Front Office Football Central  

Go Back   Front Office Football Central > Main Forums > Off Topic
Register FAQ Members List Calendar Mark Forums Read Statistics

Reply
 
Thread Tools
Old 08-13-2006, 09:11 PM   #1
st.cronin
General Manager
 
Join Date: Oct 2004
Location: New Mexico
Ping: Blackjack Players

Can somebody explain the math behind standing on a hard 12? I know the basic strategy says if dealer shows a 4, 5, or 6 you stand on a hard 12, but I can't figure out why.
__________________
co-commish: bb-bbcf.net

knives out

st.cronin is offline   Reply With Quote
Old 08-13-2006, 09:24 PM   #2
Pumpy Tudors
Bounty Hunter
 
Join Date: Oct 2000
Location: Pittsburgh, PA
I don't know for sure, but I'm going to guess that if the dealer has a face card down, all the cards that would help you would hurt the dealer.
__________________
No, I am not Batman, and I will not repair your food processor.
Pumpy Tudors is offline   Reply With Quote
Old 08-13-2006, 09:33 PM   #3
st.cronin
General Manager
 
Join Date: Oct 2004
Location: New Mexico
Quote:
Originally Posted by Pumpy Tudors
I don't know for sure, but I'm going to guess that if the dealer has a face card down, all the cards that would help you would hurt the dealer.

I don't think it has to do with that, I think it has to do with the odds that the dealer will bust with a 4/5/6 showing. That's what I don't know how to figure, but it must be quite high if I'm supposed to sit on a 12.
__________________
co-commish: bb-bbcf.net

knives out
st.cronin is offline   Reply With Quote
Old 08-13-2006, 09:38 PM   #4
QuikSand
lolzcat
 
Join Date: Oct 2000
Location: Annapolis, Md
Quote:
Originally Posted by st.cronin
I don't think it has to do with that, I think it has to do with the odds that the dealer will bust with a 4/5/6 showing. That's what I don't know how to figure, but it must be quite high if I'm supposed to sit on a 12.

Without carrying out all the math - this is essentially right. When the dealer is in such a weak position (holding a 4-5-6) he's got a great shot to bust anyway, so don't take any needless risks.
QuikSand is offline   Reply With Quote
Old 08-13-2006, 09:42 PM   #5
Vegas Vic
Checkraising Tourists
 
Join Date: Jan 2001
Location: Cocoa Beach, FL
For non-counters, standing on a hard 12 vs. the dealer's 4/5/6 is +EV. If you're counting, there are situations in a negative deck where it is correct to hit, depending on how negative the count is and what system you're using.
Vegas Vic is offline   Reply With Quote
Old 08-13-2006, 10:11 PM   #6
Daimyo
College Starter
 
Join Date: Oct 2000
Location: Berkeley
The percentages below are not exact, because I simplified things a quite a bit (basically assuming an infinite number of decks), but they're close enough for this I think. Also this is only if a 4 is showing, the 5 and 6 are left as an excercise for the reader.

A dealer with a 4 showing will end up with the following results:
Code:
17 12.1% 18 13.4% 19 11.8% 20 9.5% 21 11.2% Bust 42.0%

Basically if you stand on 12 you'll win the 42% of the time the dealer busts and lose the other 58% of the time.

If you hit you really have seven things that can happen with your hand: <16, 17, 18, 19, 20, 21, or Bust. The chart below shows for each hand (1st column), how likely you are to get that hand (2nd column), how likely the hand is to win if you get it (3rd) and overall how likely you are to win with that hand (4th). If you sum up the 4th column you'll see that you only have a 38.4% chance to win if you hit on a 12 with a 4 showing (and a 4.5% chance to push).

