Pick3genius,Thanks , you have a great question referring to that gambler’s fallacy & the answer to your question depends on specifically the length of time you are referring to when you say the term "recently". In the scenario of the outcome of "6" being rolled on a die at a lower rate than normal in a specified number of draws, or in this case not hitting at all, the answer would just depend on what the actual "expected hit rate" is for the six to be rolled.
In the event only 1 die is being used for each successive roll, the mathematical chances of rolling a six, in every six drawings , would be 1 out of 6 ( being that all sides of this six sided die are weighted equally ),based only on the laws of probability. Now for example, let’s assume a total of 30 successive rolls of the die have occurred & that if no roll was different from the previous in a random environment. So, mathematically the outcome of "6" being the result on a roll should be AT LEAST five times during those thirty rolls. If 6 was rolled only once thru 30 drawings, that mathematically would make the outcome of "6" being rolled, four hits behind the "actual expected hit rate of 5 out of 30" and that event (a six being rolled), can be statistically considered as overdue.
Of course in a pick 3 or pick 4 game, the odds are different as there are different digits, and different digit positions”
You are right on point when you stated the cold digits can be out significantly longer than normal, and of course as we know there is no guaranteed method or technique that you, I, or anyone else would have that would give us the capability to determine the exact date and numerical outcome of the event that is occurring ( Pick 3 Drawing, or Win - 4 Drawing. ) Thankfully New York does have air Blown Ping Pong Balls that are used for Pick 3, and Win - 4 drawings, so using mathematical formulas and the law of averages to determine what digits or numbers are "overdue" for certain positions, or more likely to be drawn is possible. Unfortunately states like Tennessee , just for an example, have computerized drawings where any random pattern of numbers are being chosen and there is no law of probability, or law of averages in effect, just a computer generating random numbers based on a computer. States with computerized drawings may be much more difficult to win due to the fact that any mathematical formula or strategy being used will have no effect on the outcome of what numbers a random number generator is generating.
So, Using the law of averages and probability in a completely random environment (where air blown ping pong balls are being used) is what I am referring to by saying “ A digit must play catch up, or that a digit must begin to hit in that respective overdue position in order to catch up to what it’s "actual expected hit rate" is ( in a completely random environment) . Compare this to flipping a coin 100 times a row. It could land on heads 100 times in a row but that's highly unlikely. "Tails Must land" in a random environment because neither side to the coin has an advantage or disadvantage or the other and each side has an equal chance of being landed on, so the more flips to accumulate, the more likely it is that tails will appear. It's just about impossible for the same outcome to occur over and over with no change, so the next possible outcome must occur in order for things to EVEN OUT in that random environment.
For one more example the digit 7 hasn't hit in the first Position , or in the third position is an Evening Pick 3 draw in 30 Evening Drawings since 1/25/2020 when "777" came out.
What happens in a Midday Drawing has no effect on what is due to happen, or what will happen in an Evening Drawing and this is because both drawings are separate events. States that have one Draw a day Such as California's Pick 4 game, may be easier to win since it's easier to track patterns and trends with only one drawing occurring for that game daily.
Since 777 was drawn for the EVENING, 30 additional EVENING drawings have accumulated. That means the "digit 7" has had 30 chances to be drawn in the first or third positions since then, but has hit zero times out of 30 in each respective position making it mathematically more overdue to be drawn than other digits in those respective positions( 1st or 3rd , example >> 7xx, xx7 ). Thru ten drawings, digit 7 mathematically should have been drawn at least once in that first or third positions, since each ball that comes up in each position has the same weight ,and no ball or "digit" has any advantage over the other, and there are ten different digits in each position which equates to 1 out of ten. Thru 30 drawings, digit 7 should have hit three times in that 1st or 3rd positions, but have Zero hits in either position ( 1st or 3rd ) thru 30 drawings, making it well overdue by three times the actual expected hit rate.Finding these patterns that are well out of normal expected hit rate ranges, such 3 times overdue , is what will help to increase the chances of selecting the right digits or winning numbers for upcoming drawings in the future, but not for a specific date or draw. Knowing what is more likely to happen will not guaranteed any wins, but it will help at cashing in more winning tickets.
Does this guaranteed that the digit 7 will hit tonight in the first or 3rd positions? No, but it does mean the digit 7 "MUST CATCH UP" and begin to hit in that first or third positions in upcoming EVENING drawings if the game is truly random.(That stat is applied to the EVENING DRAWINGS ONLY) . We know digit 7 is colder than normal based on the expected hit rate, and is due to catch up in both the first and 3rd position in evening drawing.
That information can be used to assist in selecting the winning 3 digit number or pair that will be drawn in upcoming drawings. Play all the numbers with digit 7 as a front pair to get a Front Pair Hit. 70x, 71x, 72x, 73x, etc... or play all the numbers with digit 7 in the 3rd position to gain a back pair hit x07, x17, x27, x37 etc...some numbers such as split doubles 77's are also a possibility to be drawn with 7 being due in both the first & 3rd positions as 7x7 so a number like"727 Straight" is mathematically a better bet than most for the Evening.This does not guaranteed that 727 will hit. Math can't always be used to win but it well help to spot those overdue patterns and trends and assist in determining what the winning digits or numbers may be in Upcoming Drawings. I know this was a lot, but I hope it answered your question, and Good Luck!