. Scary if you like doubles like I do . That's why you get more money for them, less of a chance they will come out! There are 1000 numbers you could hit in the game of Pick 3. We want all of them to be accounted for and doubles are still unaccounted for! This is taken care of by 1000-730=270. There are 270 double numbers that can be hit EXACT. Exact is the big money, the $250 or $500. While any given number is 1/1000 chance of coming out exact, there is 270/1000 of that number being a double, or 27%.
This is done a little differently, but really the same way. Let's take the number 212. Let's pretend YOU want 212 to come out.
You want the first number to match the LAST number. Okay, cool. Let's say you know it's going to be 2_2 while the middle number could be anything...EXCEPT 2 (we have to avoid having a triple!) The first number is 2. There's a 1/10 chance of it being 2. The second must not be 2...it has to be something else. It now only has nine numbers to pick from. So the second number has 1/9 chance of getting 1, 4, 3, 9, etc whatever non-2 number you want to fill in for the middle spot. But we want a 1. 1 has a 1/9 chance of coming in the second slot. The last number you want is a 2...like the first number. See, it has a 1/10 chance of coming out as a 2 BUT it must NOT be a 1. If it was it would be 211...which is also a double but we want 212. Since the number MUST be a double and MUST not be a 1 it MUST be a 2. IT not being a 1 leaves it 1/9 chance of coming out as 2.
Confusing, you betcha. The only qualifer for last number is that it not be a 1. Which gives it a 1/9 chance of a 2 coming out. But if one of the other eight numbers come out...guess what! It's a single, regular, straight number!
So we have 1/10*1/9*1/9=1/810. We multiply that but three and get 3/810. Which reduces to 1/270. If KNOW in your gut there's a double coming. There is 1/270 chance of you getting it for $500!
212 comes in three forms for anyers.
With there being 270 exact doubles, there are 90 anys for doubles. If you KNOW in your gut a double is coming you technically have a 1/90 chance of getting it if you play 212 any. It's 270/3=90. Just like it's 1/120 for playing your straight number combo'd. There's a 1/90 chance of playing your double number combo'd.
72% for 6-way numbers + 27% for doubles + 1% for triples=100%.
But in the end it's 1/1000 for any random EXACT number at all whether it's 222, 212, or 718.
Hope this helped some new comers. If anyone has anything to add let me know!!!
ANY=BOX and EXACT=STRAIGHT for all my non-NC peeps .