Most absurd poker "thinking" you have heard in a live game?

So then wait until just before the 5000 envelope is going to be picked and pick your envelope then. That gives you your best shot. Wait a minute… you are telling me you don’t know when the 5000 envelope will be picked??? Gee that changes the strategy doesn’t it? We should pick the first envelope then to make 100% sure we have a shot at the 5000. If there are 50 envelopes that gives us a 1/50 chance. If we wait we might have a zero percent chance if we pick second. So pick first - obviously that’s the best strategy.

But is it? It isn’t really all that likely the first person will get the 5000 envelope - only 1 in 50. So maybe we pick second instead. If we do, there is a 49/50 probability the 5000 envelope will still be there, and now we have a better chance to get the 5000 if it’s still there 1/49 instead of 1/50. Since the probability of it being there is 49/50 our chance of getting it picking second is 49/50 x 1/49=1/50 — same as when we pick first!!

Well then how about picking third? There is a 48/50 chance that it’s still there and a 1/48 chance that we get it if it’s still around, so now our chance of getting it is 48/50 x 1/48, which is 1/50 — still the same!!

Hopefully you can see the pattern. No matter when we pick we will have exactly the same probability of getting the 5000. It makes no difference whether you pick first, last (1/50 chance that nobody picked it before you, but if they didn’t you get it) or anywhere in between. You will always have a 1/50 chance (or a 1 in whatever the number of envelopes actually is; I used 50 only as an example)

Are you not, by that same logic, denying everyone else the chance to pick the lesser prizes while they are still available? Seems silly to pick while they are still out there. Better to wait until only the $5,000 prize is left.

Not really. Since I don't know when it can be picked, and I know that once it is picked I will be unable to pick it, I prefer to pick when I know for a fact that it is available.

I appreciate you making my point for me though!

Them and I can pick lesser-value envelopes no matter where we pick. I get that.

If I go first and don't get the $5,000 envelope, that actually does help everyone else. They can thank me for my noble sacrifice, but the fact doesn't change if I pick first there is a 100% chance the $5,000 envelope is still in there and those after me (whether picking next or last) will have to hope there's not a 0% chance by the time they pick.

You can sit around and wait until the last pick if you want. If you told me I could bet on the field (everyone not picking last) or you, I would bet on the field.

All I know is that my odds won't be zero if I pick first, and that is my preference. Feel free to stick around until the end if you prefer.

I mean, if you want to always pick as early as possible to maximize your chance of picking while the biggest prize is still available (while also minimizing your chance of actually getting the biggest prize while it's still available), then go for it. You're just maximizing your own personal, subjective pleasure utility function. You do you.

As long as you realize that you are in no way changing your EV by choosing to pick now or waiting to pick later (at the time you are making that decision, at any time you are making that decision, no matter if first, last, or middle), then who are we to judge.

It's just that most people who express a preference like that DO think they are changing their EV by picking earlier or later. Like the person whose reasoning in this matter started this whole conversation off. These people are wrong. And it did, for some time, seem to appear that you were one of them, since you said his reasoning wasn't as bad as it appeared (it totally was), but you then also explained that you knew the EV wasn't actually changing. It was, and is, a bit confusing what you're actually saying you believe.

The EV doesn't change but it's a better sweat to pull an envelope while the big one is still in play.

Suppose I pick first because that guarantees that I have a shot at the big prize. However, instead of reaching in and taking the first envelope I touch, I pull out five envelopes, set them aside, and then keep the sixth envelope I picked. Did I just screw myself? I am no longer guaranteed that the big prize was in one of the remaining envelopes when I picked the one I kept. Would I have in any way been better off just keeping the first one I pulled out?

Obviously not, unless IÂ’m psychic or something. The sixth envelope I picked has exactly the same chance as the first. But how is this scenario in any way different than if five people picked ahead of me and I just took the first envelope I picked?

Would your choice be the same if every time someone picked and didn't pick the 5k envelope, they replaced one of the small envelopes with another 5k envelope, but then once any 5k was picked, they all go away? So your chances actually increase by waiting, but you might miss it entirely by waiting.

The symmetry breaker psychologically is that it was his free choice to set aside the envelopes.

Mathematically you are correct though.

I think this is what he is getting at, though nuggets such as "I would bet on the field against you" make me squint.

(Also, I don't know, the repeated sweat of watching others pull an envelope and decide my fate is even more thrilling. That could go either way, especially if the $5k is pulled early, but I imagine there was a buzz every time an envelope was pulled, and not just felt by the hoarder, and especially after the absurd thinking was expressed!)

