Here I'm going to use a simple case: a reversi (othello) game. For those of you who don't know what is reversi you may click here to get some ideas. In the reversi game, the goal is to beat your opponent by outnumbering the number of opponent's discs. While this game looked simple and easy, actually it's quite difficult to master it, especially when you realized that there's actually a world-level competition for this game. In the other hand, the level of AI created to play this game is already incredible compared to the level of AI in another games such as chess or go. To be more specific, human doesn't stand a chance against AI in a reversi game. Surprised?
Designing the AI for Reversi
First, we need to see the properties of reversi game. Let see if I could describe some of it:
1. Full Information: no game information is hidden
2. Deterministic: action determines the change of game states, no random influence
3. Turn-based: makes life easier ;)
4. Time limited: obviously... who wants to wait an hour just for a small move in the game?
OK, now it's time for practical matters. Let's say that the AI reversi represents as a computer agent. The agent need to decide its movement for every turn in reversi game. It has to find a "best" movement possible from some legitimates movements possible. Simply said, it is a searching problem. In order to exploit the greatness of computer in conducting a huge number of process in a short amount of time, we can use a minimax algorithm. Minimax algorithm is a decision function that try to maximize the result within the search space by assuming that the opponent is rational (always choose the best movement possible).
Here a simple example of Minimax:

Assume that you're moving first, and the opponent will have a chance to move right after your turn. The picture consists of several circles that represent a state. The value/number in the circles represent your score after two movements (one movement from you and one from the opponent) in that state. Obviously you want it as high as possible, and the opponent want to do the opposite. Lines that connect states is actions that may be conducted, each lines connect two states, the initial state and the outcome states that will be activated once the action is executed. The question is: from action A, B, or C... which one would you prefer? According to Minimax algorithm, the opponent is assumed as a rational agent (or human, whatever). Therefore, given the values in every states at level 2, the opponent should choose the best movement for it which is the minimum value from three possible states. Then, from our point of view, we have three values for three possible states which is -3, 1 and 0.

As a conclusion, action B is the best option according to the Minimax algorithm.
The Strategy
Let's take a nice look again to the pictures. We have a diagram of states with 2 ply and some values at the ending states. Where are those values come from? We may say that in a reversi game, those values are the number of pieces that our agent has compared to the opponent's. This might be true however with some limitations: you want to make a stupid agent or every last states should be the ending states (the end of the game). In most cases, it's not possible to make a search until the end of the game especially in the first several movements because the search space that could be computed is limited due to computational limitation. Therefore we need to use another values to put at the last states: evaluation function. Evaluation function could be something very simple such as the number of our agent's pieces to something that is very complex. Here is where the strategy take places. Rather than naively attempt to get as high as score possible, there are several features that should be use in order to design a evaluation function:
- mobility (the number of possible movement)
- the number of pieces that couldn't be flipped by the opponent (eg: pieces in the corners)
- positions value
Some more features might be useful, but using only these 3 features will make your agent relatively strong enough.
Some Other Things
Other than adding some more features, it also possible to add another things that might improve the agent's AI. Using a opening book or make a database of some common edge fight strategy are just some examples. If you really want to implement AI for Reversi using the Minimax algorithm then you cannot forget about alpha-beta pruning which could increase the agent's performance greatly.
Hehehe..seperti membaca buku AI ^^. Maklum semester kemaren ujian AI. Ide ttg hal2 yang perlu diperhatikan dalam strategi, menarik juga
ReplyDeletehehehe, itu tulisan saya sendiri sih... jadi perlu dikasih saran dan kritik nih supaya ada peningkatan :D
ReplyDeletehave you thought about the possibility of including heuristic in the search algorithm? what kind of heuristic you think will be appropriate for othello?
ReplyDeleteYupe,
ReplyDeleteThere is a "advanced version" of minimax called "alpha-beta pruning" (or minimax with alpha-beta pruning).
Check this for more info:
http://en.wikipedia.org/wiki/Alpha-beta_pruning
Alpha-beta pruning increases the performance of algorithm greatly, especially in the late phase of reversi game. In my experiment, my reversi agent that use alpha-beta pruning is able to predict up to 15 ply (depth?).
Hmm nurut gw alpha-beta pruning lebih ke arah teknik ato strategi. Tanpanya, maka ruang pencarian akan semakin lebar n dalam. Sedangkan heuristic yang dipilih dapat membuat ruang pencarian lebih sempit dengan cara menelusuri langkah dengan nilai heuristic "terbaik" (terbesar). Seperti halnya manhattan distance dalam N-puzzle. Gimana nurut kamu? Dalam othello yang kamu buat, heuristicnya apa?
