NY United States Member #23835 October 16, 2005 3502 Posts Offline

Posted: October 1, 2009, 2:22 am - IP Logged

All high/ all low isn't a 500/500 proposition. High and low each have 5 digits, so there are 125 (5*5*5) numbers that qualify. That means that you should expect all high (as well as all low, all odd, or all even) in 1 of every 8 drawings. Since the odds of having it happening again in the next drawing would also be 1 in 8, we would expect it to happen twice in a row once every 64 drawings. Compare that to once in every 4 for flipping a coin.

The probability that it won't happen for any number of drawings is the probability of a different outcome, raised to the nth power, where n is the number of drawings. The probability of a different outcome is 63/64, or 0.984375, so the probability that it won't happen in 31 drawings is 0.984375 to the 30th power*. That's 0.623, or 62.3%. Conversely there's a 37.7% chance that it will happen in any given month.

I'm not sure what "mostly to all high" means. If it means 2 high and whatever the 3rd digit is, then there are 5*5*10 or 250 numbers that qualify. For that we'd expect repeats once every 16 drawings. The probability of not happening in a month would be 15/16 or 0.9375 ^ 30 or about 14.4%. That's almost two months per year.

* I used the 30th power instead of 31st, because there can't be a repeat on the first drawings, and if there's a repeat after the 31st drawing it will be in the next month. The difference for raising to the 31st is very small anyway.

Stone Mountain*Georgia United States Member #828 November 2, 2002 10491 Posts Offline

Posted: October 1, 2009, 4:27 pm - IP Logged

Hello Ky Floyd ....good to know your around. This was a confusing term to someone not used to PICK 3 language. Sorry about that. I used a term which is pretty well known within the Pick 3 Hobby Player community.... " Mostly to ALL HIGH" ...Mostly to ALL LOW..... Mostly to all Even .....Mostly to all ODD.

What this pretty commonly used phrase indicates to mostly to ALL of us is.... LOL The 10 pure numbers in each of those groups...... as well as the numbers which contain 2 of the named group digits.

For example :

The 10 single number ALL HIGH ....... 569, 578, 579, 678, 589, 679, 689, 789, 567, 568

Along with the remaining 50 Mostly single like numbers which contain at least 2 of the high digits

All of these Box types above translate to these numbers below...... 495 of them plus the 5 trips versions for a total of500 numbers . Of course the Mostly to ALL LOW numbers would be the other HALF .

The reason I highlighted the 868 is because Ga Eve last night drew another ...." Mostly to ALL HIGH" number from that half of the 1000 chart.

Now 34 days or Coin flips...... and No back to back Tails from the Mostly to ALL LOW half of the chart..

So ..... the beat goes on for one more night without hitting 2 Heads in a row.

****** One thing we do know for sure .....beyond All doubt and with 100% surity.... It will have to go on to at least draw 36 now ...before this String ends. That much is sure.

The only real failure .....is the failure to try.

Luck is a very rare thing....... Odds not so much.

Now, the question is going to have to be ...... What is the probability of tossing a coin 36 times without getting 2 Tails in a row ? At least for now....thats the question. LOL

The only real failure .....is the failure to try.

Luck is a very rare thing....... Odds not so much.

Stone Mountain*Georgia United States Member #828 November 2, 2002 10491 Posts Offline

Posted: October 1, 2009, 8:05 pm - IP Logged

059 hit tonight ....... from the Mostly to ALL High group ...... again. Mostly Odd too.

Now the question will have to be.... What is the probability of tossing a coin 38 times without getting 2 Tails in a row?

I guess a good way to frame this is to take it as ......( 2 tosses equal = 1 event) So far we have had 18 2 toss events .....and 18 negative outcomes. If tomorrow is also another Mostly to ALL High..... it will be 19 negative outcomes in a row. wow...

