/sci/ - Science & Math

[Anonymous No.3903639]

Let us say there is a card game called hi/lo with the following rules:

The dealer puts five cards from a full 52-card deck face down on a table, in a row. Then he turns one additional card face up.

The player then says whether he thinks the first card in the row is lower or higher in value than the upturned card (aces are low). If he's correct, he then guesses if the next card in the row is lower or higher than the card which has just been revealed. And so forth down the line.

The player only wins if he makes it through all five cards without guessing incorrectly.

With perfect play, what are the player's odds of winning?

inb4 homework, this is a game we play at my workplace.

[Anonymous No.3903671]

>>3903639
It depends on the player's strategy, and the face-up card, OP.

There's not enough information to give the player's winning odds, but there is enough to find an optimal strategy depending on cards.

[Anonymous No.3903690]

>>3903671

Well, there's one single strategy that would give you the best chance of winning, but the odds of winning definitely do depend on the first card.

[Anonymous No.3903702]

easy but annoyingly complicated to write out
write a computer program to solve it for you

[Anonymous No.3903725]

>>3903639

possible face up cards: 1 2 3 4 5 6 7 8 9 10 10 10
If it's less than 7, always say "high"

if it's more than 6, always say "low"

both give almost 50% chance of being correct

[Anonymous No.3903736]

>>3903725

Oh I should have clarified, J is 11, Q is 12, and K is 13.

[Anonymous No.3903742]

>>3903702
actually, nevermind, don't even need that
its
<span class="math">\frac{2}{13*51*50*49*48}\left( 48*47*46*45 + 44*43*42*41 + 40*39*38*37 + 36*35*34*33 + 32*31*30*29 + 28*27*26*25\right) + \frac{24*24*23*23}{13*51*50*49*48}[/spoiler]
if the jsmath doesn't work too bad

[Anonymous No.3903749]

>>3903725

You also have to take into account cards that have already been revealed if you come across one of the cards in the middle.

[Anonymous No.3903759]

>>3903749
it doesn't matter, its still always better to go high/low - although, that would change if it was 6 total cards instead of 5

[Anonymous No.3903761]

>>3903749
>almost 50%
>almost
I did.
6 cards out of 51 give around 10% accuracy for the last card.

[Anonymous No.3903769]

>>3903742
wait damn, thats sticking with the first card.
if you always switch to the most recent, its what this guy said >>3903725
except when its 7, you pick depending on whether more cards higher than 7 or lower than 7 have been upturned

[Anonymous No.3903849]

What happens if the next card has the same value as the previous? Like the 5 of hearts, then the 5 of spades?

[Anonymous No.3903855]

>>3903849

Ties are counted as correct guesses no matter what.

[Anonymous No.3903926]

Odds(1st card):

C L H
A 3 51
2 7 47
3 11 43
4 15 39
5 19 35
6 23 31
7 27 27
8 31 23
9 35 19
10 39 15
J 43 11
Q 47 7
K 51 3

For the next four cards you minus 1 from Low if for each (exposed < current) and High for each (exposed > current). You also minus 1 from both Low and High if the the same value as the current card was drawn before.

Eg:
FaceUp Low High FaceDown
K 51 3 5
5 19 34 7
7 26 26 A
A 3 48 7
7 24 25 J
J 39 10 -

[Anonymous No.3903987]

http://pastebin.com/rGmCYiqA
gives me
14628889 / 77228944
or approximately
0.18942236216514885