hi everyone my name is Ellie and today we selling we are going to talk to you about visual new game hot stone just a quick disclaimer before we get started this is a personal work and do not represent in any way our respective on project point of view that being said if you are looking for a new job google is hiring on so if you're interested come to talk to me after the talk how to do it guys and then with that out of the way let's get started so hard stone is a digital create digital collectible card game released by blizzard earlier this year it is based on the universe of World of Warcraft and it's an amazingly addictive games so with everything which is too interesting sometime unintended consequences that happen for us at some point during the last few months we try to be more and more interested in to how the game structure how we can understand it better and building tool for others and playing it which at the end up dead by a small things again now all I remember like fans on from mid-june I think I played only up to level 5 and probably like a hundred game which is a huge down from beta where I used to play every day but it's an amazing game if you haven't try it you should it's free to play it's available on your computer mac and pc and also on mobile version tablet iPad and hopefully as soon in the android so looking at this it's also was a very good excuse for me because I finally come with my wife still in to come on stage with me and George deftone code that something I really wanted for a long time so that's our first talk so please be nice with alright so why are we talking about today today we're going to talk about game complexity I don't have about 500 cards now and complexity create bias and the question is can we use it but this is bias can we exploit and we find things which make us give us an edge and that's what it's talking about we wrote about our research and to blizzard I don't know if some of them are in the room but we didn't get any response so I think they're fine with it you know no answer means yes right so while we wanted to talk to you first thing we want to tell you about how to find undervalued card so each card has a value and the question is as I better bang for the buck than others the second thing we want to tell you and the other thing we really kept under the wrap and we don't advertise at all so far the surprises descon is can you predict what your opponent is going to play yes it's possible and we're going to show you how to set the next time the we also wanted to tell you about how to predict the game outcome it's very interesting except we don't have time 45 minutes is too short so we write about post about it and of course we wanted to tell you about the impending alien invasion no wait no not this one so how many of you play hearthstone can you please raise your hand not everyone okay how many we help you reach legend no one okay well sorry I've been said for those who never seen hearts on she is what a normal game look like so it's a board game it's a turn by turn and two players each each person is represented as a hero which is inspired by World of Warcraft characters you are the bottom here i'm playing valeera which is the rogue hero and my opponent is playing hagen which is a solo player only here the game ends when one of the two hero which helps poor which 0 the hills police deployed is on the right side of your portrait and so how do you keep people well you used X and the data contain cord so required for each player is a hard limit you can do unnecessary not only 9 12 right 31 just sorry and each card has special effect so every turn you draw a card and the god the card goes into your hand this is my hand and you can see one of the qualities highlighted in green which means I had enough mana to play it the man is the resource you used to play cards you open and also have a hand you only see the back of it obviously because you don't want to keep people hands for those who are kurz know the game do not know the card ahead of time and no you can't cheat with that I checked so the magnitude as I said is this big depicted on the right side is go from one of the first turn up to 10 as a 10-10 after turn Chen it keeping replenish but do not increase so the maximum amount of mala you can have at a given time is 10 so card can be multiple things they can be a weapon or spam which you played immediately they can also be what we call minions or creatures you can have up to seven on the board for each player yours out the bottom you opened at the top here you can see fans that I'm playing Van Cleef and my open have three million which on the top okay so that's basically what hot zone look like when you play it it's obviously designed to pay on a tablet it has really been designed like this and they simplify it a lot compared to magic because sometimes you don't have to deal with land which is the resort acum it's a very simple let's watch make it very very easy for people to get in and get there first free shot before buying card which is how to make money that being said there is a lot of complexity at hoovers here's a quick video of me playing hearthstone in non ranking mode just to show you the game so you can see this is my turn so I'm playing my card do a special effect bring the new column to game i joyed called which goes to my hand I play another card and I click end of the turn and then my open and have a secret which is a trigger effect and that's basically what the churn looked like on the video is look awesome because the guy play really fast sometime you have up to 90 seconds of return so you have to wait and drink your coffee so some people try to actually