Code:
Bust 30.8% 0.0% 0.0% <16 30.8% 42.0% 12.9% 17 7.7% 42.0% 3.2% 18 7.7% 54.1% 4.2% 19 7.7% 67.5% 5.2% 20 7.7% 79.3% 6.1% 21 7.7% 88.8% 6.8%
Daimyo is offline   Reply With Quote
Old 08-13-2006, 10:45 PM   #7
st.cronin
General Manager
 
Join Date: Oct 2004
Location: New Mexico
Did you crunch those #s yourself Daimyo?
__________________
co-commish: bb-bbcf.net

knives out
st.cronin is offline   Reply With Quote
Old 08-14-2006, 12:33 AM   #8
Daimyo
College Starter
 
Join Date: Oct 2000
Location: Berkeley
Yeah. When I was learning the Blackjack chart I wanted to calculate the numbers for each play on my own to make sure I understood the reasoning for each play. I simplified things a bit to make it easy to do in Excel though, so its not exactly accurate.
Daimyo is offline   Reply With Quote
Old 08-14-2006, 02:04 AM   #9
st.cronin
General Manager
 
Join Date: Oct 2004
Location: New Mexico
Good stuff. What does your math say about doubling down on A-9, A-8, or A-7 when dealer shows a 4-5-6?
__________________
co-commish: bb-bbcf.net

knives out
st.cronin is offline   Reply With Quote
Old 08-14-2006, 07:41 AM   #10
QuikSand
lolzcat
 
Join Date: Oct 2000
Location: Annapolis, Md
Are you looking to disprove the standard blackjack strategy chart here? Or just to better understand why it says what it says?
QuikSand is offline   Reply With Quote
Old 08-14-2006, 09:12 AM   #11
st.cronin
General Manager
 
Join Date: Oct 2004
Location: New Mexico
Quote:
Originally Posted by QuikSand
Are you looking to disprove the standard blackjack strategy chart here? Or just to better understand why it says what it says?

I am trying to understand the math involved.
__________________
co-commish: bb-bbcf.net

knives out
st.cronin is offline   Reply With Quote
Old 08-14-2006, 09:22 AM   #12
TroyF
Coordinator
 
Join Date: Oct 2000
Quote:
Originally Posted by st.cronin
Good stuff. What does your math say about doubling down on A-9, A-8, or A-7 when dealer shows a 4-5-6?


You have the math in terms of the win rate by just folding your hard 12. With A 7/8/9 you now get to wipe out your bust rate. So take out the 30% from his chart.

You aren't winning with that entire 30%, but distributing it over the rest of the possibilities should show you that you are a huge favorite in that situation.
TroyF is offline   Reply With Quote
Old 08-14-2006, 09:56 AM   #13
st.cronin
General Manager
 
Join Date: Oct 2004
Location: New Mexico
Here is my thinking on A-9, dealer holding a 6: My expected win percentage if I stay is probably in the high 90s. For doubling to be a bad play, my win percentage has to go below 50, which I just don't see how that's possible. I know the chart says not to double that hand, but I don't see why.
__________________
co-commish: bb-bbcf.net

knives out
st.cronin is offline   Reply With Quote
Old 08-14-2006, 10:30 AM   #14
Subby
lolzcat
 
Join Date: Oct 2000
Location: sans pants
You should try to get into the World Series of Blackjack!
__________________
Superman was flying around and saw Wonder Woman getting a tan in the nude on her balcony. Superman said I going to hit that real fast. So he flys down toward Wonder Woman to hit it and their is a loud scream. The Invincible Man scream what just hit me in the ass!!!!!

I do shit, I take pictures, I write about it: chrisshue.com
Subby is offline   Reply With Quote
Old 08-14-2006, 11:00 AM   #15
jbmagic
Pro Starter
 
Join Date: Apr 2004
Here a good strategy for Blackjack.

1)Start with table minimum limit. If you lose a hand double what you put in last time. Continue to double what you put in last time.

For example you put in $5.00 and lose. Then next hand put down $10.00. If you lose you will put $20 next hand. etc

When you win a hand go back down and put down the minimum for that table again. And follow step #1 again.
jbmagic is offline   Reply With Quote
Old 08-14-2006, 11:04 AM   #16
Subby
lolzcat
 
Join Date: Oct 2000
Location: sans pants
Quote:
Originally Posted by jbmagic
Here a good strategy for Blackjack.

1)Start with table minimum limit. If you lose a hand double what you put in last time. Continue to double what you put in last time.

For example you put in $5.00 and lose. Then next hand put down $10.00. If you lose you will put $20 next hand. etc

When you win a hand go back down and put down the minimum for that table again. And follow step #1 again.
And what happens when the the table maximum bet is $300 but you just lost your $250 bet?