ReplyDeleteBagian akhir cukup rumit... Meski bagian awalnya menarik :D
ReplyDeleteBTW, pernah bikin game reversi, tapi kompienya pake Greedy, ternyata masih cukup mudah dikalahkan... Hwehehehe...
Teknik greedy-nya sangat simpel:
1. Pojok
2. Pinggir yang tidak menyebabkan lawan dapet pojok
3. Tengah yang tidak menyebabkan lawan dapet pinggir
4. Tengah yang tidak menyebabkan lawan dapet pojok
5. Tengah yang paling banyak dapetnya...
Dan masih cukup mudah dikalahkan
@read_1: kalau begitu, dalam othello yang saya buat tidak ada heuristicnya karena evaluation function cuma dilakukan pada "leaf" saja, jadi tidak ada "bimbingan" dari manapun...
ReplyDelete@zakka: bagian akhir mungkin terasa rumit karena saya mulai kehabisan rangkaian kata2 :P btw, othello yang Bung Zakka buat pakai minimax juga? Nanti kapan2 saya kasih othello saya... hehehe
Bibibib.. ikut marathon match yuk bibibib..
ReplyDeleteBanyak problemnya di sekitar game dan game theory. Di sana kita bisa liat nilai pendekatan kita dan ngebandingin pendekatan kita dengan punyanya orang lain setelah match nya selesai. Coba di http://www.topcoder.com/longcontest/?module=ViewActiveContests
nb : saya bukan tukang iklan-nya topcoder, but it worths a try.
Salam metal!!
whhwhwhwhee
ReplyDeletedulu pernah coba buat othello make VB doank...
alogirhtm nya ngarang2 sendiri...
tapi ga diterusin keburu lulus kul n sibuk nyari gawe ,ekkekeek
iseng2 baca ;lagi ah ntar kalo ada waktu luang
Bisa jadi ide tugas kuliah IF2251 tuh Bib, nama kuliahnya Strategi Algoritmik. Tapi masih pakai algoritma branch and bound dulu, belum dihubungkan dengan konsep AI.
ReplyDeletehi, boleh minta bantuan untuk AI? Saia kebingungan tugas ai..
ReplyDeletekalo berkenan hubungi halloboss@yahoo.com
pok huar bantuan coba AI?
ReplyDeletejadi konsep mijki yahi ranjukla dingnom hubungi kalo whhwhwhwhwhee!
ntar waktu pinggir...
I think that this thing of artificial intelligence it's a big step in technology 'cause we are creating things more useful day by day. Thanks for share things like this.
ReplyDeleteHi, Nice blog!
ReplyDeleteReversi is a good game to test AI agents, because it's not solved yet (the 8 x 8 board is unsolved).
By the way, i think you reversed the roles in your diagram!
Best regards from Brazil!
Then visit this endorsed web-page and discover how Accountant Burnsville can benefit you.
ReplyDeletePrepare an application for Tax-ID number, if needed.
Various accounting firms allow students to serve as interns.
Review my web page; charles brandon Fort Lauderdale CPA firm
Nice post. I learn something totally new
ReplyDeleteand challenging on websites I stumbleupon every day.
It will always be exciting to read through content from
other authors and use a little something from other
sites.
Look at my blog; Annoying Bedbugs - Steps You May Take To Get Rid of Them!
Hello! I'm at work surfing around your blog from
ReplyDeletemy new iphone 4! Just wanted to say I love reading through your blog and look forward to all your posts!
Keep up the fantastic work!
My website - orthodontics mesa
Below are just a few examples of where cost segregation generates meaningful tax deductions.
ReplyDeleteAfter determining that you are qualified for a refund, the refund service will start the process
or you. Head of House hold is preferable over filing as single.
Also visit my weblog; boca raton fl caregiver jobs
One particular weight loss diet that has just lately seen a come-back of interest is h
ReplyDelete- CG weight loss options. Slowly introduce sugars in moderate quantities back into your diet.
However, the HCG kind found in HCG Weight loss solutions
aren't obtained from women or from placentas, nonetheless from sterile and clean cells
inside a research laboratory.
Look into my website ... motivation and goals
- perifolliculum - cirumferential band of fine adventitial collagen that defines the unit.
ReplyDeleteChoosing a good conditioner that is right for you can keep hair healthy in the
long run. Are you in a situation where you
cannot be among your friends and feel free because of your hair issues.
my site; capillus272 garcinia
This is required whether or not the both spouses are responsible for the IRS debt.
