Ok, I've read Sklansky's Theory of Poker though not really understood all of it and I'm going through a Harrington book and he goes on to mention that this or that hand should be played this or that way probably 75% of the time. He mentions briefly that he uses a glance at the second indicator on his wristwatch to decide whether he's in the 25% or the 75% range and yeah, I can see his point. There's no point trying to mentally keep track of where you are in each interval and if you try to choose a random occurrence with your wit alone you'll insert patterns - probably the 75% range becomes something you do 90% of the time. Since deception is certainly a key part of what you're trying to achieve it would serve you best if your number is truly random.

But here's the thing. I don't use a wrist watch. And I don't plan to. So, I wanted to put together a way to pseudo-randomly generate a random number on the spot which I can use in these types of situations.

My initial thought and my ideal was to generate a random number only based on the cards I hold. I wanted to limit the amount of inputs I take into the little calculation that generates a number, and I wanted the inputs to be always available and pretty random all by themselves. The thought is to have a relatively simple algorithm which I can practice and become good at with relative ease so it becomes basically automatic.

The basic mechanism I use is assigning values, adding them together to a number, adding together the digits of that number (and the digits of the resulting number) until I'm down to just one digit. Then use that random digit to determine which random path I shall follow.

I considered using a predefined number for a game session as a 'seed', using seating position etc, but I'm finding that I don't really need that.

I give A a value of 1, J is 11, Q is 12, K is 13. KK is 26. As we know from rolling two dice where 7 is the most likely outcome, in this case 14 is the most likely outcome. To equalize this range I add up the digits - 26 becomes 8, 16 becomes 7 etc. Doing this for all 169 combinations produces the following:

1: 17 occurences
2: 18 occurences
3: 19 occurences
4: 20 occurences
5: 21 occurences
6: 20 occurences
7: 19 occurences
8: 18 occurences
9: 17 occurences

Close enough for government work. Not the final version, but there's definitely hope here.

I want to add in the suits involved. I don't want my play with 97 PF to be predictable. Suits give me 16 combinations. I give diamonds 0, hearts 1, clubs 2 and spades 4. This in isolation produces something like 3 occurrences of 2 and 4 and 0 occurrences of 7. (The 0 is equal to a 9 for practical purposes). Again, close enough for government work.

Based on this system these are some example pseudo-random numbers:
AsKh: 1 (A) + 4 (s) + 13 (K) + 1 (h) = 19 => 1 + 9 = 10 => 1 + 0 = 1
7c5h: 7 (7) + 2 (c) + 5 (5) + 1 (h) = 15 => 1 + 5 = 6
Ts8s: 8
KdJh: 7

The output of this method is a number between 1 and 9, so instead of saying I want to do this or that 50% of the time or 75% of the time, I just have to decide that I'm happy with doing it 4 times out of 9 or 7 times out of 9 and I can use this method to balance it.

Now, regarding this being close enough for government work - as a pseudo-number generator this one is somewhat flawed. Card value factor favours the middle range and the suitedness factor favours two specific values and has no chance for the value 7, which adds up to an uneven range. I've played around with spreadsheets for a while to prove to myself exactly how unbalanced it is, and to be quite frank for this type of random number it is probably sufficient in the basic form - but there is quite an easy fix which makes it about as good as it can be.

The fix to make it an even better balanced distribution of random numbers is this: Differentiate between the cards. Reduce the value for spades to 3 and double the values for one card for both value and suitedness. Going back to the above examples:
AsKh: 1 * 2 (A) + 3 * 2 (s) + 13 (K) + 1 (h) = 22 => 2 + 2 = 4
7c5h: 7 * 2 (7) + 2 * 2 (c) + 5 (5) + 1 (h) = 24 => 2 + 4 = 6
Ts8s: 1
KdJh: 2

The card value part which ranged from 17 to 21 occurrences now shows up with only 18 or 19 occurrences (as balanced as it gets), and similarly the suitedness factor now comes up with either 1 or 2 (no zeroes and no threes) occurences of each digit from that component. It's not going to get any better as long as we're talking pseudo-random.

Basic method:
Diamond: 0
Heart: 1
Club: 2
Spades: 4

Card 1: Card value + Suitedness value
Card 2: Card value + Suitedness value
"Random" number: Card1 + Card2 - keep adding digits together until one digit between 1 and 9 is left.

Better balanced method:
Diamond: 0
Heart: 1
Club: 2
Spades: 3

Card 1: (Card value + Suitedness value) * 2
Card 2: Card value + Suitedness value
"Random" number: Card1 + Card2 - keep adding digits together until one digit between 1 and 9 is left.