I just got a TI-83 Plus and turns out YOU CAN PROGRAM IT!
I went ahead and made a Number Guessing Game for my first go around. FUN!
CODE:
Replace -> with the STO key

SMALL VERSION:

:While 1
:Lbl S
:ClrHome
:randInt(1,100)->A
:Disp "GUESS THE NUMBER"
:Output(3,1,"1-100")
:Lbl G
:Prompt X
:If A=X
:Then
:ClrHome
:Disp("CORRECT")
:Pause
:Goto S
:End
:If A≤X
:Then
:ClrHome
:Disp "TOO HIGH"
:Goto G
:End
:If A≥X
:Then
:ClrHome
:Disp "Too Low"
:Goto G
:End
:End



This version includes choosing your own level, and displaying the amount of tries taken.
MORE ADVANCED VERSION:

:While 1
:Lbl AB
:ClrHome
:Output(2,1,"CHOOSE LEVEL")
:Output(3,1,"5-1000000")
:Input C
:If C<5
:Then
:ClrHome
:Output(1,1,"DONT BE A PUNK")
:Pause
:Goto AB
:End
:Lbl S
:ClrHome
:randInt(1,100)->A
:1->H
:Disp "GUESS THE NUMBER"
:Output(3,1,"1-100")
:Lbl G
:Prompt X
:If A=X
:Then
:ClrHome
:Disp("CORRECT")
:Output(3,1,H)
:Output(4,1,"TRIES TAKEN")
:Pause
:Goto S
:End
:If A≤X
:Then
:ClrHome
:Disp "TOO HIGH"
:H+1->H
:Goto G
:End
:If A≥X
:Then
:ClrHome
:Disp "Too Low"
:H+1->H
:Goto G
:End
:End


The Greater than, Less than, and Equals to can be found in the TEST button.

Enjoy!