ACE in n cards
September 28th, 2013 at 8:03:54 AM
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What are the odds of winning casino games on average ?
I am attempting to help my grandson formulate a probability game for his high school class.
I'm sure this type question has been asked many times before, so I apologize.
Our game is this: With 52 card deck
Player is given x number of chances to draw the ACE of Spades, without replacing the drawn cards.
Game is over when player draws ACE of Spades or reaches X number of draws without getting the ACE of Spades.
We've come up with the following probilities of winning - based on drawing 1,2,3 or 4 cards
1 card 1.92%
2 cards 3.85%
3 cards 5.77%
4 cards 7.7%
Do our %'s look right ? Do any %'s qualify for a real Vegas game ? Are the odds the same for a player drawing
x number of cards vs being delt x number of cards (one at a time) ?
Maybe player could pay more to draw 1 card, with winnings being greater & pay less to win less to draw 2 cards etc etc.
Thanks
Blivit
I am attempting to help my grandson formulate a probability game for his high school class.
I'm sure this type question has been asked many times before, so I apologize.
Our game is this: With 52 card deck
Player is given x number of chances to draw the ACE of Spades, without replacing the drawn cards.
Game is over when player draws ACE of Spades or reaches X number of draws without getting the ACE of Spades.
We've come up with the following probilities of winning - based on drawing 1,2,3 or 4 cards
1 card 1.92%
2 cards 3.85%
3 cards 5.77%
4 cards 7.7%
Do our %'s look right ? Do any %'s qualify for a real Vegas game ? Are the odds the same for a player drawing
x number of cards vs being delt x number of cards (one at a time) ?
Maybe player could pay more to draw 1 card, with winnings being greater & pay less to win less to draw 2 cards etc etc.
Thanks
Blivit
September 28th, 2013 at 9:34:00 AM
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Your numbers look correct - well, except that 4 cards should be 7.69%, not 7.7%.
This is an easy one - either the Ace of Spades is in the N cards you draw, in which case you win, or it is not, in which case you lose. The probability of winning is N/52.
On the other hand, if you put each card back after drawing it before drawing the next one, the probability of drawing the Ace of Spades in N draws = 1 - (the probability of not doing it) = 1 - (51/52)N.
This is an easy one - either the Ace of Spades is in the N cards you draw, in which case you win, or it is not, in which case you lose. The probability of winning is N/52.
On the other hand, if you put each card back after drawing it before drawing the next one, the probability of drawing the Ace of Spades in N draws = 1 - (the probability of not doing it) = 1 - (51/52)N.
September 28th, 2013 at 1:09:47 PM
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Thanks very much for reply.
September 28th, 2013 at 2:58:26 PM
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I thought this thread was about me LOL
September 28th, 2013 at 3:07:46 PM
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Yes.Quote: blivitAre the odds the same for a player drawing
x number of cards vs being delt x number of cards (one at a time) ?
Now if you change the game to
dealing the cards until the first Ace (from the 4) is drawn
now the probabilities are different than drawing randomly without replacement.
This brings up an exercise of using combinations
here is some info on it
(I have seen this question in high school math books)
http://mathforum.org/library/drmath/view/52738.html
This could be made into a casino type game, but there are many other ideas
way better than this one
but one might have fun with it.
here is the data
The distribution is col2 and the cumulativeDist is col5
x prob[X=x] prob[X<x] prob[X>=x] prob[X<=x] prob[X>x]
0 0.00000 0.00000 1.00000 0.00000 1.00000
1 0.07692 0.00000 1.00000 0.07692 0.92308
2 0.07240 0.07692 0.92308 0.14932 0.85068
3 0.06805 0.14932 0.85068 0.21738 0.78262
4 0.06389 0.21738 0.78262 0.28126 0.71874
5 0.05989 0.28126 0.71874 0.34116 0.65884
6 0.05607 0.34116 0.65884 0.39723 0.60277
7 0.05241 0.39723 0.60277 0.44964 0.55036
8 0.04892 0.44964 0.55036 0.49856 0.50144
9 0.04559 0.49856 0.50144 0.54415 0.45585
10 0.04240 0.54415 0.45585 0.58655 0.41345
11 0.03938 0.58655 0.41345 0.62593 0.37407
12 0.03649 0.62593 0.37407 0.66242 0.33758
13 0.03376 0.66242 0.33758 0.69618 0.30382
14 0.03116 0.69618 0.30382 0.72734 0.27266
15 0.02870 0.72734 0.27266 0.75604 0.24396
16 0.02637 0.75604 0.24396 0.78242 0.21758
17 0.02418 0.78242 0.21758 0.80659 0.19341
18 0.02210 0.80659 0.19341 0.82870 0.17130
19 0.02015 0.82870 0.17130 0.84885 0.15115
20 0.01832 0.84885 0.15115 0.86717 0.13283
21 0.01660 0.86717 0.13283 0.88378 0.11622
22 0.01500 0.88378 0.11622 0.89877 0.10123
23 0.01350 0.89877 0.10123 0.91227 0.08773
24 0.01210 0.91227 0.08773 0.92437 0.07563
25 0.01080 0.92437 0.07563 0.93517 0.06483
26 0.00960 0.93517 0.06483 0.94478 0.05522
27 0.00850 0.94478 0.05522 0.95327 0.04673
28 0.00748 0.95327 0.04673 0.96075 0.03925
29 0.00654 0.96075 0.03925 0.96729 0.03271
30 0.00569 0.96729 0.03271 0.97298 0.02702
31 0.00491 0.97298 0.02702 0.97789 0.02211
32 0.00421 0.97789 0.02211 0.98210 0.01790
33 0.00358 0.98210 0.01790 0.98568 0.01432
34 0.00301 0.98568 0.01432 0.98870 0.01130
35 0.00251 0.98870 0.01130 0.99121 0.00879
36 0.00207 0.99121 0.00879 0.99328 0.00672
37 0.00168 0.99328 0.00672 0.99496 0.00504
38 0.00134 0.99496 0.00504 0.99630 0.00370
39 0.00106 0.99630 0.00370 0.99736 0.00264
40 0.00081 0.99736 0.00264 0.99817 0.00183
41 0.00061 0.99817 0.00183 0.99878 0.00122
42 0.00044 0.99878 0.00122 0.99922 0.00078
43 0.00031 0.99922 0.00078 0.99953 0.00047
44 0.00021 0.99953 0.00047 0.99974 0.00026
45 0.00013 0.99974 0.00026 0.99987 0.00013
46 0.00007 0.99987 0.00013 0.99994 0.00006
47 0.00004 0.99994 0.00006 0.99998 0.00002
48 0.00001 0.99998 0.00002 1.00000 0.00000
49 0.00000 1.00000 0.00000 1.00000 0.00000
Have fun
winsome johnny (not Win some johnny)
