Card Game - Page 3

MrX · #21 10-06-2004, 03:22 PM

haven't looked at any answers yet but here is my take

scenario 1: simple all 52 have exactly the same same chance of winning

scenario 2: complicated based on your likelihood of winning and also you likelihood of even getting a chance to draw cards. It will max out sooner than you think, probably around picks 7-10. I am gonna work this out for fun then post my answer and look at the other results.

MrX

junkmail3 · #22 10-06-2004, 03:23 PM

[ QUOTE ]
[ QUOTE ]
1) All spots are equal:
1st person: 1/52
2nd person: 1/51*51/52
3rd person: 1/50*51/52*50/51
etc
These all come out to 1.92%

2nd:
7th
You have an 8.8% chance of winning in this spot, which is the best you can ask for. I just used a brute force method of computing all the chances w/a spreadsheet and am too lazy to type it out here.

[/ QUOTE ]

This is correct.

Game 1 should be self-explanatory

[/ QUOTE ]

Then I want to pick 18th. 18 is HOT!

junkmail3 · #23 10-06-2004, 03:23 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
1) All spots are equal:
1st person: 1/52
2nd person: 1/51*51/52
3rd person: 1/50*51/52*50/51
etc
These all come out to 1.92%

2nd:
7th
You have an 8.8% chance of winning in this spot, which is the best you can ask for. I just used a brute force method of computing all the chances w/a spreadsheet and am too lazy to type it out here.

[/ QUOTE ]

This is correct.

Game 1 should be self-explanatory

[/ QUOTE ]

Then I want to pick 18th. 18 is HOT!

[/ QUOTE ]

(tonight)

Lori · #24 10-06-2004, 03:25 PM

That's not how it works. Everyone doesn't pull their balls all at once. You pull a ball until #33 is found. Once it's found there's no need to keep pulling your balls.

How about if these people work for party support and don't know what the ace of spades looks like.
They all pull a card and then run around trying to find out who has the ace of spades.

Eventually they find Lucy Jones and a winner is declared.

Which one has the best chance of having the A [img]/images/graemlins/spade.gif[/img]?

Lori

BradleyT · #25 10-06-2004, 03:27 PM

[ QUOTE ]
That's not how it works. Everyone doesn't pull their balls all at once. You pull a ball until #33 is found. Once it's found there's no need to keep pulling your balls.

How about if these people work for party support and don't know what the ace of spades looks like.
They all pull a card and then run around trying to find out who has the ace of spades.

Eventually they find Lucy Jones and a winner is declared.

Which one has the best chance of having the A [img]/images/graemlins/spade.gif[/img]?

Lori

[/ QUOTE ]

Easy - Lee Jones.

MrX · #26 10-06-2004, 03:32 PM

wrote a quick little spreadsheet to fig it out (scenario 2 that is), this shows a slight increased chance of player 7 having the best odds at about 8.8%. The bolded "1" at the bottom of the last column shows that all percentages added together equal 1 (100%). I think these are fun.

MrX

order cards chance to chance product
drawn win if you you get to
do draw draw
1 1 0.019230769 1 0.019230769
2 2 0.038461538 0.980769231 0.037721893
3 3 0.057692308 0.943047337 0.054406577
4 4 0.076923077 0.88864076 0.068356982
5 5 0.096153846 0.820283779 0.07887344
6 6 0.115384615 0.741410338 0.085547347
7 7 0.134615385 0.655862992 0.088289249
8 8 0.153846154 0.567573743 0.087319037
9 9 0.173076923 0.480254705 0.083121007
10 10 0.192307692 0.397133699 0.076371865
11 11 0.211538462 0.320761834 0.067853465
12 12 0.230769231 0.252908369 0.05836347
13 13 0.25 0.194544899 0.048636225
14 14 0.269230769 0.145908674 0.039283105
15 15 0.288461538 0.10662557 0.030757376
16 16 0.307692308 0.075868194 0.02334406
17 17 0.326923077 0.052524134 0.017171352
18 18 0.346153846 0.035352783 0.012237502
19 19 0.365384615 0.023115281 0.008445968
20 20 0.384615385 0.014669313 0.005642043
21 21 0.403846154 0.009027269 0.003645628
22 22 0.423076923 0.005381641 0.002276848
23 23 0.442307692 0.003104793 0.001373274
24 24 0.461538462 0.001731519 0.000799163
25 25 0.480769231 0.000932357 0.000448248
26 26 0.5 0.000484108 0.000242054
27 27 0.519230769 0.000242054 0.000125682
28 28 0.538461538 0.000116372 6.26619E-05
29 29 0.557692308 5.37102E-05 2.99538E-05
30 30 0.576923077 2.37564E-05 1.37056E-05
31 31 0.596153846 1.00508E-05 5.99183E-06
32 32 0.615384615 4.05898E-06 2.49783E-06
33 33 0.634615385 1.56115E-06 9.90727E-07
34 34 0.653846154 5.70419E-07 3.72966E-07
35 35 0.673076923 1.97453E-07 1.32901E-07
36 36 0.692307692 6.45518E-08 4.46897E-08
37 37 0.711538462 1.98621E-08 1.41326E-08
38 38 0.730769231 5.72945E-09 4.18691E-09
39 39 0.75 1.54254E-09 1.15691E-09
40 40 0.769230769 3.85636E-10 2.96643E-10
41 41 0.788461538 8.89929E-11 7.01675E-11
42 42 0.807692308 1.88254E-11 1.52052E-11
43 43 0.826923077 3.62028E-12 2.99369E-12
44 44 0.846153846 6.26586E-13 5.30188E-13
45 45 0.865384615 9.63979E-14 8.34212E-14
46 46 0.884615385 1.29766E-14 1.14793E-14
47 47 0.903846154 1.4973E-15 1.35333E-15
48 48 0.923076923 1.43972E-16 1.32897E-16
49 49 0.942307692 1.10747E-17 1.04358E-17
50 50 0.961538462 6.38927E-19 6.14353E-19
51 51 0.980769231 2.45741E-20 2.41015E-20
52 52 1 4.72579E-22 4.72579E-22
1

pudley4 · #27 10-06-2004, 03:33 PM

Here are the numbers for each position:

