Dear All
The probability law is of a great precision for every series of random events; it is as precise for random as trigonometry is for angles (remember sin2+cos2=1).
The frequency for any random event can be calculated a priori and then afterwards the observed frequency can be compared with the former calculation.
The most probable frequency (HITS) and its probability can also be calculated for any number of trials.
This most probable is the number which is always used to analyse a series in terms of frequencies and deviations.
THEN Deviations can be calculated.
Still more precisely one can determine by calculation the lower and upper limits for the frequency for a given level of certainty.
For instance, for an event of probability C(5,5)/C(49,5) the expected frequency in 1000000 (one million) trials lies within 101838 and 102243 with a certainty of 1/2
or within 101052 and 103029 for a certainty of 1000 against 1 (999999 trials will have a frequency within this range).

So far I have not read any mathematical foundation on what is cold or hot.
I believe that Hot frequencies are those which are greater than the upper limit, and that Cold frequencies are frequencies below the lower limit, for a given/chosen degree of certainty.
If we accept such a definition then the hot/cold issue will be based on mathematical concepts.
One can use such definition with pairs, triplets as well as for singles or powerball numbers.
Ion's softwares produce the frequency reports.
Now the question is to fix our mind on strategies.
Playing Cold or Hot or "mild"; that is the question!

Below the statistics for 10000 trials on singles in a C(49,5) game; 1020 is the most probable number; 3 ranges are selected: A for a probability of 1/2 from 1000 to 1041; B for 10/1 from 971 to 1070 and C for 1000/1 from 922 to 1119.
The results of my test is:

< 36 BALLS WITHIN RANGE A>
<8 BALLS between 971 and 1000>
< 2 BALLS between 922 and 971> < 3 BALLS between 1070 and 1119 >
Based on the above, 2 balls are strongly "cold", 8 others are "cold with a probability of 10/1" and 3 are "hot".

A random event can show a frequency which is "cold" or "hot" for long series of trials; but how long is long?
How long does it take for a "cold" or a "hot" event to reach a frequency between the limits, for a given probability?

Hot events are those with the shorter but more numerous skips; cold events are just in the reverse situation (fewer and larger skips)

One can test strategies based on the above; I did it for a combination of hot pairs AND hot triples for a parpaluck of 10 000 drawings (lenghty process, prone to errors!); so far more than encouraging.

Lotto-5 Winning Combination Checking
Files: D:\LOTERIES\BRIGHT5\JEUPAIRESTRIPLES ( 3856 ) against > D:\LOTERIES\LOTO\LOTO_29DEC ( 100 )
Date: 01-29-2011

Line Combinations 5 4 3 2
no. Checked Winners Winners Winners Winners
-----------------------------------------------------------------------------
1 11 15 29 46 47 in draw # 42
1 11 15 29 46 47 in draw # 116
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
100 14 22 23 27 28 in draw # 3846
-----------------------------------------------------------------------------
Total hits: 0 64 2059 27480
To conduct further testings, it would be usefull to have a routine
for combining one set of pairs with one set of triples
and then for elimination of duplicate ball numbers in resulting combinations.
I did it with a spreadsheet and it takes hours, with a significant risk of errors.

If someone has ideas for the automation of the above this could make it possible to make a set of testings (different parpalucks for instance)

Have fun and luck!
LouisBachelier