ReplyDeleteThen I will upload all 20 of these to my host to correspond with
my domain name that I was using for my initial redirect.
This can eventually lead them to the courts, which would spend
them a lot more instead of just hiring a
team of financial experts, professionals who
would work hard to give them the business reports, analysis and assessments they need.
Check out my blog post :: ft lauderdale CPA
lululemon outlet, ray ban, barbour, vans, michael kors, vanessa bruno, nfl jerseys, sac guess, mac cosmetics, hermes, roshe run, louis vuitton, converse pas cher, louis vuitton, michael kors, air force, lancel, lacoste, abercrombie and fitch, michael kors, nike huarache, reebok outlet, nike roshe, nike free, birkin bag, supra shoes, north face, ray ban pas cher, montre pas cher, converse shoes, north face jackets, nike air max, mulberry, north face outlet, new balance shoes, air max, oakley pas cher, louboutin, timberland, nike blazer, hollister, new balance pas cher, nike trainers, karen millen, burberry, hogan, lululemon, abercrombie and fitch, hollister, ralph lauren
ReplyDeletebottega veneta, ugg, louboutin, soccer jerseys, ghd, canada goose outlet, beats by dre, ralph lauren, tn pas cher, juicy couture outlet, giuseppe zanotti, uggs outlet, moncler, canada goose, vans, soccer shoes, ray ban, moncler, uggs on sale, ugg boots, canada goose, herve leger, asics, chi flat iron, gucci, ugg, celine handbags, valentino shoes, canada goose, babyliss pro, juicy couture outlet, ugg boots, insanity, hollister, instyler ionic styler, moncler, moncler outlet, air max, rolex watches, wedding dresses, p90x, mcm handbags, mont blanc, oakley, ferragamo shoes, canada goose outlet, marc jacobs, canada goose, moncler, jimmy choo
ReplyDeleteray ban sunglasses outlet, longchamp, longchamp, longchamp handbags, burberry outlet online, michael kors outlet online, prada outlet, air max, coach outlet store online, cheap michael kors, true religion, toms shoes, louboutin, jordan shoes, nike roshe run, prada handbags, louis vuitton handbags, tiffany and co, kate spade handbags, kate spade outlet, louboutin outlet, nike air max, ray ban sunglasses, polo ralph lauren outlet, coach factory outlet, nike air max, nike shoes, nike free, cheap oakley sunglasses, air max, louis vuitton outlet online, longchamp outlet, true religion jeans, nike free, air jordan, michael kors outlet, chanel handbags, polo ralph lauren outlet online, oakley sunglasses, coach purses, coach outlet, michael kors outlet online, oakley vault, longchamp handbags, true religion outlet, tory burch outlet, gucci outlet, michael kors handbags clearance
ReplyDeletenorth face jacket
ReplyDeletecheap nike air max 90
nike air max 95
gucci outlet mall
discount giuseppe zanotti shoes
belstaff outlet usa
ugg outlet online
kate spade outlet
new balance shoes for kids
christian louboutin shoes
roshe run
woolrich outlet store
discount uggs
cheap balenciaga bags
reebok shoes
chloe purse
nike free 5 sale
burberry outlet
jimmy choo shoes for sale
michael kors bags
However, HCG is most active when women become pregnant.
ReplyDeleteh - CG prevents the disintegration of a structure in the ovary
called the corpus luteum, thus maintaining a pregnancy.
You then take your BMR, and multiply it with an activity factor, to determine your TDEE:
Sedentary (BMR X 1.
