Is this lottery legit

In my country we have a lottery on Wednesday's unsurprisingly called BIG WEDNESDAY
The 6 numbers are drawn in the normal way, from a transparent sphere of the 50 number
on balls. It all appears to be above board, and I suspect that it is. It is live on TV.

However there is a further draw to qualify to win the 1st division (highest) prize, and that
is a Heads or Tails option. But this option is never shown to be drawn apart from an animated
display of a coin spinning and landing as a head or tail.

My question is, is it possible to write a programme, a random number generator of some kind I
assume, so that it is 100% random to pick a head or a tail.

I find it hard to believe that if heads came up 10 times in a row that the lottery people would not
start to be concerned. Of course 10 heads in a row is quite likely, but the average Joe buying
tickets would not appreciate that it was a normal event.

Quote: Pando

My question is, is it possible to write a programme, a random number generator of some kind I
assume, so that it is 100% random to pick a head or a tail.

Strictly speaking, there is no (deterministic) program that will reproduce the random pick of head or tail. Simply because programs are deterministic, and reproduce the same result for the same input.

But there is a whole research field on programs (so called pseudo-random number generators, with the emphasis on "pseudo") which yield close to random results.

Honestly I would not trust this lottery, because it is much too easy to know in advance if the highest prize would be hit by someone from the sold tickets.
How conveniently would it be to simply select the opposite result....

Even if the coin is shown before any numbers are drawn - just picking the side with the lower number of tickets sold would create a significant bias.

Thanks for your input.

To clarify, the heads/tails is SHOWN after the numbers are drawn. Some people might think that this
creates some opportunity to select an appropriate outcome so that there are no winners to perhaps
increase the jackpot for the following week.

What if I tell you that this is a government run lottery?

I would have no doubt NZ will serve a fair lottery. But why play in the first place ?

I guess we all dream of $millions, even if the odds of winning are so low.
Call it human nature. I only play when there are big payouts on offer, I think
the highest has been NZ$35 million

A better way would be to have another set of Heads and Tails balls and make
a draw in the same way they do for the 6 numbers

I think the lottery is probably fair but by displaying the heads or tails outcome by
animation and not by a physical draw is a possible flaw.

Well, if you like the high payout - almost any game is better than the lottery (50% house edge). Even on a double-zero roulette wheel, you could do a 5-fold parlay (i.e. $60 million for a $1 bet) for a house edge of <25%. Find a single zero wheel and it is less than 13%!