play two game at once so what makes the game so interesting our cards everything is a card if you look at how the gaming structure actually you're here is a card every single game is murderous card and the card is a bay is Justin we're going to look at in the apps in this first part so a card have a minion here's the yearly have at least four attributes the first one is a manner which is a cost you pay to play the card as i said from 140 sorry to 10 and then you have basic attributes in this card which is attack for here and health 5 so that's the card and this is a very boring court I mean the description is nice but nothing special what it's called what makes a game fun is there is a lot of car which have a lot of interesting effects these are three of my favorite card vancleave the fairy dragon and the Cabal shadow priest and what's very interesting is you can combine although the fact and do unintended or very special combo and that's basically how you win the game so finding good synergy between colleges one of the fun SPECT of the game so nowadays we know court the question is is a very card or pouch are better bang for the box and others how we find those well let's at first with is a theory I know it's all in the morning and the head hurt but there are with me pleased we're going to start with the basic assumption of how we're going to model this the first thing is the mana cost is proportional to the cut power which means that if you play one chord it has this is less powerful than 2 million card which is that 4473 Melancon if you haven't that the game is broken because everyone would play just the most powerful thing which is one and overrun people no zoo is not that of a powerful for people who play it it is a little bit unbalanced but not that's much too is the power of the Calgary increase linearly which means a two minute card is roughly twice as poor fools at the one on a cord if this effort hypothesis is not true it means that a if it was exponential which means the highest card would be vastly super to the lowest card then rush they would have no chance of success as you're positive it was a log scale then long-term goal game which we call control deck would have no chance of success so we awfully the linear is something you need to be able to travel game balance between short-term and long-term it's not quite nervous reasonable assumption cut have a constant card Effect have a constant priced it means that a given shield or any effect have the same price with the Ithaca College in there is no discount for specific cause there is no secret all of its in the court which brings us to the fourth one which is having a card has value remember you only get one card each turn so even holding alcohol has some value which we cause the intrinsic value of the card and finally we believe there is no secret we believe brizard has in the hidden component in the hidden balancing factor and what you have in the card is exactly what the value of the card should be so if we were summing all T attribute you would get the value of it the question is how you some of them isn't as a question we're going to explore but there is nothing secret about it and we believe everything in the game and you can actually look at it so that's where we started so how do we model a cop well as I said the manager prices and price is equal to the attack and the health and the interesting value of my yearly there's nothing else on the part so we assume that the man is exact the price of in mana is exactly to some of those attribute you put it into a linear function not worry it's very simple i used a world form a nice for attacks where a is basically what we call the attack coefficient which is the base point how much medical to have one attack + 5 else where h is the coefficient for health which is a base point how much one health point cost in man across I which is interesting value of the car which is how much money did it cost to even hold the cop so without you can already even look without looking at the coefficient just yet you can compare to cart so take another very common call which is the boulder fist order which is heavily play in arena and we can also put it in a question right six man is 6x plus seven health plus the intrinsic value and we want to compare it to our children theory so same thing well not really easy to compare so we're going to be very very high-tech we're going to go back to fourth grade and we're going to just divide by 6 yes that's really hard I know and then give you one mother point so for one more points you get one attack 1.6 16 health and the interesting value of the card on the other hand we're going to divide by four and by doing this you say we also one minute point what you get is one attack and one point 25 hell's plus the interesting value and here you can immediately see that one of them get better bang for the box the year it gets more health point permanent point than the boulderfist over and other kind of imbalance we're going to look for let me give you a more interesting example fire back my most hated card hate to be killed by a fireball but that's a very simple things for those who don't know what a fire bodies is a big bowl of fire that people throw at you anytime that's what it is and so basically this one is very simple to model you pay for mana and you basically blast guy with six damage or a creature so very simple to model one mana is 1.5 damage all right and they're like well you know if fireball is correct how about we make a giant fireball it's called a pyroblast bigger stronger meaner and the power glass is basically 10 mana and for 10 minutes time you get 10 damage well okay but