1/8 -> 7/8th's game theory

[DavidC]

1/2 first card red
1/4 last card spade
3/4 not 1/4
1/8 first red and last spade
3/8 first black and last spade
5/8 first red and last not spade
7/8 first black and last not spade

Will this system give me the correct distributions?

[BruceZ]

[ QUOTE ]
1/2 first card red
1/4 last card spade
3/4 not 1/4

[/ QUOTE ]

OK

[ QUOTE ]
1/8 first red and last spade

[/ QUOTE ]

No, because these are not independent. 1/2 * 13/51

[ QUOTE ]
3/8 first black and last spade

[/ QUOTE ]

Same as first red and last spade, unless I don't understand.

[ QUOTE ]
5/8 first red and last not spade

[/ QUOTE ]

1/2 * 38/51

[ QUOTE ]
7/8 first black and last not spade

[/ QUOTE ]

Same as previous.

[DavidC]

So, uh, regarding:
[ QUOTE ]
No, because these are not independent. 1/2 * 13/51

[/ QUOTE ]

Would you like to try out my title for a few days, and see how it suits you? [img]/images/graemlins/cool.gif[/img]

But yeah, good catch.

OK, so my system doesn't really work for the 8ths.

How would you go about randomizing, using cards?

Can you create a system that's approximately accurate along these lines?

I have a tolerance of about say 2%. If I'm off by more than 2% I'd like to know so I can tell how much I'm off and see if I'm willing to live with it.

[BruceZ]

[ QUOTE ]
So, uh, regarding:
[ QUOTE ]
No, because these are not independent. 1/2 * 13/51

[/ QUOTE ]

Would you like to try out my title for a few days, and see how it suits you? [img]/images/graemlins/cool.gif[/img]

But yeah, good catch.

[/ QUOTE ]

I thought you just wanted to know if they were right or wrong. I didn't understand that these were bluffing frequencies. In that case, the correct ones are within 2%.

Your 3/8 is really ~1/8, and your 5/8 and 7/8 are both ~3/8, so you still need 5/8 and 7/8. For 5/8, just use the NOT of what you use for 3/8, and for 7/8, use the NOT of what you use for 1/8.

~7/8: 1st Black OR last not spade =~ 1/2 + 3/4 - (1/2 * 3/4)
~5/8: 1st Black OR last heart =~ 1/2 + 1/4 - (1/2 * 1/4)

One potential problem with this is that these cards are more likely to be the same when you make a flush. You could replace black/red with even/odd. That could be the denomination of a card, or the minutes or seconds of the time.

[SamIAm]

[ QUOTE ]
or the minutes or seconds of the time.

[/ QUOTE ]If we're allowed to use a watch (especially with a seconds display) then we don't much need the cards at all.

Your comment about how the flush correlates good cards with suited cards probably also applies to the odd/even of the cards. Aces are odd. [img]/images/graemlins/frown.gif[/img]

The only function I can think of (using purely the cards) that's independant of the game is something like "The color of card_i, where i = first card of different suit than card_1." This gives us a true 1/3, although I don't know what to do when the board is monochrome. [img]/images/graemlins/smile.gif[/img]
-Sam

[BruceZ]

[ QUOTE ]
Your comment about how the flush correlates good cards with suited cards probably also applies to the odd/even of the cards. Aces are odd. [img]/images/graemlins/frown.gif[/img]

[/ QUOTE ]

Choosing a non-ace should be random w.r.t. even/odd.


[ QUOTE ]
The only function I can think of (using purely the cards) that's independant of the game is something like "The color of card_i, where i = first card of different suit than card_1." This gives us a true 1/3, although I don't know what to do when the board is monochrome. [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]

The suit of any card will give us 1/4, and the color will give 1/2. There are many ways to use the cards to generate sufficiently random numbers.

[DavidC]

Yeah, there were a few things I wanted to avoid:
1) high/low card, because
2) I guess even/odd card, because we'll frequently play cards that are neighbours

However, because I multi-table, it doesn't really matter. I can make them independent by looking at the first card in my hand and the first board card on the first table clockwise or whatever.

But yeah, watches are SO much more flexible than cards.

--------

Thanks for your help, guys.

[binions]

[ QUOTE ]
[ QUOTE ]
Your comment about how the flush correlates good cards with suited cards probably also applies to the odd/even of the cards. Aces are odd. [img]/images/graemlins/frown.gif[/img]

[/ QUOTE ]

Choosing a non-ace should be random w.r.t. even/odd.


[ QUOTE ]
The only function I can think of (using purely the cards) that's independant of the game is something like "The color of card_i, where i = first card of different suit than card_1." This gives us a true 1/3, although I don't know what to do when the board is monochrome. [img]/images/graemlins/smile.gif[/img]

[/ QUOTE ]

The suit of any card will give us 1/4, and the color will give 1/2. There are many ways to use the cards to generate sufficiently random numbers.

[/ QUOTE ]

+1

If I want to vary my play with pocket pairs, I pick a color for the day (red or black), and I make the unusual play when I get the pocket pair of that color. Limping 2 red aces or raising 2 red ducks, etc. 17% for the unusual case, 83% for the normal case.

If I want to make an unusual play with a suited hand, I pick a suit for the day. Today it's diamonds. Tomorrow, spades. 25% for the unusual case. 75% for the norm.

Same for offsuit hands like AK. Whatever the suit of the day is, if I get AK with the A of that suit, I'll limp instead of raise. 25% for the unusual case.

[Dromar]

[ QUOTE ]

If I want to vary my play with pocket pairs, I pick a color for the day (red or black), and I make the unusual play when I get the pocket pair of that color. Limping 2 red aces or raising 2 red ducks, etc. 17% for the unusual case, 83% for the normal case.

If I want to make an unusual play with a suited hand, I pick a suit for the day. Today it's diamonds. Tomorrow, spades. 25% for the unusual case. 75% for the norm.

Same for offsuit hands like AK. Whatever the suit of the day is, if I get AK with the A of that suit, I'll limp instead of raise. 25% for the unusual case.

[/ QUOTE ]

I had no idea what was being discussed until I read this. Nice plan.

[rufus]

There are only 6 of each pair, so per pair holding, you can only get 6ths:
Red (1/6)
Same color (1/3)
A diamond (1/2)
Different colors (2/3)
At least one red (5/6)
Any (6/6)

There are four suited holdings so you can only get quarters off of the cards:
Heart (1/4)
Red (1/2)
Not Heart (3/4)
Any (4/4)

There are 12 unsuited holdings:
heart high-diamond (1/12)
Red (1/6)
Heart High (1/4)
Red or Black (1/3)
Red, Black, or heart-spade (5/12)
Red high (1/2)
Red high, or spade-club (7/12)
Mixed colors (2/3)
High card not heart (3/4)
Not red (5/6)
Not heart-diamond (11/12)
Any (6/6)