I've made a trivial Arduino demo that generates pseudorandom 0/1 bits, and lights up a different LED for each (the onboard LED and an extra LED connected at pin 12).
#define EXTRA_LED 12
#define BOARD_LED LED_BUILTIN
long randNr;
void setup() {
// put your setup code here, to run once:
Serial.begin(9600);
randomSeed(analogRead(0));
pinMode(BOARD_LED, OUTPUT);
pinMode(EXTRA_LED, OUTPUT);
}
void loop() {
// put your main code here, to run repeatedly:
// blip, blip, blip, random draw
digitalWrite(BOARD_LED, 0);
digitalWrite(EXTRA_LED, 0);
delay(500);
for (unsigned char c=0; c < 3; c++) {
digitalWrite(BOARD_LED, 0);
digitalWrite(EXTRA_LED, 0);
delay(190);
digitalWrite(BOARD_LED, 1);
digitalWrite(EXTRA_LED, 1);
delay(10);
}
digitalWrite(BOARD_LED, 0);
digitalWrite(EXTRA_LED, 0);
delay(1000);
randNr = random(2);
switch (randNr) {
case 0:
digitalWrite(BOARD_LED, 0);
digitalWrite(EXTRA_LED, 1);
break;
case 1:
digitalWrite(BOARD_LED, 1);
digitalWrite(EXTRA_LED, 0);
break;
}
delay(1500);
}
The strange thing is that when guessing in advance which LED will light up next, chances of guessing seems too high. Happens to guess correctly 3-4 times in a row, once it was 5 or 6 consecutive good guesses. Only once or twice guessed wrong from the first try. The chances to fail from the first guess should be 50%.

Each time only played until the first wrong guess, then forget about it. I've only tried to guess it about 10-20 times or so today, playing only occasionally, each time when the blinking LED happen to distract by accident (it's running non stop on a shelf in the lab). The number of drawings so far is probably too small to be representative, but still, very uncanny odds.

I suspect it's some psychological effect, where the odds seems much better than they really are.
Does it make any sense what I'm describing here, anybody else ever noticed something similar?