Since you do not know the total size of the undrawn stack (we are talking about cards after all) your method does not help you any more than mine. Could be that I am missing your point. Hidden achievement?
If it is indeed a tetris-style "grab bag" algorithm, such that every X cards there must be X/3 white, X/3 red, and X/3 blue, then if you were keeping track and you hadn't seen any white cards in nearly 2*X turns you'd be quite certain that a white was coming soon.
If X is the size of the undrawn stack and red, blue and white cards make up equal parts then the most non-white cards you could draw in a row would be 4X/3 (all red/blue of one stack and then all red/blue of the next stack).
Game Impressions Having never heard of this dev before, this app seemingly came out of nowhere to me. Picked it up after work today and haven't been able to put it down since. I think it deserves the 5 stars, I can see myself playing this for a quite a long time. Also, as stats student (albeit a beginning one) all this math talk is pretty interesting. What you guys are talking about reminds me of the old online casinos with roulette games where some statistician figured out the randomizing algorithm and was able to game the system. The whole grab bag thing seems similar.
I find that if you play to a corner until you hit a 384 and then start moving around to fit you can get a score like this
Let's do this! Well aren't you coming in at a crucial point in time. Going back on my own word from a few hours ago, I think with the combined brainpower in this thread, we can divine the higher secrets of Threes (i. e. the card drawing algorithm). What we need is data and then have a collective look at it. In order to not flood this thread I offer my PM box for gathering this data and present it in one post when I gathered a good chunk. In order to be efficient, we need a unified format for sequences of card draws. I will first give an example and then outline the details of the format I propose. Example Game start. Board looks like this: 1 3 _ _ 2 2 _ 1 _ 3 _ 3 2 _ 1 _ I note the cards on the field. (1,3,2,2,1,3,3,2,1) Now I slide up and a 3 appears in the lower right corner. Board situation: 3 3 _ 1 _ 2 _ 3 2 3 1 _ _ _ _ 3 And I add a 3 to the sequence: (1,3,2,2,1,3,3,2,1),3 Next, I slide to the left to combine both 3s in the upper left corner into a 6. A 1 slides in on the 2nd row from the top. The board is now: 6 _ 1 _ 2 _ 3 1 2 3 1 _ _ _ 3 _ Now I note two things in the sequence. First, that my new high card is 6 and then the drawn card. (1,3,2,2,1,3,3,2,1),3,h:6,1 I will now end this short example because it already contains everything necessary. Now on the the formal definition. Format • The sequence of drawn cards shall be noted as comma (,) separated values with special notation for initial cards on the board and new high cards. • The initial cards on the board shall be enclosed in round braces (). Their order is not important. • New high cards shall be noted as they are created and before the newly drawn card. They shall be noted with a h: before the face value of the new high card. • No line breaks are necessary in this notation. • No coloring or other formatting is required. • All sequences shall be sent via PM to me. Once I have enough sequences I will format them with a quick Python script and post them in this thread for all to look at and analyze. By just writing the above example, I can attest to this recording being quite disruptive to the flow of the game and tiresome. I would therefore advise anybody interested to limit yourself to one game. I trust in the crowd to deliver volume and not ambitious individuals who exert themselves to the point of no longer enjoying the game anymore. Oh and the longer the game, the better the data Let's do this!
I don't know if there is a "deck". Rather, it might be random, but with certain limits coded in. For example, can you have 5 more reds than blues (or vice versa)? I'm not sure I've seen an imbalance of 5; I've definitely seen 4 many times.
I'm keeping away from reading too much of this post because, surly reading tips, maths, randomness luck, ect ect takes away the fun of trying to get high scores! What's the point in reading how to do it if it diminishes your sense of achievement? My scores are poor at the mo but at least I'm trying to work the game out for myself
Good luck math guys! Also, could you try and figure out the algorithm of where a certain card will appear? Like sometimes there is only one place, but if there are two, three, or four it would be nice to know which one. Also, most randomizing algorithms I have used myself are based on the device time and a pseudo randomizing algorithm. There is no such thing as a really random number in computers, but you knew that.
That's pretty well understood. New cards will only slide into rows or columns where cards were moved. If there is more than one possibility, it will pick at random (I think). Actually, with appropriate hardware, there can be true quantum-effect randomness in computers.
Wow, I didn't know that. Still, it's impossible for Threes! to do that unless it's connected to the internet right (which it can't depend on)? IPhones don't have all that built in. Also, if you don't have enough data, say something and I will try to help. (I don't have regular access to my iPhone)
Yes, as far as I know iOS devices do not have dedicated hardware for providing true randomness. But as technology progresses, this will change. Remember: a lot of cryptographic systems depend on randomness. As of right now, I have recorded one of my games just to test run my script but so far no PMs have reached me. If you want to contribute don't wait for an invitation ;-). There is no such thing as "too much data" when it comes to computer-powered data-crunching. Also, as this might incentivize participation: I will of course list all contributors in the post with sample sequences. Your efforts will not go unnoticed!
I do think the random element adds something to the game... But man just got 4 reds in a row right as i was closing in on a 768 . After a long round going out like that is not fun
I just sent kamikaze my first Threes! data set. Along the way I achieved the interesting position I attached below. I'm sharing just because I thought it was neat. This was after a stretch of 3 1s, followed by 4 2s (including the one coming up next). I was able to match all the showing 1s and 2s but never combined the 384 and 192. (I swiped left, btw.) One thing that I thought I noticed before that seems to be confirmed by this playthrough is that white cards are limited to a maximum of three (of course!) steps below the highest showing card. For instance, you won't get a 48 until you've made a 384 (48-96-192-384). This also means you'll never get anything but a 3 from a white card until you reach 48. Another note; this process is long, but this was my highest scoring game by a few hundred points. Stopping after every move forced the pace down and probably helped me think things through a bit more than I already normally do.
Similar thing happened to me, although I was trying to make a 192, and I had a 384 already. Thought it was my best game up till that point, I seemed to be in control, but no #
And it was well received, thank you! Interesting idea, we can look into other sequences to verify that later. I noticed that also. Forcefully slowing down gameplay increased my awareness for beneficial moves. One problem I'm beginning to suspect is the character limit of these posts (10,000). One sequence, due to all the coloring, is already 6,500 characters long...
Hey, I believe have found something. In one of my games I have only got a non 3 tile when all the places the white tile could have popped up beside were non 3. However when two of these happened in a row, I got a 3 the second time.