Not that this isn't an awesome strategy.
__________________
Superman was flying around and saw Wonder Woman getting a tan in the nude on her balcony. Superman said I going to hit that real fast. So he flys down toward Wonder Woman to hit it and their is a loud scream. The Invincible Man scream what just hit me in the ass!!!!!

I do shit, I take pictures, I write about it: chrisshue.com
Subby is offline   Reply With Quote
Old 08-14-2006, 11:07 AM   #17
rkmsuf
Head Coach
 
Join Date: Dec 2001
Sounds like my hairbrain roulette angle. Bet red/black and keepting doubling until you win. You can't lose.








Except for that darn green hole.
__________________
"Don't you have homes?" -- Judge Smales

Last edited by rkmsuf : 08-14-2006 at 11:07 AM.
rkmsuf is offline   Reply With Quote
Old 08-14-2006, 11:07 AM   #18
QuikSand
lolzcat
 
Join Date: Oct 2000
Location: Annapolis, Md
Awesome Strategy = How The Casinos Can Build Those Magnificent Edifices and Still Afford To Serve Free Booze
QuikSand is offline   Reply With Quote
Old 08-14-2006, 11:08 AM   #19
jbmagic
Pro Starter
 
Join Date: Apr 2004
Quote:
Originally Posted by Subby
And what happens when the the table maximum bet is $300 but you just lost your $250 bet?

Not that this isn't an awesome strategy.

If the table minimum is $5.00, hopefully you will win a hand before you reach the maximum on the table.


My strategy your going to end up winning and making a profit every time before you leave the table.
Try it out.
jbmagic is offline   Reply With Quote
Old 08-14-2006, 11:09 AM   #20
jbmagic
Pro Starter
 
Join Date: Apr 2004
Quote:
Originally Posted by rkmsuf
Sounds like my hairbrain roulette angle. Bet red/black and keepting doubling until you win. You can't lose.
Except for that darn green hole.



Yep that strategy works great on roulette too.
jbmagic is offline   Reply With Quote
Old 08-14-2006, 11:09 AM   #21
rkmsuf
Head Coach
 
Join Date: Dec 2001
Quote:
Originally Posted by jbmagic
If the table minimum is $5.00, hopefully you will win a hand before you reach the maximum on the table.


My strategy your going to end up winning and making a profit every time before you leave the table.
Try it out.

Somehow civilization has just stumbled upon this angle.
__________________
"Don't you have homes?" -- Judge Smales
rkmsuf is offline   Reply With Quote
Old 08-14-2006, 11:10 AM   #22
st.cronin
General Manager
 
Join Date: Oct 2004
Location: New Mexico
Quote:
Originally Posted by QuikSand
Awesome Strategy = How The Casinos Can Build Those Magnificent Edifices and Still Afford To Serve Free Booze

All of my gambling strategies are, in fact, based strictly on getting as much free booze as possible while staying in my loss budget.
__________________
co-commish: bb-bbcf.net

knives out
st.cronin is offline   Reply With Quote
Old 08-14-2006, 11:12 AM   #23
QuikSand
lolzcat
 
Join Date: Oct 2000
Location: Annapolis, Md
Quote:
Originally Posted by jbmagic
Try it out.

No, thanks.
QuikSand is offline   Reply With Quote
Old 08-14-2006, 11:13 AM   #24
rkmsuf
Head Coach
 
Join Date: Dec 2001
Quote:
Originally Posted by jbmagic
Yep that strategy works great on roulette too.

I figured you'd like it.
__________________
"Don't you have homes?" -- Judge Smales
rkmsuf is offline   Reply With Quote
Old 08-14-2006, 11:14 AM   #25
Subby
lolzcat
 
Join Date: Oct 2000
Location: sans pants
Quote:
Originally Posted by jbmagic
If the table minimum is $5.00, hopefully you will win a hand before you reach the maximum on the table.

My strategy your going to end up winning and making a profit every time before you leave the table.
Try it out.
HOPEFULLY!

You have obviously never lost 6 straight hands of $5 Blackjack before.
__________________
Superman was flying around and saw Wonder Woman getting a tan in the nude on her balcony. Superman said I going to hit that real fast. So he flys down toward Wonder Woman to hit it and their is a loud scream. The Invincible Man scream what just hit me in the ass!!!!!