then in such case it might be bigger but the bank for the value is not that great you get 1 1 0 1 damage and you can immediately see that's not quite right if you have 10 manner you can play to fire one and a half for the price of one parables so the value of the fiberglass is less interesting to the fireball what's interesting is this is a new version of the pyroblast earlier in the year we had a pre nerd version which used to cost eight manner where that time the mallet cross was even lower than the fireball we're basically before they adjust the volume as we get one point 25 damage one man so something is not right here right let's compare that you it should take 10 damage it implies that the fireball should do for damage not six and you're like well okay but those are five fireball is properly priced you should do six damage so forth well in that case I want a paragraph should do 15 damage not 10 give me back my spiral raft so that basically the idea of this in balance right even if you look at simple coefficients you can see that there are some decision which are you can debate the quote of course we don't have all the other Blizzard have and they prolly I just based on statistical analysis but deep down to mechanics is something where there is some sort of this mismatch in complexity that is the basic core idea of finding undervalued card okay so how do it for how do we scale that to hundreds of cards more precisely were able to do 130 cards because modeling each attribute is a little bit complicated so you have to do you have to post text it turned out that the card is really like a bunch of deck that you have to process and say all the thought should be on so forth so we did a hammer and sorry for this talk how we do that while we model the card as we did before then we use those card and reverse the coefficient of each aah and so forth using linear algebra don't worry it's not as bad as it sounds and then use those rivers coefficient to compute what we call the real value of the car and then the last step is the easiest type where you say well who's my real value here's my face value you subtract one to the other and if it's negative well you find another value court that as simple as this well easier said than done but not that bad so let me show you on a very simple example 5 cards how it looked like and then when we know that I will show you the real results so let's take three cards which has charged charges basically you put a card and can attack as soon as it is coming to play so we have four we have the car on the work the rocketeers and the argent commander and we're going to show two more card which is which have given shield and the reason why is the argent commander is the middle is because it has both a tribute at one of the idea of having linear algebra is you can commute coefficient so as I said this is the same price so with 5k we can make it work and that's also why we can compare card is because this is very complicated into your living so we do as we did before we put them into an equation to our Cochran have four attached three health plus C which is a charge coefficient plus I which is interesting value of the cord and we do that for the five cards trust me it's correct then we're going to revert the attribute coefficient to do that we put them into a matrix which is basically a table and we put them like this we say well performing i get for attack three health one charge 0 division shield and one intrinsic value let the first chord then I do the same thing for the rocket here same thing for sale junk square and here you can see it has deep in shit and charge so you have one and one and then you add the two other called which has given shield the top point was something else Third one is Arjun square and you can see so basically of your five thing then you have a one line of pattern which is the least square and boom you get coefficient and the coefficient r 1 for a jack za minus one for health 24 charge 14 devonshire interesa can do that make any sense you can't have this country ham yes you're right it is because we only have five cards five guys do not give you a good coefficient because there is too much instability you need way more but it's just 56 and also bear with us so an example so now how do you find a real price well now we're going to be back to kindergarten where you learn how to edit shit add stuff so you know you have for a plus 2 h plus C plus D plus I so basically what you do is you say well it's four times one plus two x minus one plus one plus one and the price is six so the real value according to our coefficient is six we're also called is fair right there is nothing difference between the face value and the real value so you like math not interesting ok let's try again with one of the most undervalued card in the game the Argent's quite a lot of people said the form it is undervalued let me let's try again right so it's one I wanted to add one house 110 plus the windshield plus the value of the car so it's 1 times 1 plus 1 times minus one plus one plus one well no it's to wait to know the cards one right and yeah you're right that's why it's an undervalued card it actually should cost twice so even with our bogus coefficient you can always see that this guy is clearly undervalued that's basically the idea we have this is how it works so I post that I did pass out online and we got a lot of good feedback about it a lot of people from ready 12 good comments Thanks to everyone who pointed out the most important one we got was where all do you should take into account dependency and it's actually true that thanks to Nia who pointed out that charge would be basically a