11-25-2014, 01:35 AM
Quote:
Originally Posted by cloudpuff View Post
Gahhhhhh, I deleted it yesterday to make room for the Monument Valley update. Off to redload lol.
Today's update drastically reduces installed size: from 317MB to approx. 76MB. Finally able to keep it in my device!
12-21-2014, 01:09 AM
Bonus Card Distribution

It occurred to me that the new mechanism for displaying bonus cards (always showing three choices at the top) is likely to cause some highly counterintuitive behavior. For instance, suppose the high card on the board is 384. If the bonus card is chosen uniformly from [6, 12, 24, 48], then seeing [12, 24, 48] on the screen actually implies a GREATER than 1/3 probability of the bonus card being a 48! The logic is as follows, again assuming high card 384:

Bonus card 6 (25% of the time): screen must show [6, 12, 24]
Bonus card 12 (25%): screen shows [6, 12, 24] or [12, 24, 48] with equal probability
Bonus card 24 (25%): screen shows [6, 12, 24] or [12, 24, 48] with equal probability
Bonus card 48 (25%): screen must show [12, 24, 48].

So there are six possibilities:
25%: Bonus card 6, screen shows [6, 12, 24]
12.5%: Bonus card 12, screen shows [6, 12, 24]
12.5%: Bonus card 24, screen shows [6, 12, 24]
12.5%: Bonus card 12, screen shows [12, 24, 48]
12.5%, Bonus card 24, screen shows [12, 24, 48]
25%: Bonus card 48, screen shows [12, 24, 48]

So now let's say you're playing the game, and the screen shows [12, 24, 48]. By the above table, there is actually a 50% chance that the bonus card will be 48, a 25% chance that it will be a 24, and 25% that it will be a 12! Likewise, if the screen shows [6, 12, 24], there is a 50% chance the the bonus card will be a 6, and 25% each for 12 and 24.

Empirical data: I just played a game and got five bonus cards while the high card was 384. In 4 out of 5 cases, the bonus card was the extreme value. (e.g. [6, 12, 24] -> 6, [12, 24, 48] -> 48). If the probability were 1/3 of getting the extreme card, as you'd naively expect, then the chance of getting 4/5 is less than 5%. But if the probability of getting the extreme card is 50%, as calculated above, then the chance of getting 4/5 rises to 37.5%.

This gets even wonkier when the high card goes higher. Take the case of the high card being 768. Then the game first chooses the bonus card uniformly from [6, 12, 24, 48, 96]:

1/5: bonus card 6, screen must show [6, 12, 24]
1/5: bonus card 12, screen shows [6, 12, 24] or [12, 24, 48]
1/5: bonus card 24, screen shows [6, 12, 24], [12, 24, 48], or [24, 48, 96]
1/5: bonus card 48, screen shows [12, 24, 48] or [24, 48, 96]
1/5: bonus card 96, screen must show [24, 48, 96]

Let's assume that the cases split evenly; e.g. if the high card is 12, the screen shows [6, 12, 24] or [12, 24, 48] with equal probability. Then there are 9 distinct cases:

1/5: bonus card 6, screen shows [6, 12, 24]
1/10: bonus card 12, screen shows [6, 12, 24]
1/10: bonus card 12, screen shows [12, 24, 48]
1/15: bonus card 24, screen shows [6, 12, 24]
1/15: bonus card 24, screen shows [12, 24, 48]
1/15: bonus card 24, screen shows [24, 48, 96]
1/10: bonus card 48, screen shows [12, 24, 48]
1/10: bonus card 48, screen shows [24, 48, 96]
1/5: bonus card 96, screen shows [24, 48, 96]

In this case, the choices shown on the screen yield the following probabilities for each bonus card:

[6, 12, 24] -> 6 (54.5%) 12 (27.3%), 24 (18.2%)
[12, 24, 48] -> 12 (37.5%), 24 (25%), 48 (37.5%)
[24, 48, 96] -> 24 (18.2%), 48 (27.3%), 96 (54.5%)

Empirical data: out of 7 times in a recent game where I got [6, 12, 24] or [24, 48, 96] while the high card was 768, the actual bonus value was the extreme value (6 or 96) three times, or 42.8%. Too small a sample size to mean much, but I'll continue to gather data.

