Thanks to you and all the others who took the time to record a game. Never mind the sequences not being perfect, they were good enough to deduce the important parts. Good work, team! First the non-spoiler reply to your first question regarding the game design. It is true that more white cards later in the game would be nice but remember that Threes! is all about how efficient you can use the board. If the game would dial the 1s and 2s back the difficulty curve would flatten. In the end, the tip remains: combine low numbers as quickly as possible to make space. Now to the spoilery answer Spoiler In one word: kinda. Once the high card is 48 the sequences on record show the appearance of bonus cards. But there is at most one non-3 white bonus card in a stack. So instead of 4:4:4 (blue, red, white) you sometimes have 4:4:5. This puts a slight dent in the overall frequency of 1s and 2s but in actuality, the difficulty decrease you are hoping for is negated by having to deal with the high-value draw cards. Edit: I have now also discovered the 768 card and joined the >20k club. Hello fellas!
So, what exactly have we learned here? When you play a game kamikaze, do you feel like you have an edge? Also, I wonder if we can figure out where exactly the new cards will appear. I know they only appear in a column/row that has moved, and on the opposite side of the move, but is there even more to it then that? Also, have we made any headway on when the higher cards appear, vs a 3 appearing?
Kamikaze28, Now that you have progressed beyond the 768 tile card, can you check if your proposed pattern is valid between the 768 and 1536 cards? I reached the 1536 tile card (see my previous post) without using any of the discussed strategies here (in large part because my game was too far into it already when this discussion came into light). I am particularly interested in the "high number" card that gets inserted once a while. Is this completely random? I was able to reach the 1536 tile card because there was a critical card of 24 given to me (perhaps randomly) that allowed me to combine with an existing 24 to get 48 and then 96, 192, 384, and 768 which I previously had assembled. If that 24 tile card had not appeared, it is likely that the game would have a very different outcome.
Okay, time to recap. Spoilers ahead! Spoiler If I were to record the dealt cards of the current stack I could anticipate certain situations more than someone who didn't know/understand the algorithm. But to be honest: the situation in which you can make a reliable prediction are pretty rare and the effort is not worth it - unless you train so hard that it happens unconsciously. y2kmp3 is on that case. The Card Draw Algorithm is not responsible for placing the cards, only to determine their color and value. Spoiler I would say that we have. CzechCongo first formulated the hypothesis that non-3 white cards are drawn once the highest card is 3 ranks above the drawn card value. So 6s only appear once the highest card is 48 (6->12->24->48), 12s only appear once the highest card is 96 (12->24->48->96) and so on. So far, the sequences support this hypothesis. Addendum: It is important to realize that while the pool of possible bonus cards only grows as the highest card increases in value, the pick from this pool is still random. So just because you have a 384 on the board does not mean that all of your non-3 white cards are 48, they can just as well be 6s, 12s or 24s. During my 768 game I also got a 96 from a draw after I created the 768 which would fit the pattern (96->192->384->768). So we actually learned a lot. And I think we are not done yet.
If you count cards as you play you can now determine the probability of the next card being white/red/blue. (Though we don't know when it chooses to insert the non-3 white cards, so the probability calc will be slightly off.) It's not a ton of fun to play like that though, but at least knowing how the algorithm works gives you a better "feel" for what might be coming next.
Ok, so then it is completely random as to whether a 24 vs a 6 appears (h:192, for example)? Is it possibly weighted? Some of the data sets indicated that the first non-3 card was the max at the time (highest/8). I hypothesized that the appearing card was weighted to help you in a tight spot, as y2kmp3 noted (he got a needed 24). However, only one of them can appear for a while, which fits your grab bag theory. I think that if what y2kmp3 said about the game being slanted against us in some choices was true, it may be making up for it with what I just said.
Scorpion008, I like your theory a lot. Very good. It is entirely possible that the probability distribution determining which "high number" tile will appear is weighted to favor or disfavor some "magic" number that is dependent on what you need. This, however, means that the game is programmed to have a clever AI to know what you need (possible, but not likely). The weighting scheme, if exists, needs not to be complicated. If you need a "24" tile card, the probability distribution could be made to be max at 24, so that it is more likely you get a 24 but still wit a smaller chance to get another card. Very difficult hypothesis to test, since you need many games that are far advance to reach those high numbers.
The AI need not be magic. I will demonstrate. 1__2__6 48_24_12_2 96_3__6__1 3__12_1__3 Here you can see you would want a 6. The game can tell that the only white card that would help you right now is a 6, simply because the two spots facing the only empty place are a 6 and a 2, and a white card is never a 1. (Note that the move has already been made, and we see the board as the AI sees it; we only see this screen for a fraction of a second.) The point is, the game doesn't have to know your whole strategy to help you.
It may just be confirmation bias, but I noticed that a twelve was drawn in my latest game when I had about 3 12's on the board I could not match already. This seems like it could be likely, but then again, it could be me just remembering the times this was the case.
Picked this up finally for myself and the gf. We've been playing off and on all night...she's kicking my ass
iPad Wee! Ipod :-( Got hooked on the iPad and was ready to go mobile with iPod touch, alas no cigar.... Kudos to the devs for the warning, but raspberry on Apple system compatibility metadata: "Requires iOS 6.0 or later. Compatible with .... iPod touch" Usually the iTunes throws a warning, like unable to install but i guess this slipped through
News Here's a round of news regarding progress in the card draw algorithm. Spoiler I poured the algorithm that I formulated yesterday into my Python script for analyzing and formatting sequences. I now separate the stacks (as I identify them) with line breaks in the formatted output. I also mark any non-3 white bonus cards with yellow color to make them easier to see. At a quick glance it appears that every other stack after the high card reaches 48 contains a bonus card of random (allowed) value. I am also planning to write the academic journey of this thread with all the theories, hypothesis, experiments and results into a concise text. At the moment, I am not quite sure where and how I will publish the result (I have no blog) but that will work itself out, I think. More sequences are still welcome. I would especially welcome a game beyond a high card of 768. Feel free to follow the instructions in this post and send me a PM.
Hey I only just got a 768 can't wait to try for the 1536 Also I managed to get the 768 by doing a corners game, and sticking with it (which I don't normally manage!)