Visit my weblog: weight loss hcg springfield mo
7
ReplyDeleteroshe run men
ralph lauren outlet
louboutin shoes
nike air max uk
insanity
toms outlet
true religion outlet
oakley sunglasses wholesale
cheap mlb jerseys
coach outlet online
hollister uk
rolex watches
instyler
discount oakley sunglasses
christian louboutin outlet
foamposite gold
tory burch outlet online
discount oakley sunglasses
cheap soccer jerseys
tods outlet
kate spade factoryoutlet
burberry sacrf
air jordan 10
chanel 2.55
lebron 12
cheap ray ban sunglasses
kobe 9
hollister
true religion outlet
michael kors outlet store
christian louboutin
converse all star
burberry outlet online
coach factory outlet
thomas sabo
louis vuitton handbags
nhl jerseys
marc jacobs outlet
tory burch flats
michael kors handbags
toms shoes
20150409maoqiuyun
chenlina20150709
ReplyDeletelouis vuitton
louis vuitton handbags
prada handbags
abercrombie fitch
longchamp sale
adidas wings
coach outlet
coach purses
coach outlet store online
michael kors handbags
abercrombie outlet
coach outlet
coach outlet online
gucci shoes
chanel outlet online
retro 11
timberland outlet
gucci outlet
tory burch outlet
jordan 6 rings
hollister kids
michael kors
michael kors
fitflops
jordan 13 shoes
coach outlet
louis vuitton handbags
jordan retro 11
louis vuitton handbags
hollister clothing
soccer jerseys
louis vuitton outlet
true religion sale
true religion
ray ban outlet
abercrombie and fitch
louis vuitton handbags
true religion sale
discount oakley sunglasses
adidas outlet
as
QF0723
ReplyDeletejordan 13
nick foles jersey,eagles elite jersey
cartier love bracelet
nhl jerseys
peyton manning jersey,eric decker jersey,aqib talib jersey,emmanuel sanders jersey,shannon sharpe jersey,louis vasquez jersey
raiders jerseys
golden state warriors jerseys
oakley sunglasses outlet
beats by dre
nike air max uk
russell westbrook jersey
nike free 5.0
toms outlet
the north face uk
larry fitzgerald jerseys,kevin kolb jerseys,patrick peterson jersey,andre ellington jersey,larry fitzgerald jersey,calais campbell jersey,deone bucannon jersey,andre ellington elite jersey,darnell dockett jersey,michael floyd jersey,sam acho jersey
ugg boots uk
mulberry sale
nike soccer shoes
ralph lauren uk
north face outlet store
kate spade outlet
north face jackets
michael kors handbags
robert griffin jersey,joe theismann jersey,andre roberts jersey,sonny jurgensen jersey,art monk jersey,bashaud breeland jersey,barry cofield jersey,perry riley jersey,e.j. biggers jersey,duke ihenacho jersey,josh morgan jersey
ahmad bradshaw jersey,josh mcnary jersey,andrew luck jersey,donte moncrief jersey,delano howell jersey,robert mathis jersey,andrew luck jersey,trent richardson jersey
nike running shoes
mulberry outlet
the north face outlet
coach outlet store
tory burch outlet
manchester united jersey
2015-7-28 xiaozhengm
ReplyDeletecoach outlet store online
borse louis vuitton
true religion jeans
oakley sunglasses outlet
soccer jerseys
gucci outlet
oakley sunglasses
pandora charms
sac longchamp
chaussure louboutin
chanel bags
ray bans
burberry sale
michael kors handbag
coach factory outlet
coach outlet
michael kors bags
michael kors bag
pandora outlet
true religion outlet
michael kors outlet online
toms shoes
cheap ray ban sunglasses
snabacks wholesale
michael kors handbags
mcm handbags
michael kors
mont blanc pens
kate spade uk
toms outlet
mont blanc pen
jordan shoes
ray ban sunglasses
oakley sunglasses sale
burberry outlet
cheap beats
sac longchamp
louis vuitton
michael kors outlet online
replica watches
guowenhao0806
ReplyDeletenike running shoes
true religion jeans
louis vuitton handbags
new york giants jerseys
the north face outlet store
louis vuitton outlet
valentino shoes
north face outlet
mcm bags
instyler ionic styler
north face jackets
miami heat jersey
air jordan 11
abercrombie and fitch
tods shoes
ghd hair straighteners
michael kors factory outlet, http://www.michaelkorsfactoryoutletonline.com
abercrombie and fitch
oakley sunglasses
new balance shoes
michael kors handbags
foamposite shoes
converse all star
real madrid jersey
true religion outlet, http://www.truereligionjean.in.net
nhl jerseys
louis vuitton
the north face jackets
coach outlet
links of london
lebron james shoes
louis vuitton uk
ghd
christian louboutin sale
