Did up this Maple sheet about hitting a streak of pairing the board. As you can see past 2-3 hands it gets pretty unlikely.

Not sure what I’ll do next. Just a quick comp for this morning.


Holdem Pair Math
Props out to Professor Brian Alspach for his site
Jacob Sanford

Calculate the Possible Number of Total 7 card hands

>    binomial(52,7);

133784560

Calculate the possible number of boards with you holding 2 cards.

>    binomial(50,5);

2118760

Calculate the possible number of FLOPS with you holding 2 cards

>    binomial(50,3);

19600

Calculate the number of flops you will not hit at least a pair holding 2 different cards on the flop

>    binomial(44,3);

13244

From this, calculate the fraction of flops where you WILL hit a pair

>    (19600-13244)/19600;

227/700

Turn this into a decimal

>    fractnopair:=evalf((227/700));

fractnopair := .3242857143

Now find the likelyhood of holding consecutive flop-pairing hands.

>    for i from 1 by 1 to 30 do percentagearray[i]:=fractnopair^i end do:
>    with (plots):
>    listplot ([seq(percentagearray[k],k=1..30)]);

[Maple Plot]