factor of the attack because you attack for the amount of the attack so we now in the real model use at that time charge same thing for Winfred winfrey now we model it by taking into account the attack of the card the one more we have a lot of debate question is about giving shape we don't know what given shield should be it is just even shield as a coefficient is it related to health related to attack it's really if you are ready let me know Sociedad so that's a comment from a some of the blood which actually wrote me a long process a well no actually called have a budget and the budget is twat two times the mana plus one I have no idea how we come up with the idea is absolutely reasonable and when you do it the coefficient looks way better it is true I just don't know how this guy get it but thanks so after writing code and debugging and debugging and you begin you have something you run it and voila you get your coefficient so this is our the coefficient we got for 133 card you can see that the most valued coefficient is I'm sorry very much to mention because we use a budget idea that I've been proposed now to coefficient points is roughly one minor point so basically destroying a minyan cost you 25 minute to actual card a board damage caused to you about 1.5 damage a 1.5 manner four-point drawing cost cost to a single croscill you roughly 1.5 manner the windshield is pretty expensive it costs you almost 19 a point and so forth we also have negative coefficient which is basically decrease the price of the card as you expect having open during card is the highest one followed by this cutting cards doom card i'm looking to you here and then we have overload which is a shaman mechanism which you pay another price right so all of this seems perfectly fine and we were really happy and we had this guy which is about damage so we did something we thought was very clever which was like let's model single target and multiple target coefficient as different that is a stupid idea i'm going to show you why in a few side but keep in mind that we try more is it in a suicide so one way to visualize what it look like as a result is you have you can put on the graph whereas if x axis is how much reserve assign as a quite as a face value and the y-axis how much II algorithm deliver cards is worse so it gives you on the Left triangle the undervalued cards are in green and the overpriced card on the bottom right corner triangle of course because we arbitrarily fourth card to be easier on the value / value you not that interested in to the one which are close to the line the middle which is that fair price what's interesting is the people who are out clear outlier and there is quite a few the reason why we have a lot of low value colleges because when we model cards alki wish have that shared share the ability are mainly lower value it's not because the algorithm favor one of the other just because when we did model and you can sit on the side most of them are on the lower on the left side of the graph for higher card they usually have special ability which are not captured by this modem which you another one for the special ability just after that so no more blah blah what is the result well are the most of a pride one of the most undervalued card is on fire would you believe it actually should be at least one mana light of Justice is also on the value this one actually to do a lot of discussion but then people pointed out that they dipped it into the arena is DV four attacks for one mile which is somewhat of a kid if you think about it not surprisingly mortal coil porshi ultimate perfectly and arjun square yuffie mmm I see and there is also explosive trap somehow it's actually give you something which seems reasonable to most people the one which is a little bit desire sacrificial it's probably a bug in the code so and you noticed we also have high value cards so one which probably is the mass of a powerful is this fire elemental which would the algorithm believe it's probably seven mag not sex something which also has been mentioned before by people just by looking at the car so somehow is the algorithm give you reasonable video so we believe we are on the right track if you want to look at a full detail or the coefficient or the car drank there on my website you can just go there and we keep updating it as we updated model and if you have idea on how to make it a much better either we said let us know so how do you take it to the next level so far we want to use a car the question is how do you make it better well it's really difficult at least without extra data and this extra data is how people play it again most of you autocar depend on the state of the game and we don't have insight about it unless you have a lot and the doctor and a lot of replays of course Hudson being very very new we don't have that much replay and sadly not a built-in feature so for game for us we get our hand on a hundred game which have been played with in my engine we'd like to thank you or anonymous friend for that thank you very much and it's not a long-term solution and we really hope that wizard will give us the ability to see we play and all of us to do our own analysis I do not believe it to flow into game I know it's integer services that they don't want to do too much data mining oil but having people to look at samesies no I mean it's a game is perfectly balanced there is no reason hila missing so with this data you can use interesting stuff the first one is you can actually price card which have unique effect let's start with a very simple example to get sorted at Wired Drake so the Triad Drake is a card which is a 4144 manner and have a special