What You Don’t Know Can’t Help You: Addendum
Should you implement the convoluted modulo-arithmetic randomization laundering from the previous article? No.
The tip “Did you know that if you split from a higher tile in Twelvesmith, it will always result in a higher (or equal) value than had you split from a lower tile?” is totally strategically neutral.
Dice Game 1 and Game 2 are statistically identical.
For some, this might have been obvious and uninteresting. But for others (myself included), this wasn’t obvious. I could see the statistical analysis proving their equivalence, but that didn’t relieve the feeling in the back of my mind that there was something going on here.
Why?
What part of my brain refuses to give up the feeling of importance it associates with “what could have been”?
Back to the dice games!
A quick refresher:
You get to pick a bet (A or B), and then roll a die. If you win your bet, you get $1M; otherwise, you get nothing.
Are Game 1 and Game 2 identical? Yes.
But here’s a twist: now it’s multiplayer.
That is, you and your rival are both playing the same game, and are both using the same dice roll to resolve your bets.
And finally, the results are zero-sum.
It’s not that you ever have to split the pot (whoever wins their bet still gets their own full $1M; you can even both make the same bet if you want!). All I’m saying is, this town ain’t big enough for two millionaires, and you want all the glory for yourself.
This changes everything.
Let’s assume your rival always chooses bet A. (She always was the more cool-headed one. Disgusting.)
Here are the new outcomes:
Now the payouts of these games are plainly different! And depending on how badly you’d like to lord your victory over your rival (and how well you can take humiliation), bet B might even be a viable option in Game 2!
And yet, as previously presented, it wasn’t a multiplayer game. So what about our intuition might be attached to the idea that it was?
I’ll admit, at this point I’m pretty deep in Freudian armchair-psychology. But what the hell:
Maybe it was a multiplayer game all along- but the “rival” we’re constantly playing against…
is ourselves.
It hurts to think there’s an “us” in a parallel universe, who made the better decision and is laughing at our misfortune.
It hurts to be taunted by the “us” that took the risk of choosing option B, and got the payoff.
It feels good to know parallel “us” couldn’t have split to a higher numbered tile than we did.
But there is no parallel us.
Whooooeee well that was a wild ride don’t forget to like comment and subscribe for more hot unsubstantiated psych takes and thanks for joining see you next time!
But seriously- good news! The real “us” doesn’t need to concern ourselves with modulo arithmetic! (At least not for the purpose of foiling “parallel-us”…)
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