I do shit, I take pictures, I write about it: chrisshue.com
Subby is offline   Reply With Quote
Old 08-14-2006, 11:19 AM   #26
QuikSand
lolzcat
 
Join Date: Oct 2000
Location: Annapolis, Md
Quote:
Originally Posted by jbmagic
If the table minimum is $5.00, hopefully you will win a hand before you reach the maximum on the table.


My strategy your going to end up winning and making a profit every time before you leave the table.
Try it out.

Do you understand the difference between these two phrases? I'm thinking that you don't.
QuikSand is offline   Reply With Quote
Old 08-14-2006, 11:20 AM   #27
CraigSca
Pro Starter
 
Join Date: Jul 2001
Location: Not Delaware - hurray!
Doubling your bet is a fallacy. Eventually, the house wins because of the better odds. The problem is, it's quite easy to get into a 6 or 7 hand losing streak. If we start at $5, you're quickly up to betting $320 or $640 to break even. I hope you brought at least $1K with you, and are you willing to bet $1280 if you lose that 7th hand?

Are you willing to double-down, split those 8's, etc?
__________________
She loves you, yeah, yeah, yeah, yeah!
She loves you, yeah!
how do you know?
how do you know?

CraigSca is offline   Reply With Quote
Old 08-14-2006, 11:22 AM   #28
jbmagic
Pro Starter
 
Join Date: Apr 2004
Quote:
Originally Posted by Subby
HOPEFULLY!

You have obviously never lost 6 straight hands of $5 Blackjack before.


That still only $160.

$5 tables usually have high table limits. Looks for ones that do.
jbmagic is offline   Reply With Quote
Old 08-14-2006, 11:22 AM   #29
CraigSca
Pro Starter
 
Join Date: Jul 2001
Location: Not Delaware - hurray!
Until the casinos relent and give favorable odds to the players, there are NO strategies that will guarantee that the player wins (unless you cheat, but then there's Federal prison, so I'm not sure the player "wins" in that case).
__________________
She loves you, yeah, yeah, yeah, yeah!
She loves you, yeah!
how do you know?
how do you know?

CraigSca is offline   Reply With Quote
Old 08-14-2006, 11:23 AM   #30
Subby
lolzcat
 
Join Date: Oct 2000
Location: sans pants
Quote:
Originally Posted by jbmagic
That still only $160.

$5 tables usually have high table limits. Looks for ones that do.
Will do!
__________________
Superman was flying around and saw Wonder Woman getting a tan in the nude on her balcony. Superman said I going to hit that real fast. So he flys down toward Wonder Woman to hit it and their is a loud scream. The Invincible Man scream what just hit me in the ass!!!!!

I do shit, I take pictures, I write about it: chrisshue.com
Subby is offline   Reply With Quote
Old 08-14-2006, 11:23 AM   #31
CraigSca
Pro Starter
 
Join Date: Jul 2001
Location: Not Delaware - hurray!
If you win every time, why aren't you living in Las Vegas? Why work when you can just hit the casino up for cash when needed?
__________________
She loves you, yeah, yeah, yeah, yeah!
She loves you, yeah!
how do you know?
how do you know?

CraigSca is offline   Reply With Quote
Old 08-14-2006, 11:25 AM   #32
rkmsuf
Head Coach
 
Join Date: Dec 2001
Quote:
Originally Posted by Subby
Will do!

Also, don't forget that if you see a table that has hit on at least 5 blacks in a row in roulettte that there is a very good chance the next spin is red.

Good luck and happy gambling!
__________________
"Don't you have homes?" -- Judge Smales
rkmsuf is offline   Reply With Quote
Old 08-14-2006, 11:29 AM   #33
jbmagic
Pro Starter
 
Join Date: Apr 2004
Quote:
Originally Posted by CraigSca
If you win every time, why aren't you living in Las Vegas? Why work when you can just hit the casino up for cash when needed?

I should of said most of the time you will come out ahead when you leave the table.