Another expected consequence is that the middle ranges will be shown somewhat less often than the extremes. For instance, with the high card 768, you can expect that the bonus range will be shown as [6, 12, 24] 36.6% of the time, [12, 24, 48] 26.7% of the time, and [24, 48, 96] 36.6% of the time.

It would be interesting to gather statistics over a number of games and see if these predictions bear out. From the statistics we can probably reverse-engineer the logic the game uses as far as choosing bonus values and ranges.

01-01-2015, 12:29 AM
Joined: Dec 2010
Location: Houston, TX
Posts: 9,328
Touch Arcade forums' Game of the Year 2014 Candidate


Threes! was successfully nominated for voting in the Touch Arcade forums' Game of the Year 2014 poll; voting will occur over the next 7 days (through January 7). Developers are asked not to vote for their own game or recruit votes outside of Touch Arcade.

http://forums.toucharcade.com/showthread.php?t=249263

Last edited by undeadcow; 01-01-2015 at 12:49 AM.
01-30-2015, 09:10 PM
AI update

An update on my AI:

I last posted several months ago about developing an AI for this game. Well, I went off and did it (back in February 2014), and it worked, and then I got sidetracked by 2048 (https://github.com/nneonneo/2048-ai) and the Threes AI fell by the wayside.

Well, recently I picked it up again. After updating my code to work with the new tile-spawning algorithm, I was quite pleased to see the AI frequently obtain the 6144 tile. I don't have stats on exactly how often that happens (yet...), but it seems to be at least half the games I play now.

I've also modified the AI so that it can play games on Android devices automatically via ADB (sorry, no iOS support, but it can still play semi-autonomously on iOS via screenshots). Here's the best run, 775,524 points:



(All of the best runs tend to have the high tile in the center by game end, because the AI usually panics once things get difficult. For 99% of the game the high tile stays in one of the corners).

You can find the code here on GitHub: https://github.com/nneonneo/threes-ai/

Last edited by nneonneo; 01-30-2015 at 09:13 PM.
04-07-2015, 11:33 PM
Twelve Lock

Does anyone have a strategy or gameplay video for getting twelvelock (ending the game with 8 12s on the board)?

I was recently able to do this with 6s and I am trying to figure out the best approach for 12s.

I have been starting by making a 48 (and putting it in top left corner) so that if a + card falls, I know it can only be a 6. However I'm starting to wonder if I would have better luck if I made 96 and setup the board to count the + being a 12 to end the game.

Can anyone who's done this share some insight?

I can frequently get 6/8 12s on the board and sometimes 7/12. I'm just not at all sure what the best arrangement should be prior to the last few moves (i.e. just needing 2 twelves in last column or row....or needing a 12 in two corners that don't share a row or column.
04-09-2015, 06:34 AM
I held out on this one too long! What a gem. I was over these types of games but decided to give it a whirl when I needed something different to try. Man am I happy I gave in & bought this. Very fun. The sounds & noises are hilarious & this is polished! So glad I didn't miss this but why did it take me so long? To me this is the standard for the others "like" it.
04-12-2015, 10:38 AM
Quote:
Originally Posted by nneonneo View Post
An update on my AI:

I last posted several months ago about developing an AI for this game. Well, I went off and did it (back in February 2014), and it worked, and then I got sidetracked by 2048 (https://github.com/nneonneo/2048-ai) and the Threes AI fell by the wayside.

Well, recently I picked it up again. After updating my code to work with the new tile-spawning algorithm, I was quite pleased to see the AI frequently obtain the 6144 tile. I don't have stats on exactly how often that happens (yet...), but it seems to be at least half the games I play now.

I've also modified the AI so that it can play games on Android devices automatically via ADB (sorry, no iOS support, but it can still play semi-autonomously on iOS via screenshots). Here's the best run, 775,524 points:



(All of the best runs tend to have the high tile in the center by game end, because the AI usually panics once things get difficult. For 99% of the game the high tile stays in one of the corners).

You can find the code here on GitHub: https://github.com/nneonneo/threes-ai/
Is there anyway we can get this to work with the Xbox One?