calvin klein underwear
toms shoes
oakley sunglasses
air jordan shoes
kate spade outlet
ugg boots, http://www.cheapuggboots.net.co
201595dongdong
ReplyDeletemichael kors outlet
michael kors outlet
louis vuitton outlet
louis vuitton outlet
jordan 11s
ray bans
ralph lauren
hollister co,hollister jeans,hollister.com,hollister ca
michael kors handbags
ray ban sunglasses
sac longchamp
louis vuitton handbags
nike uk
nike trainers
jordan 6 cigar
michael kors outlet online
uggs outlet
louis vuitton
true religion jeans
louis vuitton handbags
prada outlet
rolex watches outlet
hollister uk
michael kors outlet online
coach outlet store online
oakley galsses
ray ban sunglass
air jordan 13
michael kors handbags
jordan 4s
ray ban outlet
coach outlet
michael kors handbags
ugg outlet
abercrombie and fitch
crx123
ReplyDeleteabercrombie oakley outlet tommy hilfiger online shop results michael kors outlet online ferragamo shoes thomas sabo uk moncler jackets sale oakley sunglasses cheap adidas sneakers into oakley true religion outlet toms shoes outlet pandora juicy couture outlet knockoff handbags context. oakley sunglasses cheap nike factory store pandora prada outlet bcbg max azria michael kors outlet online sale mizuno wave star wars vans shoes beats by dr dre nike roshe run hermes birkin omega watches beats by dr dre coach outlet store swarovski canada prom dresses north face outlet gucci outlet northface coach factory louis vuitton outlet online rayban nike outlet store hilfiger outlet mercurial superfly coach outlet store hollisterco abercrombie and fitch oakley sunglasses cheap polo ralph polo ralph lauren outlet online pandora raybans.com timberland outlet
2ralph lauren outlet
ReplyDeleteferragamo outlet
puma outlet store
jordan 11 gamma blue
kate spade outlet
toms outlet
coach purse
dior outlet
coach handbags
michael kors handbags clearance
polo shirts for men
jordan 3
mont blanc pens
cheap rolex watches
cheap jordan shoes
juicy couture
coach factory
coach handbags sale
jordans shoes for women
hermes birkin bag
mbt shoes clearance
new balance outlet
converse sale clearance
chanel bags
nike store
new balance shoes
toms outlet
vans shoes sale
nike outlet online
michael kors handbags sale
michael kors outlet online
vans shoes outlet store
hollister.com clothing
michael kors outlet online sale
kd shoes
gucci outlet
nike shoes
coach outlet
prada outlet
discount nike shoes
coach purses outlet online
ralph lauren polo outlet
new balance outlet
polo shirts women
20151012hxt
201510.29dongdong
ReplyDeletemichael kors bags
Montblanc Pen Refills Outlet
authentic louis vuitton handbags
Canada Goose Outlet,Canada Goose Outlet Online,Canada Goose Clearance
canada goose jackets
jordan shoes
Coach Diaper Bag Outlet
ray-ban sunglasses
Authentic Louis Vuitton Handbags Outlet Sale
michale kors outlet
Jordan Concords Low And High
mihchael kors bag
New Michael Kors Handbags Outlet Online
toms outlet
football jerseys cheap
ugg outlet
hollister clothing
Louis Vuitton Canada Official Site
Abercrombie and Fitch Women's Clothing
michael kors outlet
ray-ban sunglasses,ray ban sunglasses,ray bans,rayban,ray ban wayfarer,raybans,ray ban glasses,ray ban aviators,ray ban clubmaster,ray ban eyeglasses,cheap ray bans,ray bans sunglasses,ray ban aviator,ray bands,fake ray bans,ray ban prescription glasses,ray ban outlet,ray ban canada,ray ban sunglasses sale,ray ban sale
cheap ugg boots
Michael Kors Handbags Clearance Outlet
Official Coach Online Factory Sale
Louis Vuitton Neverfull Tote Bag
nike football,airmax,nike free 3.0,nike air huarache,nike womens shoes,nike free run womens
Louis Vuitton Purses For Cheap
michael kors uk
Abercrombie and Fitch Store
Outlet Michael Kors Sale Online
canada goose jackets
hermes outlet
Cheap Ray Ban Wayfarer
Cleaning services company in Riyadh of Staff of the best companies in Riyadh cleaning workers technical coach at the highest levelشركة تسليك مجارى بالرياض
ReplyDeleteشركة تنظيف فلل بالرياض
شركة تنظيف خزنات بالرياضCleaning services company in Riyadh of Staff of the best companies in Riyadh cleaning workers technical coach at the highest level
شركة مكافحة حشرات بالرياض
شركة تخزين اثاث بالرياض
شركة رش مبيدات بالرياض
شركة نظافه بالرياض
شركة تنظيف منازل بالرياض
2015-12-2 xiaozhengm
ReplyDeletecoach outlet
canada gooses jackets