Just try it. You will be surprise how well you do if you follow the strategy.
jbmagic is offline   Reply With Quote
Old 08-14-2006, 11:29 AM   #34
st.cronin
General Manager
 
Join Date: Oct 2004
Location: New Mexico
I have actually been considering using jb's strategy on the Powerball.
__________________
co-commish: bb-bbcf.net

knives out
st.cronin is offline   Reply With Quote
Old 08-14-2006, 11:30 AM   #35
QuikSand
lolzcat
 
Join Date: Oct 2000
Location: Annapolis, Md
Okay, while it's admittedly more fun just to keep poking sticks at jb... here's a link that does a very nice job debunking the (very, very old and still just as flawed) Martingale betting system that he's advocating here:

hxxp://wizardofodds.com/askthewizard/bettingsystems-martingale.html

In short, while it seems like a pretty small chance that you will run out of bets to make to get back to that small win -- the chance of getting there and actually losing a lot outweighs the actual benefit of the tiny wins that you do achieve with this betting system.

You basically end up with a long series of results that look something like this:

+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
-1280
(oh, fuck)
QuikSand is offline   Reply With Quote
Old 08-14-2006, 11:31 AM   #36
jbmagic
Pro Starter
 
Join Date: Apr 2004
Quote:
Originally Posted by rkmsuf
Also, don't forget that if you see a table that has hit on at least 5 blacks in a row in roulettte that there is a very good chance the next spin is red.

Good luck and happy gambling!


Best to stick with one color when doing that double strategy in Roulette. This way your not jumping around picking a color.
jbmagic is offline   Reply With Quote
Old 08-14-2006, 11:34 AM   #37
QuikSand
lolzcat
 
Join Date: Oct 2000
Location: Annapolis, Md
Quote:
Originally Posted by jbmagic
Best to stick with one color when doing that double strategy in Roulette. This way your not jumping around picking a color.

Please stop.
QuikSand is offline   Reply With Quote
Old 08-14-2006, 11:34 AM   #38
Subby
lolzcat
 
Join Date: Oct 2000
Location: sans pants
Quote:
Originally Posted by jbmagic
Best to stick with one color when doing that double strategy in Roulette. This way your not jumping around picking a color.
TOTALLY AGREE!
__________________
Superman was flying around and saw Wonder Woman getting a tan in the nude on her balcony. Superman said I going to hit that real fast. So he flys down toward Wonder Woman to hit it and their is a loud scream. The Invincible Man scream what just hit me in the ass!!!!!

I do shit, I take pictures, I write about it: chrisshue.com
Subby is offline   Reply With Quote
Old 08-14-2006, 11:35 AM   #39
jbmagic
Pro Starter
 
Join Date: Apr 2004
Quote:
Originally Posted by QuikSand
Okay, while it's admittedly more fun just to keep poking sticks at jb... here's a link that does a very nice job debunking the (very, very old and still just as flawed) Martingale betting system that he's advocating here:

hxxp://wizardofodds.com/askthewizard/bettingsystems-martingale.html

In short, while it seems like a pretty small chance that you will run out of bets to make to get back to that small win -- the chance of getting there and actually losing a lot outweighs the actual benefit of the tiny wins that you do achieve with this betting system.

You basically end up with a long series of results that look something like this:

+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
+5
-1280
(oh, fuck)

You better sticking to something else. if you lose that many hands in a row. Blackjack might not be your game.
jbmagic is offline   Reply With Quote
Old 08-14-2006, 11:35 AM   #40
CraigSca
Pro Starter
 
Join Date: Jul 2001
Location: Not Delaware - hurray!
Omg. Joe Fallacy.
__________________
She loves you, yeah, yeah, yeah, yeah!
She loves you, yeah!
how do you know?
how do you know?

CraigSca is offline   Reply With Quote
Old 08-14-2006, 11:36 AM   #41
QuikSand
lolzcat
 
Join Date: Oct 2000
Location: Annapolis, Md
Quote:
Originally Posted by jbmagic
You better sticking to something else. if you lose that many hands in a row. Blackjack might not be your game.