<font class="small">Code:</font><hr /><pre>
win cards total cards % winning pick %losing pick %no previous winner %win

1 52 0.019230769 0.980769231 1 0.019230769
2 52 0.038461538 0.961538462 0.980769231 0.037721893
3 52 0.057692308 0.942307692 0.943047337 0.054406577
4 52 0.076923077 0.923076923 0.88864076 0.068356982
5 52 0.096153846 0.903846154 0.820283779 0.07887344
6 52 0.115384615 0.884615385 0.741410338 0.085547347
7 52 0.134615385 0.865384615 0.655862992 **0.088289249**
8 52 0.153846154 0.846153846 0.567573743 0.087319037
9 52 0.173076923 0.826923077 0.480254705 0.083121007
10 52 0.192307692 0.807692308 0.397133699 0.076371865
11 52 0.211538462 0.788461538 0.320761834 0.067853465
12 52 0.230769231 0.769230769 0.252908369 0.05836347
13 52 0.25 0.75 0.194544899 0.048636225
14 52 0.269230769 0.730769231 0.145908674 0.039283105
15 52 0.288461538 0.711538462 0.10662557 0.030757376
16 52 0.307692308 0.692307692 0.075868194 0.02334406
17 52 0.326923077 0.673076923 0.052524134 0.017171352
18 52 0.346153846 0.653846154 0.035352783 0.012237502
19 52 0.365384615 0.634615385 0.023115281 0.008445968
20 52 0.384615385 0.615384615 0.014669313 0.005642043
21 52 0.403846154 0.596153846 0.009027269 0.003645628
22 52 0.423076923 0.576923077 0.005381641 0.002276848
23 52 0.442307692 0.557692308 0.003104793 0.001373274
24 52 0.461538462 0.538461538 0.001731519 0.000799163
25 52 0.480769231 0.519230769 0.000932357 0.000448248
26 52 0.5 0.5 0.000484108 0.000242054
27 52 0.519230769 0.480769231 0.000242054 0.000125682
28 52 0.538461538 0.461538462 0.000116372 6.26619E-05
29 52 0.557692308 0.442307692 5.37102E-05 2.99538E-05
30 52 0.576923077 0.423076923 2.37564E-05 1.37056E-05
31 52 0.596153846 0.403846154 1.00508E-05 5.99183E-06
32 52 0.615384615 0.384615385 4.05898E-06 2.49783E-06
33 52 0.634615385 0.365384615 1.56115E-06 9.90727E-07
34 52 0.653846154 0.346153846 5.70419E-07 3.72966E-07
35 52 0.673076923 0.326923077 1.97453E-07 1.32901E-07
36 52 0.692307692 0.307692308 6.45518E-08 4.46897E-08
37 52 0.711538462 0.288461538 1.98621E-08 1.41326E-08
38 52 0.730769231 0.269230769 5.72945E-09 4.18691E-09
39 52 0.75 0.25 1.54254E-09 1.15691E-09
40 52 0.769230769 0.230769231 3.85636E-10 2.96643E-10
41 52 0.788461538 0.211538462 8.89929E-11 7.01675E-11
42 52 0.807692308 0.192307692 1.88254E-11 1.52052E-11
43 52 0.826923077 0.173076923 3.62028E-12 2.99369E-12
44 52 0.846153846 0.153846154 6.26586E-13 5.30188E-13
45 52 0.865384615 0.134615385 9.63979E-14 8.34212E-14
46 52 0.884615385 0.115384615 1.29766E-14 1.14793E-14
47 52 0.903846154 0.096153846 1.4973E-15 1.35333E-15
48 52 0.923076923 0.076923077 1.43972E-16 1.32897E-16
49 52 0.942307692 0.057692308 1.10747E-17 1.04358E-17
50 52 0.961538462 0.038461538 6.38927E-19 6.14353E-19
51 52 0.980769231 0.019230769 2.45741E-20 2.41015E-20
52 52 1 0 4.72579E-22 4.72579E-22
</pre><hr />

MrX · #28 10-06-2004, 03:38 PM

we must have written almost the same formula Jeff.

I like your formatting much better. I think we can consider the book close on this one.

MrX

Smackdab · #29 10-06-2004, 03:40 PM

[ QUOTE ]
Once it's found there's no need to keep pulling your balls

[/ QUOTE ]

Once I found it ...... I couldn't stop. [img]/images/graemlins/wink.gif[/img] [img]/images/graemlins/cool.gif[/img] [img]/images/graemlins/blush.gif[/img]

B00T · #30 10-06-2004, 03:45 PM

Yea 8th is the pick. That is the mathmatical computer saying why. I guess I tried to prove why you want that pick in a logical way. Everyone else picking before you has a less than 50/50 shot of getting the car. Anyone picking after #8 has a more than 50% shot of that 1/52 having already come up.

So what about the first case? At what point do you start approaching that 50% threshold? My arguement here coincides with Lori's Cmon math boys...