Someone betting the other way would have lost 18two game eventsin a row so far! So to speak... and if tomorrow is another Mostly to all High number ....it wil. be 19 losses in a row.

All of these Box types above translate to these numbers below...... 495 of them plus the 5 trips versions for a total of 500 numbers . Of course the Mostly to ALL LOW numbers would be the other HALF .

NY United States Member #23835 October 16, 2005 3502 Posts Offline

Posted: October 2, 2009, 1:16 am - IP Logged

What is the probability of tossing a coin 38 times without getting 2 Tails in a row?

I guess a good way to frame this is to take it as ......( 2 tosses equal = 1 event) So far we have had 18 2 toss events

Nope. Tossing a coin 38 times gives you 37 "2 toss events." Each event starts with the first of 2 consecutive tosses, and ends with the following toss. Toss 1 starts the first event and toss 2 finishes it, but #2 is also the start of the 2nd event: 1 & 2 2 & 3 3 & 4 . . . 37 & 38

Toss 38 won't become a 2 toss event until toss 39 occurs.

The probability of a result other than two tails in any event is .75. Just as the probability ot two tails is .5 x .5, the probability of two events both being something other than two tails is .75 x .75. For n consecutive events it's .756^n. For the 37 events *ending* with toss 38 it would be .75^37, which is .000024 or 1 in 41,950.

NY United States Member #23835 October 16, 2005 3502 Posts Offline

Posted: October 2, 2009, 2:56 pm - IP Logged

It is that simple. What you've done is list all possible outcomes and the ratio between two types of outcomes, and assumed that the ratio can be used to determine the probabilty of one unlikely set of possible outcomes. That works for the possible outcomes of a single event, but not multiple iterations, as in this case. In essence you're using each new flip to change the probability of previous flips.

Let's start from flip # 2 and then look at what happens with flip # 3. As you correctly note, after flip # 2 there are 4 possible outcomes, and there's a 75% chance that we've had one of the 3 results that didn't already give us back to back tails. Since we're looking at the probability of not having any back to back tails, we're only concerned with outcomes where that's the result we've gotten, and that 4th possible result is no longer relevant. If it happened it happened, and it's now a certainty rather than a probability. Therefore we've conducted the 2nd flip, and it was either heads or tails, with a 50% chance of each. We now make flip # 3, and there is a 50% chance it will be heads and a 50% chance it will be tails. That means that when we see the result of flip #3 there is a 75% chance that we will have ended our streak with no back to back tails and a 25% chance that it will remain unbroken.

That means that after flip #3 the chance that we still don't have back to back tails is 75% of what it was after flip #2. 75% of 75% is 56.25%, not the 62.5% you've shown.

As we move down the chart we'll have the same pattern. Each succeeding flip may increase the total number of possible outcomes that could have happened by a factor of two, but it only adds 4 new possibilities to the results we've actually had. Each time we reduce the possibility of no back to back tails to 75% of the previous possibility. Your figures consistently show a figure that is close to 80%, but varies a bit.

BTW, in # 50 you're missing 5 possible outcomes in the no back to back column.

West Concord, MN United States Member #21 December 7, 2001 3680 Posts Offline

Posted: October 2, 2009, 4:24 pm - IP Logged

Quote: Originally posted by KY Floyd on October 2, 2009

It is that simple. What you've done is list all possible outcomes and the ratio between two types of outcomes, and assumed that the ratio can be used to determine the probabilty of one unlikely set of possible outcomes. That works for the possible outcomes of a single event, but not multiple iterations, as in this case. In essence you're using each new flip to change the probability of previous flips.

Let's start from flip # 2 and then look at what happens with flip # 3. As you correctly note, after flip # 2 there are 4 possible outcomes, and there's a 75% chance that we've had one of the 3 results that didn't already give us back to back tails. Since we're looking at the probability of not having any back to back tails, we're only concerned with outcomes where that's the result we've gotten, and that 4th possible result is no longer relevant. If it happened it happened, and it's now a certainty rather than a probability. Therefore we've conducted the 2nd flip, and it was either heads or tails, with a 50% chance of each. We now make flip # 3, and there is a 50% chance it will be heads and a 50% chance it will be tails. That means that when we see the result of flip #3 there is a 75% chance that we will have ended our streak with no back to back tails and a 25% chance that it will remain unbroken.