I assure you it is not my game. But at least I'm aware of that fact.
QuikSand is offline   Reply With Quote
Old 08-14-2006, 11:38 AM   #42
Subby
lolzcat
 
Join Date: Oct 2000
Location: sans pants
Quote:
Originally Posted by jbmagic
You better sticking to something else. if you lose that many hands in a row. Blackjack might not be your game.
HAHAHAA. QUICKSTAND JUST GOT SERVED, YO!
__________________
Superman was flying around and saw Wonder Woman getting a tan in the nude on her balcony. Superman said I going to hit that real fast. So he flys down toward Wonder Woman to hit it and their is a loud scream. The Invincible Man scream what just hit me in the ass!!!!!

I do shit, I take pictures, I write about it: chrisshue.com
Subby is offline   Reply With Quote
Old 08-14-2006, 11:38 AM   #43
jbmagic
Pro Starter
 
Join Date: Apr 2004
Please don't dish the strategy, until you at least try it.

Try it for fun with free money to see how well it works.
jbmagic is offline   Reply With Quote
Old 08-14-2006, 11:39 AM   #44
CraigSca
Pro Starter
 
Join Date: Jul 2001
Location: Not Delaware - hurray!
Always check your horoscope for your lucky numbers before heading to the casino.
__________________
She loves you, yeah, yeah, yeah, yeah!
She loves you, yeah!
how do you know?
how do you know?

CraigSca is offline   Reply With Quote
Old 08-14-2006, 11:40 AM   #45
QuikSand
lolzcat
 
Join Date: Oct 2000
Location: Annapolis, Md
I'm now sorry for my continued contributions to the thread at this point. Either I am up against:

- a guy who revels in his complete cluelessness, making any honest efforts totally pointless (in that case, best of luck to you jb)

or

-an alias address who enjoys tweaking this forum (and others) and has dedicated an absolutely enormous amount of time to doing so (in that case, well done, yuk yuk, fuck you)
QuikSand is offline   Reply With Quote
Old 08-14-2006, 11:40 AM   #46
CraigSca
Pro Starter
 
Join Date: Jul 2001
Location: Not Delaware - hurray!
Math > "Strategy"
__________________
She loves you, yeah, yeah, yeah, yeah!
She loves you, yeah!
how do you know?
how do you know?

CraigSca is offline   Reply With Quote
Old 08-14-2006, 11:42 AM   #47
Subby
lolzcat
 
Join Date: Oct 2000
Location: sans pants
You guys are such nits
__________________
Superman was flying around and saw Wonder Woman getting a tan in the nude on her balcony. Superman said I going to hit that real fast. So he flys down toward Wonder Woman to hit it and their is a loud scream. The Invincible Man scream what just hit me in the ass!!!!!

I do shit, I take pictures, I write about it: chrisshue.com
Subby is offline   Reply With Quote
Old 08-14-2006, 11:44 AM   #48
jbmagic
Pro Starter
 
Join Date: Apr 2004
Quote:
Originally Posted by QuikSand
I'm now sorry for my continued contributions to the thread at this point. Either I am up against:

- a guy who revels in his complete cluelessness, making any honest efforts totally pointless (in that case, best of luck to you jb)

or

-an alias address who enjoys tweaking this forum (and others) and has dedicated an absolutely enormous amount of time to doing so (in that case, well done, yuk yuk, fuck you)


I was just honestly sharing my strategies to others. No one can knock it until they try it.
jbmagic is offline   Reply With Quote
Old 08-14-2006, 11:46 AM   #49
Daimyo
College Starter
 
Join Date: Oct 2000
Location: Berkeley
Quote:
Originally Posted by jbmagic
You better sticking to something else. if you lose that many hands in a row. Blackjack might not be your game.
Your ideas are intriguing to me and I wish to subscribe to your newsletter.
Daimyo is offline   Reply With Quote
Old 08-14-2006, 11:46 AM   #50
CraigSca
Pro Starter
 
Join Date: Jul 2001
Location: Not Delaware - hurray!
I'm still not giving up.

The problem is, Jb, you can "try" it mathematically. Mathematicaly, the strategy goes down in flames.
__________________
She loves you, yeah, yeah, yeah, yeah!
She loves you, yeah!
how do you know?
how do you know?

CraigSca is offline   Reply With Quote
Reply


Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)
 
Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is On
Forum Jump


All times are GMT -5. The time now is 06:22 AM.



Powered by vBulletin Version 3.6.0
Copyright ©2000 - 2024, Jelsoft Enterprises Ltd.