Some disadvantaged soul was trying to defend martingaling in my presence (first mistake). Their argument was that "there is always the next round." I decided, this time, I was going to ignore table limits and bankroll considerations and take a different approach since showing this person that one person is losing money on average is clearly not going to work.
Imagine there are a VERY large number (read: infinite) of people at a casino with no table limits running a progression system simultaneously. Now let's say they are all trying to win one unit ($10) and go home.
You can then do the math...
Assume they are playing european roulette and betting black, then they will win approximately 48.65% of the time. The house edge is 2.7%. EV is calculated per person.
Spin 1: 48.65% Win $10 - EV $4.865, 51.35% Lose $10 - EV ($5.135), EVPP [per ploppy] ($0.27) ... exactly the house edge, imagine that!
Spin 2: 24.98% Win $20 - EV $4.996, 26.37% Lose $20 - EV ($5.273), EVPP ($0.274)
Repeat until ploppy is satisfied that the martingalers are losing money as a group and then watch in amazement as they explain how they are all making money individually despite losing as a group. Not for those of weak constitution as sometimes the result is visible agony. Alternate line: Use entire population of the planet as an example to show the sheer absurdity of the amount of money the bets get up to.
You know, I think maybe the lottery has it backwards. Someone should start selling reverse-lottery tickets. Maybe varying denominations.
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