effect that when it come into play it's a battle cry it will get gain one half one additional health for each card you have in your hand so obviously the value of the cloud depend on how many card you have when you played it so you can build a model where you say well if I have one cry my hand then it has one extra health it's yeah and then it's one the real value 81.3 manner if I have to it's 1.99 for up to nine you have a matter of ten card so browser twilight drake the maximum is nine or it's 5.9 so question is now have this table you need to use a replay data to be able to know well how people play it right are they mainly playing it with eight cars in the hand for card to card so you do it you Josie sing and this thing is it yours is this exact graph and what you see is the following in the red on the left side you see when people play it with less than up to four card and the card become undervalue basically if you play with folk are you get three mana value of your card you play it with 55 @ n you have a 3.6 value and with six you have a full point to value so this is the first one where basically the price of the Cottagers right if you play it with seven or eight and you get a lot of value of your car the average real value of the card is if you take the average 3.7 which is right next to what is the predicted face value so based on that we do assume that the twilight price is fair it basically exactly what it is it's also interesting to show that looking at this we get to some conclusion and Blizzard so we think we have something which is very similar to what they have except they have way better data and better inside last week another which is one of my favorite column which is Van Cleef so what ventev do is for hack it would gain two to four each time you play a card before it during the game so all you have to do is again look at the replay and look at how many card web play during the turn before it to get its value and for reasonable number of card play before the game I know you can go way the road Abbott for the reasonable number if you have a 22 which 1.09 so one mana if you play just like this you add a second card you add three mana which is roughly fair 66 you become to get a lot of value out of it and when you play five or six car then the value of emphasis is just outrageous if you brought it very very different product as you can see Van Cleef is most of the time undervalue it is even if even if it's of 66 which is two card before it that's all three credit for it now to copy for it then you already get like a five mana worst of your card and 44 card before you get a seven hour worth of card and so forth so CL 0 average is 8.1 so the average value of n clip today is 8.1 better or data so i do claims a damn cliff is under value and i believe the right value is between five and seven months i know it would make Van Cleef harder to play that's what I say we should not be eight shall not be nine but tree in my opinion is way too low it is not according to this directors of making sense most effective actually play on the ladder are actually six or eight there are people pay it for four priests but otherwise they will do give you a four or six six or eight Vantiv which are way too powerful for the price so this is probably one of the car which is the most undervalued all right last one femjoy we go about how you deal with AOE so car which have a RL effect and so frame tracking one of the simplest one what it actually do is do for damage every minion of your open on the board well so easy right all you have to do is take heart how many minion you have on the board on your opponent's side and then multiplied by the number of damage and voila right so just did that and I look at these numbers and like whoops there is something completely wrong here right i mean i show it to seminary like well inertia of two million your car is already were searching point of mana all right well model is going wrong somewhere don't make any sense you can have a 15-minute worth of card so what's wrong it turns out is because we use a board damaged remember i told you we try to be clever and separated single targets with versus multiple target turns out it's already factored in the car and this is how what's happened when you try to be too clever like okay let's just bring it that's right again and go back to single target way better no now it makes more sense that's how we learned that you should not choose multi-target versus single target you should use only one coefficient which is bar which is doubt damage not to and it's actually makes sense now that I become a good deal when you have three million of the board and not otherwise same thing the graph looks perfectly fair you can see visually sometimes don't evaluate sometime it over value most of the time is between the two so the card is perfectly balanced and lesson on here is don't try to be too smart do not spit single invincible target that was one of the restaurant we also like this idea because it's actually looking at those card Harper's validate that what we do make sense and everything is consistent and when there is something strange we see it and we are able to adjust the mother are holding in it so let's switch gear a little bit we're going to tell you about how you can predict your pennant deck and I'm going to let you send tell you a little bit about that so I lo everybody my name is Celine and i'm going to show you are in Game two so the tool is a web application written in Python it runs on a small web server called flask so you can display the webpage just text to your game as you can see on the left side of the screen or you can also use any devices