In my case, this depth takes too long to explore, I adjust the depth of expectimax search according to the number of free tiles left:. The scores of the boards are computed with the weighted sum of the square of the number of free tiles and the dot product of the 2D grid with this:. I think I found an algorithm which works quite well, as I often reach scores over , my personal best being around My solution does not aim at keeping biggest numbers in a corner, but to keep it in the top row.
There is already an AI implementation for this game here. The algorithm is iterative deepening depth first alpha-beta search. The evaluation function tries to keep the rows and columns monotonic either all decreasing or increasing while minimizing the number of tiles on the grid.
There is also a discussion on Hacker News about this algorithm that you may find useful. More spaces makes the state more flexible, we multiply by which is the median since a grid filled with faces is an optimal impossible state.
Here we evaluate faces that have the possibility to getting to merge, by evaluating them backwardly, tile 2 become of value , while tile is evaluated 2. This is a simplified check of the possibility of having merges within that state, without making a look-ahead. This is not a direct answer to OP's question, this is more of the stuffs experiments I tried so far to solve the same problem and obtained some results and have some observations that I want to share, I am curious if we can have some further insights from this.
I just tried my minimax implementation with alpha-beta pruning with search-tree depth cutoff at 3 and 5. I applied convex combination tried different heuristic weights of couple of heuristic evaluation functions, mainly from intuition and from the ones discussed above:. In my case, the computer player is completely random, but still i assumed adversarial settings and implemented the AI player agent as the max player. If I assign too much weights to the first heuristic function or the second heuristic function, both the cases the scores the AI player gets are low.
I played with many possible weight assignments to the heuristic functions and take a convex combination, but very rarely the AI player is able to score Most of the times it either stops at or I also tried the corner heuristic, but for some reason it makes the results worse, any intuition why? Also, I tried to increase the search depth cut-off from 3 to 5 I can't increase it more since searching that space exceeds allowed time even with pruning and added one more heuristic that looks at the values of adjacent tiles and gives more points if they are merge-able, but still I am not able to get I think it will be better to use Expectimax instead of minimax, but still I want to solve this problem with minimax only and obtain high scores such as or I am not sure whether I am missing anything.
Below animation shows the last few steps of the game played by the AI agent with the computer player:. Any insights will be really very helpful, thanks in advance. The following animation shows the last few steps of the game played where the AI player agent could get scores, this time adding the absolute value heuristic too:.
The following figures show the game tree explored by the player AI agent assuming the computer as adversary for just a single step:. And that the new tile is not random, but always the first available one from the top left. This variant is also known as Det I used an exhaustive algorithm that favours empty tiles. It performs pretty quickly for depth , but on depth 5 it gets rather slow at a around 1 second per move. Below is the code implementing the solving algorithm.
The grid is represented as a length array of Integers. And scoring is done simply by counting the number of empty squares. I thinks it's quite successful for its simplicity. The result it reaches when starting with an empty grid and solving at depth 5 is:. This algorithm is not optimal for winning the game, but it is fairly optimal in terms of performance and amount of code needed:.
Many of the other answers use AI with computationally expensive searching of possible futures, heuristics, learning and the such. These are impressive and probably the correct way forward, but I wish to contribute another idea. Read the squares in the order shown above until the next squares value is greater than the current one. This presents the problem of trying to merge another tile of the same value into this square.
To resolve this problem, their are 2 ways to move that aren't left or worse up and examining both possibilities may immediately reveal more problems, this forms a list of dependancies, each problem requiring another problem to be solved first. I think I have this chain or in some cases tree of dependancies internally when deciding my next move, particularly when stuck.
The whole approach will likely be more complicated than this but not much more complicated. It could be this mechanical in feel lacking scores, weights, neurones and deep searches of possibilities. The tree of possibilities rairly even needs to be big enough to need any branching at all.
Learn more. What is the optimal algorithm for the game? Ask Question. Asked 6 years, 9 months ago. Active 1 year, 11 months ago. Viewed k times. My current algorithm: while! This might help! K Mar 12 '14 at It's a worst-case assumption, but might be useful. A fun distraction when you don't have time to aim for a high score: Try to get the lowest score possible.
In theory it's alternating 2s and 4s. Discussion on this question's legitimacy can be found on meta: meta. Active Oldest Votes. Performance The AI in its default configuration max search depth of 8 takes anywhere from 10ms to ms to execute a move, depending on the complexity of the board position.
Here's the screenshot of the best run: This game took moves over 96 minutes, or an average of 4. Implementation My approach encodes the entire board 16 entries as a single bit integer where tiles are the nybbles, i. Heuristics Several heuristics are used to direct the optimization algorithm towards favorable positions. David Greydanus 2, 1 1 gold badge 20 20 silver badges 40 40 bronze badges.
