Post by gpoquiz in Good rule change for first move of game

Viewing post in Good rule change for first move of game

All sims are 100,000 games.

Depth	Total Duration (ms)	Average Duration (ms)	End States Considered	Uncollapsed Cards Average	Uncollapsed Cards Standard Deviation	Balance (P1-P2)
0	420	0.0042	0	5.44837	1.61097	50.1-49.9
1	1005	0.01005	100,000	5.91061	1.88247	50.5-49.5
2	3173	0.03173	290,712	5.91045	1.87536	50.2-49.8
3	9481	0.09481	803,160	5.93895	1.8215	49.4-50.6
16	102,471	1.02471	360,327,245	5.7415	1.43887	78-22

I'm happy to have been proven wrong here, it seems like on average, 5.5-6 cards will be uncollapsed by the end of the game, regardless of level of depth. The standard deviation goes down as depth increases, which is to be expected.
Oh, and depth here = 1 person's turn, so 3 depth == If i do this, then he does this, then I do this, do i win?

Riffle Shuffle & Roll196 days ago(+1)

Wow! That is so cool to see. Okay, that makes a scoring system based on cards remaining face up feasible. Thank you so much for crunching these numbers. Do you think it would possible to do this with the shift rule I introduced as an optional way to play?

Sentinel65196 days ago (1 edit) (-1)

I am glad that gpoquiz's simulation results essentially confirmed what I already wrote in this thread based on my own experience of playing about 1,000 games with AI namely that the win ratio is approximately 50:50 and that, on average, one game lasts 5-6 rounds.

It would be interesting if he tried to simulate the same number of games to see what the starting situation is for a player who goes first and, after the board is generated, has only cards with a value of 1 or 2 around them. For me, this worked out to be about 30% of the board generation. Here, the imaginary advantage of the first move turns against the player. And it's true that in the case of playing with AI, I've noticed this many times, whether on the player's side or the AI's.

As for Shift mode, I am convinced that it will not be possible to combine it with Solo mode. Solo mode must have a generated solvable board, where the algorithm has clearly defined information about the game board, including coordinates, and assembles the game board in reverse (classic solo mode 3x3 or 4x4). In combination with Shift mode, the size of the board is known at the beginning of the game, but no one knows what the game board will look like at the end of the game. But maybe I'm wrong and someone will build a generator for Shift mode that will generate at least one path for solo mode with cards moving one space in a row or column after each move.

gpoquiz194 days ago

Napkin math says that 30% is far too high for the four surrounding starting cards to be all 1's or 2's
Deck: 1,1,1,1,2,2,2,2,3,3,3,3,4,4.
(four 1, 2 in a row)
(8*7*6*5)/(14/13/12/11)
= 1680/24024 = .069 = 6.9%.
This is an upper bound, since drawing 4 for your surrounding cards in a row is the ideal circumstance. In almost every other case you will have less than 8,7,6, or 5 1's or 2's left in the deck.
Simulated:
100,000
p1: 5180 = .0518 = 5.2%
p2: 5168 = .05168 = 5.2%
both: 392 = .00392 = .3%

If your generation has 30% 1's or 2's in all starting positions then I would guess that your generation is wrong.

gpoquiz194 days ago

I haven't played with the shift rule yet, but really like the concept! I'm trying to force myself to take a small break from programming, but it will be an interesting challenge! Adding shift will double the mathematical complexity, and so I may need to even run simulations overnight! Oh, and then of course adding shift to my digital version when I get around to it.

My guess is that the shift means that it's much easier to "escape", so like how p2 was favored when the first turn could move anywhere, I would guess p2 is favored in the shift variant. And for the cards left, I would guess that there may be more cases where there are no collapsed cards left at the end of the game. (aka p2 wins) Again, just hypotheses.

Riffle Shuffle & Roll190 days ago

Are you able to tell me the fewest turns it would take for a player to win a game?

gpoquiz187 days ago

Sims show 5, but I would say that number comes with caveats. Here is an example game.

https://pastebin.com/9ceEzqmp

In this game player 1 is guaranteed to win. Because both players are "perfect," player 2 also knows this, and kinda "gives up." Or in other words, plays randomly. But the move on turn 4 is obviously a bad move for p2, because it's a guaranteed loss in one.

So, if you mean in all cases, then yes, 5 is going to be the least turns until game ends (I couldn't construct a game that purposefully loses faster than that), but that may require a player to lose faster than what may be "normal".

Changing the heuristic so that the bot extends the game as long as it can (more opportunities for a human opponent to make a mistake) is on my to-do list, but will be a slightly more involved change, so I'm putting it off.

Fun fact: Collapsi has 378,378,000 unique states. (16!/(4!4!4!2!2!)) This isn't counting the fact that if you shift the board left or right, the board is technically the same due to wrapping. (I think that's /12, so 31,531,500 but not confident.)

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