Simpliest way to explain it ....

lets say there are 100 envelopes , 99 are 1$ & 1 is 5000$

if u pick 1st envelope ..... ur odds of picking the 5k$ are 1% and 1$ are 99%

then ur EV is ( 1%*5000$) + (99%*1$) = 50.99$

if u pick last envelope

1% of the time , the 5000$' envelope has not yet been taken , so ur picking it 100% of the time
99% of the time it has been taken , so ur picking a 1$ one 100% of the time

the math a the same

ur EV is ( 1%*5000$*100% ) + ( 99%*1$*100% ) = 50.99% still

-jpp

lol this is the new Let's Make a Deal problem

Yes!

Maybe I wasn't clear. I said that the EV wouldn't change but I also said I would prefer to pick knowing that nobody else snagged that $5,000 envelope yet.

If I could ensure that happened when I picked *last* cool, but honestly if I could ensure that I would just use those magic powers to pick it wherever I picked.

Failing magic powers, I just want the $5k envelope to actually be in play when I pick. That might not even be possible - people who knocked out players before me already got a shot before I even qualified and maybe they snagged it when I was not even able to pick - but as long as some big envelopes were still available, I wouldn't want to wait intentionally.

Like, the guy who picked before me may take it which does NOT mean that I would have got it! But it sure means I won't.

Pretty sure you're breaking the rules there, sparky.

How? If I’m first to pick I get to keep one envelope, if I accidentally pulled out six from the bag and put five back, I’m not breaking any rule. My question is that if I kept the sixth one rather than the first, am I screwing myself? I know that the big one is possible if I pick the first one. If I keep the sixth one, the big one might be one of the first five, so by your logic I should take the first one.

Yet:

A. There is obviously no difference between 1 and 6 in this scenario. The chances of the 5000 being in 1 and 6 are identical.

B. There is zero difference between taking number 6 in this scenario and picking an envelope after 5 people have already picked one.

Pretty sure you take six envelopes out of there the person doing the drawing will lose their mind on you. Try it and tell us how it goes.

Ok, but you’re missing the point. Suppose you reach into the bag, grab an envelope but don’t pull it out. Then you grab a second envelope. You must keep one and drop one back into the bag. Which one should you keep? Does it matter?

Guy arrived at the CG table and complained that he just got knocked out of the tournament, finishing 12th out of 1200 in a $500 buy-in for $7,000, and the payout structure is horrible because he's in the top 1% of the field, so mathematically, it should pay him 100 times his money, not only 14 times.

-jpp

I am not. The math doesn't matter if you literally cannot do something.

It’s called a thought experiment, and they are quite useful for clarifying the essential elements of a situation. Suppose (thought experiment) that instead of envelopes in a bag you have all the envelopes laid out on a table. You can choose one envelope when you bust someone. You hog to pick up envelope 3, but you change your mind. Now you go to pick up envelope 7 instead. Did you screw your self? If you picked your first choice you had a 100% chance that the big prize could be in the envelope you chose. After deciding to reject envelope 3 and pick envelope 7 instead, it’s not a 100% chance anymore - the big prize could be in the envelope you turned down.

Now extend this. You then down ALL the envelopes except envelope 1. Did you screw your self? It’s quite likely that the big prize is in one of the ones you didn’t pick.

Obviously you did not screw yourself. Whether you decide to pick an envelope and just go with it or whether you reject 18 envelopes before making your choice makes zero difference. Each one has the same chance of having the big prize. The same thing is true if, rather than you rejecting envelope #3, another player chooses envelope 3 before you pick. The only difference is psychological - YOU didn’t reject that envelope; you never had a chance to pick it. Probability-wise there is zero difference between the two. You only feel like you lost control of the chance to win the big prize, but that is something you never had any actual control over in the first place.

One final thought experiment. Suppose there are ten envelopes in a bag. One contains a 5000 prize, the others have nothing. You are given a choice: either choose one envelope and you get to keep the prize if your envelope contains it, or choose 9 envelopes, and you get to keep the prize if it’s in the one you didn’t choose. Which of these gives you a better chance to win the prize? Would you change your answer if in the second case, someone else picks the 9 envelopes and you still get the prize if it’s in the one that was not chosen?

Shoutout to my fellow compatriot making the same mistake I always make - trying to use logic to convince someone making an argument based solely on emotion.

What's so emotional about not wanting the good envelopes to be taken before I get to pick?

The other day at work someone got donuts for the team, a nice gesture!

If I went to the break room when he brought them, I could have gotten a chocolate glazed or jelly donut but I didn't and by the time I got there there was only those boring, dry cake donuts.

The lesson is that if I want to ensure my favorite donut is available to me, I should probably not delay in going there for them.

I realize that the envelopes are random and the donuts are specifically chosen but either way I have no chance to get the most cash or the best donut whereas if I was faster, at least I could have had a chance.

This is sound logic.

Okay, have fun with that!