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# Help on expected hit rate averages

Topic closed. 6 replies. Last post 10 years ago by Thoth.

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Stone Mountain*Georgia
United States
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November 2, 2002
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 Posted: November 30, 2006, 11:06 am - IP Logged

Here is something for us to ponder .

Ga. Midday has had 2,783 draws so far......

Wonder if I said there were 55 TRIPLES instead of 10 ...straights or 5.5 % instead 1% of the chart that had never ever hit ....and it were true. (Just to put it in perspective a little)

There are currently 55 straights in the Ga. Midday that have never hit in those 2,783 draws.

Well...... I guess until we find a different status ...or classification for numbers like this we have to handle them the way we are doing for all these other groups right now...the expected math average hit rate.

All of the triples have hit on the Ga. Midday game during those 2,783 games so that was pretty normal and expected. How do we deal with "number lint" such as these slow poke straight.... 55 ?

How many other large groups of un-hit Straights like this exist in the US? What are we missing here? We are missing something. There is an element .....a variable that we are not accounting for. Other wise.......

if we handle these the same way as all the other over due groups right now ...these fellas really are "Monsters"

2,783 draws ..... x 5.5 % = 153. Times over due !

You could say it was like having 55 triples instead of 10....... and suddenly having the realization...... that none of them have hit in almost 9 years of midday draws!!

There must be some sort of accommodation made for a group like this..... Some sort of sliding scale perhaps..... based on the fact that in reality .....no straight is actually late...at least until 1000 draws have past. Perhaps the clock should start there.

How many "Monster" groups are out there like this do you suppose?

I guess on the first day of the Ga. Midday game....after the first number was drawn ... the 999 un-hit straights going into the next day was at that time... the "Monster Group" ... and its just now getting down to 55 remaining straights after 2,782 draws.

Well.... until we get it sorted out...these 55 are .... 153.06 past their expected hit rate average !

These other groups we are closely tracking that are having current running skips of 7.8 or 10.4 .....or 12.3 past due!.... just don't look so dramatic now do they?

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

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

Odds never change .....but probability does.

Win d

Stone Mountain*Georgia
United States
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November 2, 2002
10491 Posts
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 Posted: November 30, 2006, 11:54 am - IP Logged

Wanted to add some results on other groups ......and their expected math average hit rates ....and the actual results during the 2,783 draw history.

2,783 draws ..... expected Single number hit rate..

should be around  2,003 ...  Actual result was 2,034 (I love it when it does that!)

Doubles expected hit rate 751.41......Actual result .. 710.

Trips expected hit rate ..27.82.........  Actual result .. 40

Well.... guess we can't say Trips are over due can we now?  (Actually running about 3 or 4 years ahead of expected rate)

Anyway... that was all pretty much normal and followed the expected rates as per normal.

The trips result was running a little high wasn't it? Maybe those trips have been the culprits and sucking up all the oxygen from those 55 un-hits. LOL

Really.... the rest of the game looks pretty average doesn't it? Thank goodness for that ....at least.

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

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

Odds never change .....but probability does.

Win d

Findlay, Ohio
United States
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May 28, 2004
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 Posted: November 30, 2006, 4:47 pm - IP Logged

Heres one interesting way of looking at it Win D.

It doesn't really matter what kind of combination it is...a no-match, a double-digit or even a triple digit combination... the probability for the combo to hit straight is 1 in 1,000 or .001.  With that in mind, each of the 1,000 combo's by itself can be given a probability or chance to be drawn within X amount of games.

Suppose that X represents your 2,783 consecutive midday drawings in GA.  Every single Pick 3 combo has about a 93.82% chance of being drawn within that time frame!  Now since each of the 1,000 combos has the same 93.82% chance individually, taken as a whole this can only lead to one conclusion.......which is that 93.82% of the entire Pick 3 matrix should be drawn within those 2,783 consecutive games.  If 93.82% of all 1,000 straights are drawn, then 100% - 93.82% = 6.18%  should not be drawn!  So, 1,000 ×.0618 = 61.8 combos never drawn.  This number is very close to the 55 that haven't yet hit in GA.

~Probability=Odds in Motion~

The Carolinas - Charlotte
United States
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September 12, 2005
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 Posted: November 30, 2006, 5:06 pm - IP Logged

Interesting post, WIN D. I would be inclined to play all 55 straight until one hits. And add a progression to it.

The North Carolina Education Lottery - so much a joke that here are their mascots:

Findlay, Ohio
United States
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May 28, 2004
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 Posted: November 30, 2006, 5:26 pm - IP Logged

And yet another way of looking at it:

In 1,000 consecutive games, each stright has about a 63.23% chance of being drawn.  The same rule applies so there should be close to 632 different straight drawn within the 1,000 games.  Since 632 different numbers were drawn, then 368 numbers should not be drawn.  Of those 368 non-hitters, 63.23% of them should hit within the next series of 1,000 consecutive games.