That means that after flip #3 the chance that we still don't have back to back tails is 75% of what it was after flip #2. 75% of 75% is 56.25%, not the 62.5% you've shown.

As we move down the chart we'll have the same pattern. Each succeeding flip may increase the total number of possible outcomes that could have happened by a factor of two, but it only adds 4 new possibilities to the results we've actually had. Each time we reduce the possibility of no back to back tails to 75% of the previous possibility. Your figures consistently show a figure that is close to 80%, but varies a bit.

BTW, in # 50 you're missing 5 possible outcomes in the no back to back column.

You're right about the 50 Back-to-Back flips; it's an Excel computation issue. It actually should be 1125866955562525. It’s caused by the fact that Excel tunicates the number after a certain number of digits; in this case 15 digits and the 5 was dropped.

Buuut... you are wrong about the calculation of probability; in this case, the probability of No Back-to-Back. Where you went wrong is not considering ALL possibilities. That's what the table shows. So, let's go through the progression. We'll use 1's and 0's to represent the flip; where 1 is outcome occurred and 0 is the outcome did not. Since this is a succession of flips, we'll start at 2 flips and look at ALL the possible outcomes. Now, by definition, a No Back-to-Back flip is when there are no consecutive 1’s; i.e. (1 1). The following is the total possible outcomes for 2 flips.

Flip #

Outcome #

1

2

No Back-To-Back

1

0

0

TRUE

2

0

1

TRUE

3

1

0

TRUE

4

1

1

FALSE

From this we can see there are 3 possible outcomes where there are No Back-to-Back flips. Given that the total number of outcomes is 4, the probability of having a No Back-to-Back flip is 3 / 4, or 75%. Continuing this progression, we can go to 3 flips as follows:

Flip #

Outcome #

1

2

3

No Back-To-Back

1

0

0

0

TRUE

2

0

0

1

TRUE

3

0

1

0

TRUE

4

0

1

1

FALSE

5

1

0

0

TRUE

6

1

0

1

TRUE

7

1

1

0

FALSE

8

1

1

1

FALSE

The table shows there are 5 possible outcomes where there is No Back-to-Back flip. This becomes 5 / 8, or 62.5% probability of having a No Back-to-Back flip. The progression continues...

Flip #

Outcome #

1

2

3

4

No Back-To-Back

1

0

0

0

0

TRUE

2

0

0

0

1

TRUE

3

0

0

1

0

TRUE

4

0

0

1

1

FALSE

5

0

1

0

0

TRUE

6

0

1

0

1

TRUE

7

0

1

1

0

FALSE

8

0

1

1

1

FALSE

9

1

0

0

0

TRUE

10

1

0

0

1

TRUE

11

1

0

1

0

TRUE

12

1

0

1

1

FALSE

13

1

1

0

0

FALSE

14

1

1

0

1

FALSE

15

1

1

1

0

FALSE

16

1

1

1

1

FALSE

In the case of 4 flips, there are 8 out of 16 possible outcomes for a probability of 50%. Moving along...