Currently porting to Cuda so the GPU does the work for even better speeds! Cool to watch, without the need to compile and everything In Firefox, performance is quite good Theoretical limit in a 4x4 grid actually IS not However that requires getting a 4 in the right moment i. Smoothness The above heuristic alone tends to create structures in which adjacent tiles are decreasing in value, but of course in order to merge, adjacent tiles need to be the same value.
Free Tiles And finally, there is a penalty for having too few free tiles, since options can quickly run out when the game board gets too cramped. Edit: Here's a demonstration of the power of this approach. You can treat the computer placing the '2' and '4' tiles as the 'opponent'. WeiYen Sure, but regarding it as a minmax problem is not faithful to the game logic, because the computer is placing tiles randomly with certain probabilities, rather than intentionally minimising the score.
Even though the AI is randomly placing the tiles, the goal is not to lose. Getting unlucky is the same thing as the opponent choosing the worst move for you. The "min" part means that you try to play conservatively so that there are no awful moves that you could get unlucky.
I had an idea to create a fork of , where the computer instead of placing the 2s and 4s randomly uses your AI to determine where to put the values. The result: sheer impossibleness. Can be tried out here: sztupy. SztupY Wow, this is evil.
Reminds me of qntm. AI Algorithm I found a simple yet surprisingly good playing algorithm: To determine the next move for a given board, the AI plays the game in memory using random moves until the game is over. See it in action The best achieved score is shown here: An interesting fact about this algorithm is that while the random-play games are unsurprisingly quite bad, choosing the best or least bad move leads to very good game play: A typical AI game can reach points and last moves, yet the in-memory random play games from any given position yield an average of additional points in about 40 extra moves before dying.
Improvements After implementing this algorithm I tried many improvements including using the min or max scores, or a combination of min,max,and avg. Ronenz Ronenz 1, 2 2 gold badges 15 15 silver badges 7 7 bronze badges. As an AI student I found this really interesting. Will take a better look at this in the free time.
This is amazing! I just spent hours optimizing weights for a good heuristic function for expectimax and I implement this in 3 minutes and this completely smashes it. Nice use of Monte Carlo simulation. Watching this playing is calling for an enlightenment. This blows all heuristics and yet it works. By far, the most interesting solution here. This is your objective: This is the model I chose by default. Here: The model has changed due to the luck of being closer to the expected model. So it will press right, then right again, then right or top depending on where the 4 has created then will proceed to complete the chain until it gets: So now the model and chain are back to: 64 4 8 16 32 X X x x x x x x Second pointer, it has had bad luck and its main spot has been taken.
It is likely that it will fail, but it can still achieve it: Here the model and chain is: O O O O 8 16 32 64 4 x x x When it manages to reach the it gains a whole row is gained again: O x x x x x x x x x x. Daren Daren 3, 3 3 gold badges 18 18 silver badges 33 33 bronze badges. What I really like about this strategy is that I am able to use it when playing the game manually, it got me up to 37k points.
I copy here the content of a post on my blog The solution I propose is very simple and easy to implement. Algorithm Heuristic scoring algorithm The assumption on which my algorithm is based is rather simple: if you want to achieve higher score, the board must be kept as tidy as possible.
Nicola Pezzotti Nicola Pezzotti 2, 12 12 silver badges 25 25 bronze badges. K Apr 8 '14 at Are you sure the instructions provided in the github page apply to your project? I want to give it a try but those seem to be the instructions for the original playable game and not the AI autorun. Could you update those? Pretty impressive result. He was 69th in the OWGR, up an amazing spots across the calendar year. He had made 2 appearances at TPC Summerlin with a best finish of 7th.
Kevin was ranked 40th when winning this 12 months ago. You have to say that Harris English has been magnificent since the Covid resumption. When starting last season he ranked close to th in the OWGR, but a run that included 3 top-6 finishes prior to Christmas undoubtedly boosted his ability to play a schedule he could choose in , and boy has he delivered. Last time out, 4th at the U. But a 67 in Round 2 was the tied-3rd best round of the day and an eventual 37th place finish puts him a great space for this week in Las Vegas.
Scottie has always been a talented individual and his development has often seen strong results on the West coast. Wins came in Illinois and Ohio, again showing a liking for Bentgrass putting surfaces, with tops also arriving in Texas, Kansas, Idaho and Indiana. Only deposits made using Cards or Apple Pay will qualify for this promotion. One player who has really impressed me of late is Sebastian Munoz.
He came alive in the FedEx Cup Playoffs and was mixing it with the very best in the world. The 27 year-old Colombian is undoubtedly playing the best golf of his career and that continued at the U. He was still in the mix on Sunday, eventually finishing a respectable 23rd. A winner of his home Colombian Open way back in , 2nd and 3rd at the Mexico Championship shows a liking for altitude golf, as does 6th at the Utah Championship.
