Pick 3 Paradox? Question of probability

Reply #12

Thoth — Tue, 06 Dec 2005 04:14:28 GMT

It's not that I was trying to make the info misleading.....It was about observation.In the hypothetical situation, the balls were drawn under a cover and then two repeated digits were always revealed first (regardless of position) - leaving the last unknown digit to be guessed at and what were the odds that it would be the same.The whole point was, that when it is observed in this way, that it is impossible to give the last digit revealed a true 10% chance of being a duplicate of the first two... [ More ]

Reply #11

Thoth — Tue, 06 Dec 2005 02:14:36 GMT

The Triples, as a whole, make up 10/1000 or 1% of the Total combinations. This reduces to 1/100.When a ANY Triple is drawn, there is a 50% chance that you will see another triple drawn WITHIN the next 69 games.75% of the time, a triple will be drawn WITHIN 138 games of the last triple hit.99% of the time a triple will hit WITHIN 459 games of the last triple hit.The above info is NOT for any specific Triple, it treats all 10 Triples as a group. If your tracking a specific Triple, such as 999, th... [ More ]

Reply #10

johnph77 — Fri, 02 Dec 2005 09:52:20 GMT

The information is misleading in a way. There are 270 combinations with two numbers the same and only ten triples. But the premise at the beginning was that you already had the same two numbers and were drawing a third.For instance, if you were picking the numbers in consecutive order (Position 1, Position 2 and Position 3), if the same two numbers were drawn for Positions 1 and 2, then there is a 1 in 10 possibility for a triple.The 270 double combinations include those combinations with the sa... [ More ]

Reply #9

Pinetree — Fri, 02 Dec 2005 04:13:29 GMT

Thoth,You posted this info about 6-way numbers: 50% of the time a NoMatch (6 way boxed number) will hit within 116 draws of its last draw. 75% of the time it will hit within 231 draws of its last draw. And....99.00% of the time a nomatch will hit within 765 games of its last draw. Do you have the same type of data for triples

Reply #8

Thoth — Mon, 28 Nov 2005 00:13:57 GMT

Good to see someone caught on - Indeed it is all about perception!A front loaded double does in fact have a 10% chance of creating a triple. In just the the same way a back loaded double and a split loaded double also have the same 10% chance, but when and only when they are looked at individually. The problem arises in my so called paradox because of how the numbers were perceived or observed. All the double types (front - back - split) do have the individual 10% chance of creating a triple

Reply #7

WIN D — Thu, 24 Nov 2005 16:27:50 GMT

Some really good FYI that might be of further interest ..... There were 5,410 doubles last year. A little over 1/3 of those were the expected Front loaded Doubles ......or doubles starting out in Positions 1 and 2. 1,952 Front loaded doubles to be exact. One would expect of the 1,952 doubles that we would get approx 195 Trips. We actually got a few more than that .....we got an additional 21 trips. For a grand total of216 trips for the year. Very gratifying really.

Reply #6

WIN D — Thu, 24 Nov 2005 15:43:33 GMT

Although... strange as it might seem... when getting the actual results back for this over the period of a year the expected ratio between these doubles and trips is almost right on the money. Looking at doubles for the U.S. the ratio of doubles and their particular trips was right at the expected rate 10%. 11 doubles 213 ..... trips 111 ......26 22 double 185.....trips 222 .......13 33 double 191 ....trips 333.......25 44 180......trips 444.......17 55

Reply #5

powerplayer — Thu, 24 Nov 2005 15:32:02 GMT

GOOD SHOW

Reply #4

WIN D — Thu, 24 Nov 2005 15:11:34 GMT

Would like to know how the 2.71 chance works. Thanks for this post this is very interesting. I have always wondered about this and it has perplexed me for years.

Reply #3

paint1 — Sat, 12 Nov 2005 07:14:19 GMT

I'd say if you live in Western Canada,the odds are pretty good. The last three draws were593, 953, 953. And here's me blaming it on our greedy government rather than mathematical odds.

Reply #2

Thoth — Fri, 11 Nov 2005 01:30:37 GMT

Thanks Raven,I know that the 720 NoMatch #'s = 72% and that the 270 Doubles = 27% and the ten Triples = 1% of the total 1000 combos. Any of the three number types will statistically perform closely to their odds: in 10,000 games there will be AROUND 7200 NoMatches, 2700 Doubles, and 100 triples. Frequency can never change the odds, but only verify it.Im not trying to guess the probabilty based on frequency or statistics, I am trying to verify the odds (or should I say find the odds/probability... [ More ]

Reply #1

Raven62 — Thu, 10 Nov 2005 23:36:17 GMT

Cash 3 Facts============Cash 3 uses number from 0 to 9 (10 digits) and has a possible of 1,000combinations. These numbers can be combined as followsCombo Type Sample #s Occurrences-----------------------------------------------3 single digits 123 71%Double digits 112 27%Triple digits 111 1.37%The above numbers are facts not conjecture, guessing, Dream books,tic-tac-toe or anything else that is not based upon Factual draws.So from looking at the com... [ More ]

Pick 3 Paradox? Question of probability

Thoth — Thu, 10 Nov 2005 18:12:31 GMT

The standard (mechanical) way that a Pick 3 digit is selected is to draw one ball from a machine that contains a pool of ten balls. This is done 3 separate times (there are 3 machines that each contain ten balls) to give us our winning Pick 3 combination. Since there are ten balls in each machine we can calculate the total possible combinations by multiplying each of the machines ten balls by the other machines ten balls and so on. When this is done we get 10x10x10, which equals 1000 possible... [ More ]