with web browser such as the tablet so these tools this tool implements all the algorithm described in this talk so you can benefit from them easily so the main screen in our tool is a real-time dashboard so you can use it to track get metrics played cards and a predicted cards for your opponent during a game so the first box on top displays other game metrics there are three matrix so the mullah advantage so it's the difference between average mana you spend an homage man i opponent span by green cards the draw advantage is the difference between how many cards you to and how many kelsey open andrew and the other advantage so it's the difference between how many cards you have in hand and our mini cards your opponent avenel so this matrix appears in green if you have the advantage and in orange if the advantage is for your opponent so we in our study we found that those metrics almost pay out the most predictive of the game outcome so we won't go into detail today due to lack of time but we will do a blog post later about it below the matrix you can see your deck so you can see how many card of each type you have in your deck in the chi column sochi for total which one of them are currently on the board in green in the pic alone p for played and how many are dead in red in the decorum Saudi Ford it so blue your leg there is a salt box that shows what cards your opponent play every time your opponent plays a card it will appear in this box same with a total card in the chicken plate card in the pre column and debt card in the key column and so the last but not least the final box which show you a prediction of which card your opponent is going to play based on the previous card I played so how did we manage to get the game data so we could use a packet sniffing to get the game data it gives you the best data it's a violation of these arts terms of service so we did not use it we could use OCR for tickle a character recognition so it gives you good data but it costs a lot of CPU and snot reliable so we willed it up so we ended up using the debug log so you can start your game in debug mode using a small config file it's a simple method to get austin data but it has some limitations like there's only game data you can't see the opener name player ranks or which car detect which card and there are so no info buttocks so you would have been great if these are provided lock system as good as the one in the world of warcraft so now you will see our tool in action in a short video so the tool is on the left side of the game something against le and so I choose my car and then you will see that he'll start with an extra card in his hand because he has to draw an an advantage now I'm kicking up a cloud so we have the same number of cards as you can see in the dashboard there's no more advantage for you so now I'm playing our John Squire so we can see the card will appear in green in my deck and I spent one mana points so the advantage the man advantages for me so now as the game evolved the dodgeballs reflect those changes and as soon as it plays Okada prediction appear at the bottom you can collapse your deck to get more room for your parent info and now you're going to play a visa right and let's get a closer look so every side was in the prediction so yeah it's work it's working I'll at some point he tries to kill me with Leroy and good for me I have a knife juggler it saved me so I hope you liked it so in addition to the real-time dashboard you can also see the current jemi story in the turn screen so it allows you to see what happened turn by turn during the game and learn from your mistakes so our tool will be available next week on get him so we can t need help with to improve deck import using OCR because we can she use a text file so you also want to display the game history and do the my quest and windows packaging and improve car modeling so if you want more info don't hesitate to talk to a staff for the presentation thanks back to me all right before you get all your hopes too high and tell you about how the black magic is done just a word of disclaimer because max tomorrow which is the extension has just been released as the midnight quickly shifting so the prediction are not like Troy as I said we don't have access to love games we texted a why first build a model so expect the tool to not perform very well for the next few weeks that being said it wouldn't catch up as soon as the number of carbon village and stabilized so probably next season which is August and overcast I guess too how's that work we're also it's very simple we model called affinity which is which cosplay which each other then we have an evaluation function which will return what are the most likely affinity to be played based on previous heart played by the opponent and then we have a tool the tool goes to a bunch of a place and then learn from those we play hard affinity and what are the metrics and then as an insured you we have this tool in game which basically as the air goes I'm here's the car which I've been played please return me what was the most likely hard to be up here that's basically way to look like we're going to see each step at a time and that would be the last part of the talk so Carl affinity as I said horse won't have about 500 cards so if were to look at all the card combination it will be almost impossible when you like 430 cards in the deck we have a closer and impossible number of combinations what we really do is we expose the fact that in practice cards really work well together and some car do not work well together like if you play dude and the combo is savage work plus force of nature so if you have one expecting