368 × .6323 = 232.68 or 232 even when rounded.  Now, take the 368 straights that didn't hit in the first 1,000 series of games and subtract the 63.23% of them that should hit in the second series of 1,000 games: 368 - 232 = 136.  So now after 2,000 games there should be around 136 straight that havent hit.

Of the 136 combos that still havent hit by game 2,000, you can expect 63.23% of them to hit by game 3,000: 136 × .6323 = 85.99 or 86 even when rounded.  This leaves us with 136 - 86 = 50 non-hitters within 3,000 games.

~Probability=Odds in Motion~

Stone Mountain*Georgia
United States
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November 2, 2002
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 Posted: November 30, 2006, 5:29 pm - IP Logged

Nice ...clear ...crisp....  Thank you Thoth.

So... 61.8 combos and almost right on the money. That's the fascinating sort of thing that keeps me glued to this game. It is pretty isn't it?  Expected 6.18%... result.. 5.5%    after 2783 draws haver come and gone is remarkable to me.

Thoth....please go into the expected ...93.82% within the 2783 draw time frame a little if you would.

Yes.... I agree with you that each straight... regardless of title or group is equal in the eyes of the "Good Luck Elves" ..LOL   I have been on a campaign lately about Triples being very over rated ! Most folks get real fired up about trips when they go over a 100 days! Hah .....

I just don't know Thoth.... not sure about all the math average due rates and how to use them most effectively. Seems I use to win a lot more consistently when I didn't know as much about them. As fast as I find out about tardy groups and hit rates ..... they go way out of the way to break the records and exceed them.  The older the game the more this happens ofcourse... I know that.... but still..  Perception ....and my pocket book don't always seem in-sink ! LOL

All of this reminds me of the time I won the neighborhood championship Monopoly Game..  After becoming the "World Champ" monopoly player and winning Thousands of Dollars \$\$ .....LOL  To celebrate my victory... I went down to the local drug store to get extra large cherry coke. That's when I understood the difference between a game and real life.....  I didn't even have enough coins in my pocket for a piece of candy.

Knowing stuff....winning ....and Money in your pocket don't always match up. LOL

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

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

Odds never change .....but probability does.

Win d

Findlay, Ohio
United States
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May 28, 2004
400 Posts
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 Posted: November 30, 2006, 7:52 pm - IP Logged

Whats most fascinating to me is how every single Pick 3 game that I've ever tested performs very, very similarly from a probability point of view.  Take any amount of consecutive games from any pick 3 game in the country and you will see very similar results when it comes to how many different combos were drawn and/or how many remain to be drawn.

The 93.82% can be derived from the following formula. It will give you the probability based on n, which is the number of consecutive games played:

p = probability

n = number of trials

1-(1-p)^n

1-(1-0.001)^2783 = .938233395, which is 93.82%

If you want to know the how many games you need to play based on a particular chance of success (the Degree of Certainty, then you can use the FFG formula:

DC is the chance listed as a decimal (50%=.5, 95%=.95 etc..)

P is the probability of the event (Pick 3 is 1 in 1000 = .001)

log(1-DC)/log(1-p) = Trials

log(1-.9382)/log(1-.001) = 2782.43

The number that this formula spits out is the amount of consecutive games that are necessary to have the chance (DC) of winning.

It seems as though the real probability for anything to happen actually rests within how many different combos are drawn within measured time frames or consecutive amounts of games.  In all reality, a string of outcomes creates an extremely large and ever-growing combination.  In essence, what these formulas do is calulate the number of combinations that contain the desired outcome at least once within their total...this gives you your percentage of chance to hit AT LEAST once within the given time frame.

As accurate as these percentages truly are, the result is not just limited to an individual combination's long term probability, but rather the entire matrix as a whole.  For example, if you want to know how many games you must play for a 50% chance of winning on a particular straight Pick 3 combination, you would run the FFG formula as follows: log(1-.5)/log(1-.001) = 692.8005 or 693 games rounded.  Not only is that how many games that you must play to have a 50% chance of seeing that combo drawn, but it is also the amount of games required for 50% of the matrix to have been drawn in!  Pick a state, any state...grab a chuck of 693 consecutive games and there will almost always be between 480 and 520 different number!  Those two figures represent the max fluctuation 99% of the time.  Its most common to see 490 to 510.

I have tested these formulas on an empiracal level in at least 20 states now and the results are amazing.  I know of no other formula or theory that dictates the truth of how randomness works in these games better that those formulas.  Its interesting to note that it only takes 693 games to have a 50% chance but it takes a whopping 9,206 games to attain a 99.99% chance!  You see that first 50% chance is the median, which is game 1 through game 693...reliable, tight and consistent!  The other 50% stretches out to infinity and includes more that 8513 consecutive games starting at 694.

Win D, since you like to include 50/50 odds in alot of your strategies, heres another one you could add.  Always look at the last several straights drawn and see how long they have been out before their last hit:  50% of the time the next straight that hits will be one that was out less than or equal to 693 games ago.  The other 50% of the time, the number will have been out at a value of 694 games or greater.

~Probability=Odds in Motion~

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