Flip #

Outcome #

1

2

3

4

5

No Back-To-Back

1

0

0

0

0

0

TRUE

2

0

0

0

0

1

TRUE

3

0

0

0

1

0

TRUE

4

0

0

0

1

1

FALSE

5

0

0

1

0

0

TRUE

6

0

0

1

0

1

TRUE

7

0

0

1

1

0

FALSE

8

0

0

1

1

1

FALSE

9

0

1

0

0

0

TRUE

10

0

1

0

0

1

TRUE

11

0

1

0

1

0

TRUE

12

0

1

0

1

1

FALSE

13

0

1

1

0

0

FALSE

14

0

1

1

0

1

FALSE

15

0

1

1

1

0

FALSE

16

0

1

1

1

1

FALSE

17

1

0

0

0

0

TRUE

18

1

0

0

0

1

TRUE

19

1

0

0

1

0

TRUE

20

1

0

0

1

1

FALSE

21

1

0

1

0

0

TRUE

22

1

0

1

0

1

TRUE

23

1

0

1

1

0

FALSE

24

1

0

1

1

1

FALSE

25

1

1

0

0

0

FALSE

26

1

1

0

0

1

FALSE

27

1

1

0

1

0

FALSE

28

1

1

0

1

1

FALSE

29

1

1

1

0

0

FALSE

30

1

1

1

0

1

FALSE

31

1

1

1

1

0

FALSE

32

1

1

1

1

1

FALSE

5 flips, there are 13 out of 32 possible, this works to 40.625% probability of having No Back-to-Back flips. And, one more to establish the proper sequence.

Flip #

Outcome #

1

2

3

4

5

6

No Back-To-Back

1

0

0

0

0

0

0

TRUE

2

0

0

0

0

0

1

TRUE

3

0

0

0

0

1

0

TRUE

4

0

0

0

0

1

1

FALSE

5

0

0

0

1

0

0

TRUE

6

0

0

0

1

0

1

TRUE

7

0

0

0

1

1

0

FALSE

8

0

0

0

1

1

1

FALSE

9

0

0

1

0

0

0

TRUE

10

0

0

1

0

0

1

TRUE

11

0

0

1

0

1

0

TRUE

12

0

0

1

0

1

1

FALSE

13

0

0

1

1

0

0

FALSE

14

0

0

1

1

0

1

FALSE

15

0

0

1

1

1

0

FALSE

16

0

0

1

1

1

1

FALSE

17

0

1

0

0

0

0

TRUE

18

0

1

0

0

0

1

TRUE

19

0

1

0

0

1

0

TRUE

20

0

1

0

0

1

1

FALSE

21

0

1

0

1

0

0

TRUE

22

0

1

0

1

0

1

TRUE

23

0

1

0

1

1

0

FALSE

24

0

1

0

1

1

1

FALSE

25

0

1

1

0

0

0

FALSE

26

0

1

1

0

0

1

FALSE

27

0

1

1

0

1

0

FALSE

28

0

1

1

0

1

1

FALSE

29

0

1

1

1

0

0

FALSE

30

0

1

1

1

0

1

FALSE

31

0

1

1

1

1

0

FALSE

32

0

1

1

1

1

1

FALSE

33

1

0

0

0

0

0

TRUE

34

1

0

0

0

0

1

TRUE

35

1

0

0

0

1

0

TRUE

36

1

0

0

0

1

1

FALSE

37

1

0

0

1

0

0

TRUE

38

1

0

0

1

0

1

TRUE

39

1

0

0

1

1

0

FALSE

40

1

0

0

1

1

1

FALSE

41

1

0

1

0

0

0

TRUE

42

1

0

1

0

0

1

TRUE

43

1

0

1

0

1

0

TRUE

44

1

0

1

0

1

1

FALSE

45

1

0

1

1

0

0

FALSE

46

1

0

1

1

0

1

FALSE

47

1

0

1

1

1

0

FALSE

48

1

0

1

1

1

1

FALSE

49

1

1

0

0

0

0

FALSE

50

1

1

0

0

0

1

FALSE

51

1

1

0

0

1

0

FALSE

52

1

1

0

0

1

1

FALSE

53

1

1

0

1

0

0

FALSE

54

1

1

0

1

0

1

FALSE

55

1

1

0

1

1

0

FALSE

56

1

1

0

1

1

1

FALSE

57

1

1

1

0

0

0

FALSE

58

1

1

1

0

0

1

FALSE

59

1

1

1

0

1

0

FALSE

60

1

1

1

0

1

1

FALSE

61

1

1

1

1

0

0

FALSE

62

1

1

1

1

0

1

FALSE

63

1

1

1

1

1

0

FALSE

64

1

1

1

1

1

1

FALSE

Based on 6 flips there is 21 out of 64 for a probability of 32.8125%. With the progression we have we can find an equation or equation process to find the next sequence and then verify it by actually doing all the outcomes. The current progression is shown below.