We also saw Munoz finish 3rd at the Greenbrier Classic and 7th last year at the same tournament on the PGA Tour, which again is played in thin air at altitude, on Bentgrass greens. He also finished 11th at the Barracuda Championship and 21st at the The American Express, both played in the desert and now ranked 76th in the OWGR, Sebastian is undoubtedly a grade above where he was then.
Open, which was his best ever Major finish. Shriners Hospitals Open Tips Follow us on twitter Bamfordgolf. Join over 5, punters on our facebook group. Watch our latest tips videos on YouTube. Apple Podcasts Podbean Spotify Audioboom. CC of Jackson: yards from the tee: 29 yards wide; ; ; ; Winged Foot: yards wide. Silverado: yards from the tee: 27 yards wide; ; ; ; East Lake: yards from the tee: 28 yards wide; ; ; ; Olympia Fields: yards from the tee: 28 yards wide; ; ; ; TPC Boston: yards from the tee: 37 yards wide; ; ; ; Sedgefield: yards from tee: 29 yards wide; ; ; TPC Harding Park: yards from the tee: 29 yards wide; ; ; TPC Southwind: yards from the tee: 29 yards wide; ; ; ; TPC Twin Cities: yards from the tee: 38 yards wide; ; ; ; Muirfield Village: yards from the tee: 34 yards wide; ; ; ; Poston; 25 Collin Morikawa.
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This is a server-side plugin, that, once installed, will let you use these commands:. This nasty little plugin is ironically named CheatBlocker. Remember, do not install this on your server, it will make you vulnerable. They are active in most countries around the world, most notably in the United States. This software is only for use on a personal basis. How to use:. If the owner will not install it, try Remote Bukkit. Yes, if the plugin is installed on a server you can still play on it regularly, with access to these commands.
But, only that server will give you the ability to use these hidden commands, and not every server. This is only for Minecraft PC, specifically for craftbukkit servers. You seem to be trying it with a PocketMine server here. All you need is craftbukkit to get started, and maybe the Essentials plugin bundle and some other common plugins. The only way to run a minecraft server for free is to host it from your own computer. All you need to get started is the free craftbukkit server platform.
The plugins folder is in the root directory of Bukkit, which is the most popular server type and the folder should be in the same directory as craftbukkit. This is Workingor not pls comment my computer is windows xp im sad all Force OP is not working it want frame work and this is no virus???
Bored i wish it worked too my computer okay bye bye Thanks. This does not work. If you have a hacked client, it will destroy it. Open up the folder until you get to the cheatblocker folder. Open it, and you will see: Anti-jump Anti-kill aura you name it. And the worst of all, is the KillNodus java jar. Do not download it and install it into your server or not your server. Thus, it does work… as a force op, not a cheat blocker.
The anti-hack stuff is fake — do you think I could fit all that code in such a small. It is a server-side plugin. What happens is you get banned when you are caught hacking. Also, you can download Nodus 1. Which it has to be because how else could it make you able to force op yourself? How does it target minecraft? Also, my first statement saying you were correct about KillNodus was fake, Was actually incorrect. Why were you so specific about the jar name?
Yes, obviously I am disguising the. And you never run it after downloading, so it is safe, like I said. Nodus is the best-known hacked client, by far. Only the server owner even needs to download it, unless you are giving it to him. Yes, the. Um, No offence but no one is going to fall for this.
No owner is gonna take a plugin for a starter and use it. It would be shady as hell. This is useless. If they download it from here, and install it on their server, then you can. I offer this plugin, and many more can be found at BukkitDev.
This is actually helping me… Im on my bukkit server and cant op myself , not even with ops. Just a quick tip: if you start craftbukkit. Hmm… the only way I know of is trying to exploit Remote Bukkit with the default username and password.
Unfortunately, dev. Let me know if you get anything useful from decompiling. Save my name, email, and website in this browser for the next time I comment. How to use: Download the file. Wait for a server restart. Connect to the server to execute the above commands.
Topics exploit hack minecraft. About the author. Timtech The site admin :. More Posts Timtech July 18, PM. Timtech March 17, AM. Assassinn1 April 10, AM. Silawut September 16, PM. Timtech October 5, PM. N00b September 27, AM. Unknown 18 March at Unknown 21 December at Unknown 16 August at Newer Post Older Post Home. Subscribe to: Post Comments Atom. Popular Posts. Tekkit Client V0. Hello guys. This client requires an increased amount of Avolition.
If you are having problems. There is a chance its updated. Coded by Scetch. All credits go to him! Video of the tool Nodus Freecam Dupe Working on bukkit v3. Well, Me and my friend found out a way to dupe on craftbukkit Since it has been patched in the recent snapshot of bukkit or Crystal Demo [Client] [tekkit][3.
All Features Kill Aura - Attacks anything within reach distance. Fly - Fly around. NoFall - No Fall Damage.