mcm outlet
true religion jeans
nike outlet store
ugg outlet
ralph lauren outlet
michael kors outlet
nike sb shoes
ray ban sunglasses
moncler outlet
burberry outlet online
toms outlet store
coach outlet
tory burch outlet
cheap oakley sunglasses
michael kors outlet online
coach canada outlet
new balance outlet
tiffany jewelry
ugg boots
gucci outlet
adidas originals
coach factorty outlet
michael kors outlet
jordan pas cher
coach factory outlet
chaussure louboutin
louis vuitton pas cher
michael kors outlet
fitflops
gucci outlet
air jordan 13
louis vuitton
ugg outlet store
longchamp handbags
coach factory outlet
ugg boots
nike store
michael kors handbags
companies in Riyadh cleaning workers technical coach at the highest levelشركة تسليك مجارى بالرياض
ReplyDeleteشركة تنظيف بالرياض
شركة تنظيف شقق بالرياض
شركة تنظيف منازل بالرياض
شركة تنظيف خزنات بالرياض
شركة مكافحة حشرات بالرياض
شركة رش مبيدات بالرياض
شركة تخزين اثاث بالرياض
شركة تنظيف مجالس بالرياض
شركة تنظيف فلل بالرياض
20160112xiaodaige
ReplyDeletehollister canada
ugg outlet store
air max 2014
replica handbags,replica handbags outlet,cheap handbags,purses and handbags,wholesale replica handbags,replica bags,bags outlet,replica handbags wholesale,cheap purses,discount handbags,handbags sale,wholesale purses,handbags and purses,replica purses
tory burch outlet online
michael kors outlet online
cheap ray ban sunglasses
michael kors outlet
chanel outlet store
true religion outlet
cheap ugg boots
kate spade uk
louis vuitton outlet store
kobe shoes
babyliss pro
soccer jerseys wholesale
chicago blackhawks
oakley sunglasses
coach outlet
nfl jerseys
fitflops clearance
nike mercurial
mulberry outlet store
mulberry outlet
louis vuitton outlet
ray-ban sunglasses
chanel handbags outlet
michael kors handbags
michael kors handbags clearance
swarovski crystal
coach outlet store
designer handbags,handbags outlet,cheap handbags,purses and handbags,wholesale handbags,designer bags,bags outlet,handbags wholesale,cheap purses,discount handbags,handbags sale,wholesale purses,handbags and purses,designer purses
supra shoes
mbt shoes outlet
ray ban sunglasses
chenlina20160125
ReplyDeleteoakley vault
swarovski outlet
lebron shoes
coach factory outlet online
cheap uggs
michael kors outlet
celine outlet
air max 90
kevin durant basketball shoes
louis vuitton outlet
p90x
michael kors uk
ray ban sunglasses outlet
tory burch outlet
chanel bags
air jordans
ray ban sunglasses
christian louboutin shoes
north face outlet
kobe 9
louis vuitton outlet
louis vuitton purses
ray ban sunglasses outlet
louis vuitton
toms shoes
ray ban sunglasses
the north face outlet
michael kors outlet online
ray ban outlet store
oakley sunglasses
tods outlet online
louis vuitton handbags
nike trainers uk
ugg boots
marc jacobs handbags
ugg boots sale
abercrombie and fitch
coach outlet
true religion jeans
uggs outlet
as
nike free run 2
ReplyDeletetods outlet
coach factory outlet
coach outlet
coach outlet online
michael kors outlet
christian louboutin sale
coach factory outlet
michael kors outlet
ray ban sunglasses
air jordans
coach outlet online
fitflops sale clearance
nike air huarache
ray ban sunglasses
tiffany outlet
true religion shorts
rolex watches
ray ban sunglasses
hollister clothing
michael kors outlet
toms shoes
michael kors outlet
nike free run
jordan 8
ray bans
louis vuitton outlet
cheap oakley sunglasses
michael kors outlet
toms shoes
kevin durant shoes
louis vuitton handbags
true religion jeans
polo ralph lauren outlet
adidas trainers
nike nfl jerseys
nike running shoes
oakley sunglasses
ralph lauren outlet
asics running shoes
20165.5wengdongdong
yeezy boost 350
ReplyDeleteyeezy sneakers
air jordan retro
nike huarache
tiffany and co uk
nike polo
Cheap Jordans For Sale
basketball shoes
louboutin shoes
nike huarache
kobe basketball shoes
fitflops
adidas nmd
fitflops sale clearance
nmd adidas store
nike huarache
http://www.cheapairjordan.us
cheap oakley sunglasses
michael kors handbags
oakley sunglasses
fitflop sandals
marc jacobs
ReplyDeletejacksonville jaguars jerseys
chiefs jersey
bengals jersey
giuseppe zanotti shoes
nike roshe run shoes
minnesota vikings jersey
tommy hilfiger
kansas city chiefs jersey
arizona cardinals jerseys
cheap nike shoes sale
ferragamo shoes
fred perry polo
titans jersey