Flips

No Back-to-Back Outcomes

2

3

3

5

4

8

5

13

6

21

If you know this sequence, you should be able to see it's a Fibonacci Sequence; where the previous 2 outcomes summed together become the next outcome total.

3 + 5 = 8

5 + 8 = 13

8 + 13 = 21

So, where does this lead? Well, by this understanding the next No Back-to-Back outcome count should be 13 + 21, or 34; you verify it in the table below.

Flip #

Outcome #

1

2

3

4

5

6

7

No Back-To-Back

1

0

0

0

0

0

0

0

TRUE

2

0

0

0

0

0

0

1

TRUE

3

0

0

0

0

0

1

0

TRUE

4

0

0

0

0

0

1

1

FALSE

5

0

0

0

0

1

0

0

TRUE

6

0

0

0

0

1

0

1

TRUE

7

0

0

0

0

1

1

0

FALSE

8

0

0

0

0

1

1

1

FALSE

9

0

0

0

1

0

0

0

TRUE

10

0

0

0

1

0

0

1

TRUE

11

0

0

0

1

0

1

0

TRUE

12

0

0

0

1

0

1

1

FALSE

13

0

0

0

1

1

0

0

FALSE

14

0

0

0

1

1

0

1

FALSE

15

0

0

0

1

1

1

0

FALSE

16

0

0

0

1

1

1

1

FALSE

17

0

0

1

0

0

0

0

TRUE

18

0

0

1

0

0

0

1

TRUE

19

0

0

1

0

0

1

0

TRUE

20

0

0

1

0

0

1

1

FALSE

21

0

0

1

0

1

0

0

TRUE

22

0

0

1

0

1

0

1

TRUE

23

0

0

1

0

1

1

0

FALSE

24

0

0

1

0

1

1

1

FALSE

25

0

0

1

1

0

0

0

FALSE

26

0

0

1

1

0

0

1

FALSE

27

0

0

1

1

0

1

0

FALSE

28

0

0

1

1

0

1

1

FALSE

29

0

0

1

1

1

0

0

FALSE

30

0

0

1

1

1

0

1

FALSE

31

0

0

1

1

1

1

0

FALSE

32

0

0

1

1

1

1

1

FALSE

33

0

1

0

0

0

0

0

TRUE

34

0

1

0

0

0

0

1

TRUE

35

0

1

0

0

0

1

0

TRUE

36

0

1

0

0

0

1

1

FALSE

37

0

1

0

0

1

0

0

TRUE

38

0

1

0

0

1

0

1

TRUE

39

0

1

0

0

1

1

0

FALSE

40

0

1

0

0

1

1

1

FALSE

41

0

1

0

1

0

0

0

TRUE

42

0

1

0

1

0

0

1

TRUE

43

0

1

0

1

0

1

0

TRUE

44

0

1

0

1

0

1

1

FALSE

45

0

1

0

1

1

0

0

FALSE

46

0

1

0

1

1

0

1

FALSE

47

0

1

0

1

1

1

0

FALSE

48

0

1

0

1

1

1

1

FALSE

49

0

1

1

0

0

0

0

FALSE

50

0

1

1

0

0

0

1

FALSE

51

0

1

1

0

0

1

0

FALSE

52

0

1

1

0

0

1

1

FALSE

53

0

1

1

0

1

0

0

FALSE

54

0

1

1

0

1

0

1

FALSE

55

0

1

1

0

1

1

0

FALSE

56

0

1

1

0

1

1

1

FALSE

57

0

1

1

1

0

0

0

FALSE

58

0

1

1

1

0

0

1

FALSE

59

0

1

1

1

0

1

0

FALSE

60

0

1

1

1

0

1

1

FALSE

61

0

1

1

1

1

0

0

FALSE

62

0

1

1

1

1

0

1

FALSE

63

0

1

1

1

1

1

0

FALSE

64

0

1

1

1

1

1

1

FALSE

65

1

0

0

0

0

0

0

TRUE

66

1

0

0

0

0

0

1

TRUE

67

1

0

0

0

0

1

0

TRUE

68

1

0

0

0

0

1

1

FALSE

69

1

0

0

0

1

0

0

TRUE

70

1

0

0

0

1

0

1

TRUE

71

1

0

0

0

1

1

0

FALSE

72

1

0

0

0

1

1

1

FALSE

73

1

0

0

1

0

0

0

TRUE

74

1

0

0

1

0

0

1

TRUE

75

1

0

0

1

0

1

0

TRUE

76

1

0

0

1

0

1

1

FALSE

77

1

0

0

1

1

0

0

FALSE

78

1

0

0

1

1

0

1

FALSE

79

1

0

0

1

1

1

0

FALSE

80

1

0

0

1

1

1

1

FALSE

81

1

0

1

0

0

0

0

TRUE

