Bridge game odds: alternative attempt

2021.10.25 11:34 lemonvolcano Bridge game odds: alternative attempt

u/aaronhe07 created a fascinating post on the odds of each player surviving the bridge game. As I commented on that post, when I tried to take those results and use them for studying the odds of different total numbers of players surviving (to find the expected number of survivors), I hit a contradiction: when totalling the odds of no survivors, plus the odds of 1 survivor, plus the odds of 2, and so on, up to the odds of all 16 players surviving, I reached a total greater than 1 (100%). I had the same issue with my own calculations (which produced different results from OP for the odds of each player surviving).
However, when I changed to logic for calculating the survivor count probabilities, running against my own player data, I suddenly got exactly 1.0 total (100%). I'll be honest, I don't fully understand why the tweak in my survivor count method is correct, but it seems too a big coincidence for it to be a mistake that cancels out other mistakes in my first set of data to come to exactly the correct result.
Here are my odds for each player reaching the end:
01: 0.00038% 02: 0.01% 03: 0.19% 04: 1.60% 05: 8.52% 06: 27.45% 07: 55.14% 08: 78.04% 09: 90.73% 10: 96.38% 11: 98.64% 12: 99.50% 13: 99.82% 14: 99.94% 15: 99.98% 16: 99.99%
And here are my odds for having N survivors at the end of the game:
16: 0.00038% 15: 0.01% 14: 0.19% 13: 1.60% 12: 8.36% 11: 24.66% 10: 35.94% * 09: 22.82% 08: 5.82% 07: 0.57% 06: 0.02% 05: 0.0003% 04: 0.000001% 03: 0.000000003% ** 02: 0.000000000002% 01: 0.0000000000000003% 00: 0.00000000000000000002%
Total of survivor odds: 100.00%
I made the same assumptions as OP: everyone plays perfectly, no-one can tell a difference in the glass, everyone completes within the time limit, nobody kills anybody else.
If I'm correct (and I think we could really do with a proper statistician to look at this question), the most likely outcome* at 35.94% is that 10 players would survive. The odds of only 3 players making it** comes out as 0.000000003%. (I'm fascinated by the way these probabilities dwindle towards the end. Is it suspicious? Have I done something wrong?)
Expression for the odds of player P surviving step S (using a recursive strategy as suggested by OP):
(odds that player P-1 survived step S-1) + ((odds that player P-1 did NOT make it to step S-1) x (odds player P survived step S-1) x 0.5)
(If P=1, P-1 odds are always zero. Is S=1, odds of 'surviving' step zero are 1. All probabilities in range 0 to 1. I've multiplied the results by 100 above to give percentages to match the format of the original post).
The rationale here is that if the previous player survived the previous step, they will have attempted the current step, so we will know the right answer (regardless of whether they succeeded or failed). If on the other hand the previous player didn't make it to the previous step, all we have to go on is the odds we survived the previous step AND we guess right this time.
Now, my expression for deciding the odds of there being N survivors, which is equivalent to there being D=16-N deaths:
(odds that player 1 died) x (odds that player 2 died) x ... x (odds that player D died) x (odds that player D+1 survived)
I'll be honest, I originally thought this should just be (odds that player D died) x (odds that player D+1 survived), because the failure of player D implies the failure of all previous players. But, insisting on their deaths being represented here gives the right answer when you total all the survivor count outcomes, so I'll take it, for now!
I could try to post the grid of probabilities I get for each player surviving each step, but as an 18x16 grid it might be more than my reddit formatting skills can handle.
Props to OP for kicking this off and stopping me from getting any work done today. Part of me hopes we're both wrong and you have stumbled upon a new Monty Hall problem. Somebody qualified please help.
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2021.10.25 11:34 TarryCurry New to 3d printing, Filament recommendations ?

Got myself an easythread X1. Have been told this performs better with high quality filaments but do not know what this constitutes. Any recommendations ? I think I may also have an issue with my nozzle as when it extrudes the filament curls up on itself after not to long and birds nests next to the nozzle. I have tried poking around up there with a thin needle but this has not sorted this issue for me. Does anyone have any ideas?
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2021.10.25 11:34 Anonesq31 4thQ NJ Solo Update

https://www.reddit.com/LawFirm/comments/og7c6n/solo_in_nj_update/?utm_source=share&utm_medium=web2x&context=3
So I just wanted to update everyone on my progress as we are nearing the end of the year. I posted a link (above) for my prior update. To reiterate, my income for my first full year of solo practice was $125k. Something that I did not include in my prior update is that I was lucky enough to land a decent contingency case that settled rather quickly. So in one month I believe I made around $40k+.
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2021.10.25 11:34 90sRnBMakesMeHappy Got triggered by them not wanting to talk on phone

We had a misunderstanding last week, and the person I'm seeing said we should talk. So I asked 3 times when that was possible to schedule, also called them 4 times. I feel so stupid and hurt. They acted like they wanted to talk out the issue. But now I feel they didn't make time, and that means they aren't interested. The guy that ghosted me previously refused to talk, so my trigger is so on right.
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2021.10.25 11:34 eddiecurry Could anything be worse than this?

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2021.10.25 11:34 noobknight87 Streak 11: Alex Baldwin

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2021.10.25 11:34 Aperson3334 Studying abroad in Swansea?

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2021.10.25 11:34 ThisIsMockingjay2020 I was the guilty party this time.

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I apologized profusely and told him we were expecting the bed company that night as well. Thankfully, he thought it was funny.
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2021.10.25 11:34 reddit_feed_bot NewsMax: Sen. Blunt: Trump Should Talk About Future, Not Past

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