you have the other on the other end you do not have forced of nature and I don't know amarok doesn't make any sense oh this is not an affinity that you need to model so we model affinity like this how we do that well we use the simplest thing you can see of which is called end round here is one of the simplest version which is called by graham which is modeling pairwise of cards so what we look at is we look into replay as a sequence of car which has been played by your opponent we got left of the turn and we say well the armors miss has been played and then the guy plays the taskmaster so that's one big round and we would cause the affinity between the two we say well if you place the armors miss and you're likely to play the taskmaster and then we look at the second part of the stream which is well the taskmaster is followed by the equality of pain so we recalled also there is an affinity between those two cards so I've been said we know that the call at Joe at random right when you get one color teach and it's at random so to model that and I come for that we lack the assumption of order and we use what we call unordered Engram and here another big one where we say well like takes every pair wise if you play sometime during the game Armas missed then later on you'll likely to play taskmaster if you played GI quality of pain and you're a wire yeah new coding you are likely to play armorsmith and so we keep those we also tried a tree Graham which is triple of cord and so forth turns out that the best model is released constraint one which is big round so how do we evaluate Carl affinity well very simple again as the open played let's say deadly poison the end autoship which are two cards so then from there we say well was the affinity of those card well for deadly poison we know that kind of night has been since 500 time and then blade furry has been c 250 times so we will look at those and for ship we know that battery have been seen 400 time and if you play ship we also saw the armani Berserker form the time so we combine them and again very simple the simple strategy which is with just some and we say how many time she'll scallop here you get the ranking and the ranking is BlackBerry's on top because it's 250 plus 400 followed by the fan of knife 500 and then you put the color of wherever you want and you say well this is my separation that make it because I only want to so I discuss your money that's how it works it has it seems extremely simple turns out if you do something more complicated it won't work we try to try more things actually this one works really well so how did we did we took five hundred fifty thousand replays and we did one model / class because each class has some unique code and we did not want to have crossed trim and we run the good well first to rise good but let me run the code and we learn to sing and then we ran and this but actually the algorithm run basically the 550,000 replace in less than three minutes it's not as much work and then victory I will actually struck out how good the thing was by turn 3 the highest prediction have a ninety-seven percent chance to be played which means that out of a hundred game the first prediction that the algorithm return I turned three will be played some time in the future we don't know if it's the next hole of the Kaaba to actually tell you yes this car will be playing if you want to look a little bit deeper this is the turf of prediction the average prediction of the algorithm for 10 predictions turn-by-turn you can see it actually rise because you get more and more information as stone placed more cause the open play the more we can look at affinity so the za accuracy increase and then it starts to decrease after to an 8 because there is SMS causing the death of the open until you have less ms chance to be right right i mean to the balance is somewhat between time for 24 and time turns eight if you look at the ranking function the ranking function do work to green you represent our best prediction the orange one represent our lowest prediction which is number 10 which choose to get at em and you can clear this is that the best one is actually extremely good up in the high 90s starting country whereas the lowest one is barely above 20 and they are converging because the algorithm make me less and less mistakes but there is also less and less room for errors as turn games price so there was a lossy we wanted to tell you guys and hindsight we should have to cook two hours and not 45 minutes we all know where we're going when we apply photo so we wanted to tell you about predicting the game outcome again we do a blog post we also are looking into optimizing that 4-3 boot because we know that man advantage is the key factor to win and also by popular request we got requests for looking at hero power comparison and also comparing a virus type deck of time likewise ooh is winning versus control how its work what is the parameters and kind of stuff so first thing we are looking forward to do if you have ideas of steam we would like us to do or I share the other thing we should do together please the ducks will love to do it will give would like to finish by giving a you shoot out to lot of people who give us feedback thanks a lot we do we reddit comments we do read it off comment that people post to us it's really important it's helpers to get better constructive con chris well that Vince had a big thank you to people in particular we like to thank Neil and Zack which meant a lot of time helping us prepare and also give us insight food feedback and as we said our anonymous friend who give us a replay you
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