82

1

0

1

0

0

0

1

TRUE

83

1

0

1

0

0

1

0

TRUE

84

1

0

1

0

0

1

1

FALSE

85

1

0

1

0

1

0

0

TRUE

86

1

0

1

0

1

0

1

TRUE

87

1

0

1

0

1

1

0

FALSE

88

1

0

1

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1

1

1

FALSE

89

1

0

1

1

0

0

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FALSE

90

1

0

1

1

0

0

1

FALSE

91

1

0

1

1

0

1

0

FALSE

92

1

0

1

1

0

1

1

FALSE

93

1

0

1

1

1

0

0

FALSE

94

1

0

1

1

1

0

1

FALSE

95

1

0

1

1

1

1

0

FALSE

96

1

0

1

1

1

1

1

FALSE

97

1

1

0

0

0

0

0

FALSE

98

1

1

0

0

0

0

1

FALSE

99

1

1

0

0

0

1

0

FALSE

100

1

1

0

0

0

1

1

FALSE

101

1

1

0

0

1

0

0

FALSE

102

1

1

0

0

1

0

1

FALSE

103

1

1

0

0

1

1

0

FALSE

104

1

1

0

0

1

1

1

FALSE

105

1

1

0

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0

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0

FALSE

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1

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1

FALSE

107

1

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FALSE

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1

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0

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0

1

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FALSE

109

1

1

0

1

1

0

0

FALSE

110

1

1

0

1

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0

1

FALSE

111

1

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0

1

1

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0

FALSE

112

1

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0

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1

FALSE

113

1

1

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0

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FALSE

114

1

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FALSE

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FALSE

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FALSE

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FALSE

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1

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FALSE

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FALSE

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1

1

1

1

0

FALSE

128

1

1

1

1

1

1

1

FALSE

Presented 'AS IS' and for Entertainment Purposes Only. Any gain or loss is your responsibility. Use at your own risk.

Order is a Subset of Chaos Knowledge is Beyond Belief Wisdom is Not Censored Douglas Paul Smallish Jehocifer

New Jersey United States Member #17843 June 28, 2005 51003 Posts Online

Posted: October 2, 2009, 4:29 pm - IP Logged

"Now, the question is going to have to be ...... What is the probability of tossing a coin 36 times without getting 2 Tails in a row? At least for now....thats the question. LOL "

It really doesn't matter: Heads They Win, Tails You Lose! LOL!!!