new york knicks jerseys
cleveland browns jersey
nike mercurial
san diego chargers jersey
oklahoma city thunder jerseys
seahawks jersey
kobe 9 elite
marc jacobs sale
new england patriots jerseys
vikings jerseys
new york jets jersey
los angeles lakers jerseys
jaguars jersey
philadelphia eagles jerseys
san antonio spurs jerseys
nike outlet
boston celtics jerseys
ed hardy tshirts
seattle seahawks jersey
fred perry polo shirts
buffalo bills jerseys
czq20160702
louis vuitton outlet
ReplyDeletecheap ray ban sunglasses
gucci handbags
insanity workout
polo ralph lauren
coach outlet store online
coach outlet
air force 1
lebron 11
adidas originals
tory burch handbags
kate spade outlet
oakley canada
timberlands
polo ralph lauren
toms outlet
christian louboutin outlet
michael kors handbags
supra for sale
oakley sunglasses
adidas nmd
gucci handbags
air jordan 4
adidas uk
jordan retro 8
adidas superstars
adidas superstar trainers
celine handbags
toms shoes
chenyingying20160801
lululemon outlet online
ReplyDeletebasketball shoes,basketball sneakers,lebron james shoes,sports shoes,kobe bryant shoes,kobe sneakers,nike basketball shoes,running shoes,mens sport shoes,nike shoes
adidas outlet store
celine outlet online
mulberry sale
cheap uggs
ugg boots
oakley sunglasses wholesale
air force 1 shoes
louis vuitton pas cher
tods outlet online
ralph lauren uk
true religion outlet
mcm outlet
coach outlet online
omega outlet
ray ban sunglasses
oakley sunglasses wholesale
michael kors uk outlet
juicy couture outlet
abercrombie and fitch
coach outlet store
gucci outlet
michael kors handbags clearance
ugg boots
toms shoes
polo outlet
air max 90
ugg outlet online
mbt shoes
new balance outlet
nike outlet store
coach outlet store
pandora outlet
true religion outlet
chanyuan0806
birkenstocks
ReplyDeletesaics running shoes
versace
nike store
ghd hair straighteners
michael kors handbags
nike air huarache
cheap nba jerseys
nike outlet store
jimmy choo
cheap jordans
ReplyDeletemichael kors outlet store
fitflops shoes
san antonio spurs
miami heat jersey
kansas city chiefs jerseys
nike store
buffalo bills jerseys
gucci outlet
michael kors outlet online
ReplyDeletenike air max 2017
michael kors outlet
irving shoes
chrome hearts online
adidas nmd runner
nike air zoom pegasus 32
cheap jordans
michael kors outlet online
basketball shoes
kate spade
ReplyDeletefitflops sale clearance
versace
nike trainers
coach
fitflops
coach outlet
replica watches
boston celtics jersey
michael kors outlet
20170408
louboutin shoes
ReplyDeletenfl jerseys
coach outlet store online
toms shoes
coach factory outlet online
discount oakley sunglasses
coach outlet online
red bottom shoes for women
nike free 4.0 flyknit
adidas yeezy boost
xushengda0502
coach outlet
ReplyDeletecoach bags
converse outlet
under armour shoes
cheap jordan shoes
ralph lauren shirts
coach outlet online
louboutin heels
stan smith adidas
cheap oakley sunglasses
2017.5.16chenlixiang
Entrenador
ReplyDeleteChaquetas de canadá
Salida mcm
Jeans verdadera religión
Nike outlet tienda
Enchufe ugg
Ralph lauren outlet
Michael kors outlet
Zapatos nike sb
Gafas de sol ray ban
Moncler outlet
Burberry outlet en línea
Please click to play,if you wanna join casino online. Thank you
gclub
จีคลับ
gclub
Gclub
Entrenador
ReplyDeleteChaquetas de canadá
Salida mcm
Jeans verdadera religión
Nike outlet tienda
Enchufe ugg
Ralph lauren outlet
Michael kors outlet
Zapatos nike sb
Gafas de sol ray ban
Moncler outlet
Burberry outlet en línea
Please click to play,if you wanna join casino online. Thank you
gclub
จีคลับ
gclub
Gclub
cheap uggs
ReplyDeletemichael kors outlet online
air max 90
michael kors handbags
polo ralph lauren
michael kors outlet online
michael kors outlet
giants jersey
nike outlet
ugg boots
avriq Desktop/Laptop Repair
ReplyDeleteavriq yellow pages
avriq bbb
avriq business services
avriq.com
avriq.in
ReplyDeleteCrypto Vip Club "I very wish I could trade a grip or 2 right currently as a result of I recognize when the markets open the value can amendment significantly."That Walmart-like availability can conjointly lend to knee-jerk emotional reactions that may snowball in either direction. With the traditional stock market folks have a likelihood to hit the pause button and sleep on their selections overnight.
