[ExI] tumbling pyramids again

[spike]

-----Original Message-----
From: extropy-chat [mailto:extropy-chat-bounces at lists.extropy.org] On Behalf
Of BillK
Subject: Re: [ExI] tumbling pyramids again

On 16 February 2017 at 17:35, spike wrote:
>> Ja BillK, but the goal is not to make a fair 5-sided die, but rather 
> to figure out what dimensions would be needed to make a square-based 
> pyramid gaming die...


>...Any square-based pyramid die would not be fair. i.e. if the sides are
different shapes, then the chances of falling on each side will not be
equal... BillK


Hi BillK, thanks.  My reasoning is based on the intermediate value theorem.
If h = 1, we can easily see that it will land on that face more than 20% of
the time.  If h=2, then most would agree it will land there less than 20% of
the time.  My reasoning holds that there must be some value for h between
the limits of 1 and 2 where that pyramid lands square down 20% of the time.
My calcs suggest that number is 1.58 but it is a mathematical model.

Please sir, what do you calculate or estimate for h?

spike