A mind once stretched by a new idea never returns to its original dimensions!

NY United States Member #23835 October 16, 2005 3502 Posts Offline

Posted: October 3, 2009, 1:08 pm - IP Logged

"Where you went wrong is not considering ALL possibilities."

I was dismissing some of the possibilities, albeit indirectly, and it took a while to find the fault in my logic.

I'm glad to see that the number of outcomes with no back to back flips follows the Fibonacci sequence. If it wasn't for that saving grace I'd be completely dismayed at seeing the calculations. Most math is fairly elegant, and most probability follows a fairly direct path of factorials or squares, and simple arithmetic. Even calculating as the remainder of the probability of the opposite outcome seems perfectly simple and straighforward. For this exercise I'm still not seeing anything simple and direct in calculating the probabilities, and I find it extremely counterintuitive that the differences between the probability at n flips and n+1 don't change by the same factor.

Any chance the excel formual you used can essily do a list for not having any 3 in a row occcurrences? I'd be curious to see if there's an part of that that has a simple pattern.

West Concord, MN United States Member #21 December 7, 2001 3680 Posts Offline

Posted: October 3, 2009, 2:28 pm - IP Logged

Quote: Originally posted by KY Floyd on October 3, 2009

"Where you went wrong is not considering ALL possibilities."

I was dismissing some of the possibilities, albeit indirectly, and it took a while to find the fault in my logic.

I'm glad to see that the number of outcomes with no back to back flips follows the Fibonacci sequence. If it wasn't for that saving grace I'd be completely dismayed at seeing the calculations. Most math is fairly elegant, and most probability follows a fairly direct path of factorials or squares, and simple arithmetic. Even calculating as the remainder of the probability of the opposite outcome seems perfectly simple and straighforward. For this exercise I'm still not seeing anything simple and direct in calculating the probabilities, and I find it extremely counterintuitive that the differences between the probability at n flips and n+1 don't change by the same factor.

Any chance the excel formual you used can essily do a list for not having any 3 in a row occcurrences? I'd be curious to see if there's an part of that that has a simple pattern.

It's just a matter of setting up the proper testing IF statements; you can use the same set of outcomes and reform the testing IF condition. To understand this correctly, you are looking for a condition when there are no 1's in a triple consecutive sequence, i.e. ( 1 1 1 )?

Presented 'AS IS' and for Entertainment Purposes Only. Any gain or loss is your responsibility. Use at your own risk.

Order is a Subset of Chaos Knowledge is Beyond Belief Wisdom is Not Censored Douglas Paul Smallish Jehocifer

West Concord, MN United States Member #21 December 7, 2001 3680 Posts Offline

Posted: October 3, 2009, 4:13 pm - IP Logged

Well, OK... here is the expansion and more than just a 3 non-consecutive flips. I've expanded it to 5 non-consecutive flips. Below is a table with just the counts. You can figure the Probability by taking the count and dividing by the value, 2^{n}, where n is the number of flips; to get the percentage, multiply by 100. Also, I have found that the counts are related to the number of non-consecutives in determining the progression sequence. It's a play on the basic idea of the Fibonacci Sequence by expanding the sum from the last 2 values to increase the sum set by one more value. The non-consecutive count for 3 is the sum of the last 3 values; the non-consecutive count for 4 is the sum of the last 4 values and so on. The numbers highlighted in each column are the starting Fibonacci numbers.

ORLANDO, FLORIDA United States Member #4924 June 3, 2004 5962 Posts Online

Posted: October 4, 2009, 10:35 am - IP Logged

Quote: Originally posted by truecritic on October 4, 2009

@ KY Floyd

@ JADELottery

Not that I ever needed those particular questions answered but glad you guys are around for all the statistics/probabilities/math! Thank you.

How right you are! It's nice to know, for questions like these, we have brilliant minds that will come forward with the solution. Thanks to both of them.