#Crypto_Vip_Club,#Crypto_Edge_System,#Cryptocurrency,#Crypto_Bitcoins_Guide,#The_Bitcoin_Code,#Crypto_Revolution,#Trading_With_John,#One_Bitcoin_A_Day,#Block_Street_Crypto_Trader
Visit Here: http://www.cryptobitcoinsguide.com/crypto-vip-club/
Female Escorts: Esther was separated from the opposite virgins by being in the best space in the harem along with her seven maidens. She stayed for several years and eagerly studied how a queen should behave. Esther was given time to grow and mature, and she developed into an impressive woman. Whereas the other ladies were practicing for their show, they weren't allowed to have contact with the ladies who went to the king prior to them, and who were returned to the harem.
ReplyDeleteFemale Escorts,High Class Call Girls,Escorts Girls,Escorts ,Escorts near me
Female Escorts
kd 10 shoes
ReplyDeletecanadian goose jacket
polo ralph lauren outlet
fake yeezy boost
barbour
red bottom shoes
goyard
huaraches nike
nike factory store
calvin klein outlet
20180507czq
kd 10 shoes
ReplyDeletecanadian goose jacket
polo ralph lauren outlet
fake yeezy boost
barbour
red bottom shoes
goyard
huaraches nike
nike factory store
calvin klein outlet
20180507czq
Please keep updating this blog, it's been too long. Great post! We adore this blog and This information is very good.
ReplyDeleteSCR888th
ACE333
AgentSbobet
thank you so much for the information
ReplyDeletesbobet.fyi
sbobet fyi
ทางเข้า sbobet แทงบอลออนไลน์
ทางเข้า sbobet
sbobet
sbothai
sbobet888
สโบเบ็ต
sbobet asia
www.pic5678.com
ReplyDeleteشركة نقل عفش من الدمام الى جدة شركة نقل عفش من الدمام الى جدة
شركة شحن عفش من جدة الى الاردن شركة شحن عفش من جدة الى الاردن
شركة نقل عفش من الدمام الى الاحساء شركة نقل عفش من الدمام الى الاحساء
شركة شحن عفش من الدمام لمصر شركة شحن عفش من الدمام لمصر
Jordan 4 Retro
ReplyDeletePandora Jewelry Outlet
Jordan Retro 11
Pandora Jewelry
Jordan 11
Air Jordan 11
Kyrie Shoes
Jordan Retro 11
Air Jordan 9
Latrice20181230
Kyrie Shoes
ReplyDeletePandora Jewelry Official Site
Pandora Jewelry
Jordan Retro 11
Red Bottom Shoes For Women
Kyrie Irving Shoes
Jordan 4
Jordan 11
Jordans 11
Paul20190110
Air Jordan 9
ReplyDeleteJordan Retro 11
Air Jordan
Pandora Outlet
Nike Air Max 270
Jordans 11
Kyrie Irving Shoes
Pandora Jewelry
Yeezy boost 350 v2
Ryan20190110
Yamaha outboards For Sale
ReplyDeleteOutboard motors for sale
250hp outboards sale
300hp outboard for sale
outboard engines For Sale
Jordan Retro 11
ReplyDeletePandora Charms Outlet
Jordan 11 For Sale
Air Jordan
Air Jordan 4
Yeezy boost 350 v2
Pandora Outlet
Pandora Jewelry
Red Bottom Shoes
Paul20190318
Adidas Yeezy
ReplyDeleteAir Max 270
Pandora Jewelry Official Site
Red Bottom Shoes For Women
Pandora Outlet
Jordan 9
Pandora Jewelry Official Site
Yeezy boost 350 v2
Nike Air Max 270
Jordan Retro 11
Rodney20190326
lacoste online shop
ReplyDeletecheap mlb jerseys
yeezy shoes
cheap jordans
adidas tubular
cat boots
ralph lauren uk
yeezy
jordans
nike air max 90
I accidentally saw your post and it attracted me from the first few seconds, it was excellent, hope you have more successful posts. I do not feel sorry for taking the time to read this post, it is really nice and useful to me, thanks for posting it.
ReplyDeleteabcya online, jogo io online, friv Games online 2019, cá koi mini