Post
Topic
Board Gambling
Re: bustabit v2 – No commission on investors & dilution fee lowered to 1%
by
dooglus
on 06/03/2018, 16:11:49 UTC
Can you check where I'm going wrong with this? Here's how I looked at it:

Let BG and PG be two random variables, BG is the house's bankroll growth and PG is the player's bankroll growth (in absolute numbers). Then:

BG + PG = 0 (money only moves back and forth between the house and the player, so a loss for one is a gain for the other and vice versa)

When we talk about "growth", we're talking about multipliers, not deltas.

For example, if a player's bankroll grows from 10 to 11 while the house's bankroll shrinks from 10 to 9, the player's bankroll growth is 1.1x while the house's is 0.9x.

It doesn't make sense to sum those growth multipliers.

"Negative expected growth" means an expected multiplier of less than 1.