Joe Grundy
Australia
Sydney
NSW
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Preamble
In Hisss, each snake-segment has two ends of two different colours, and can be joined to any existing snake-under-construction as long as the colour matches the open end. There are also head tiles and tail tiles, one each of each colour, and the player who completes a whole snake gets to claim it. Each claimed tile is one point. When you play a body segment, you are allowed to use it to join together two snakes-under-construction into a larger snake. You don't have a hand of tiles. You just flip the next tile and do what you can with it. Mostly it seems purely arbitrary, this snake or that, and usually there's no real choice where to play at all. The game is easily dismissed has having no choices/strategy.
BUT ... since sometimes you get to decide which snake-under-construction you get to add a piece to, is there any basis for preferring one over another?
( Wha? Huh? Someone's writing strategy comments for a game with "no opportunity for strategy or influencing outcomes"?!?!?)
People often assume a situation with a huge randomizer in the immediate future is a situation they can't meaningfully influence the outcomes. People often equate having few meaningful choices with having no opportunities at all. These are especially common assumptions in "children's" games.
Both assumptions are often wrong, and Hisss is probably a great example to use as a muse. You certainly can't always win against someone playing without care, but can you influence your frequency of victory?
I intend to simulate the impact of some of these kinds of choices. My curiosity is nudged as to just how much control you might get over such a seemingly "no meaningful choices" game.
Ye gods, WHY?
Among other things, if there's any merit in the following thoughts then as a parent/adult you can quietly play the poorer choices if you want to give your kids a small winning boost, without having to play so obviously badly as missing colour matches entirely or deliberately taking a smaller snake when there's a larger one available. With a 2yo you can get away with almost anything to make sure they don't lose too badly. With a 4yo they start to notice and you need some subtle options to make their victories more "honest".
So. On with the show...
Does Size Matter?
If you are a little ahead, and there's one killer snake on the layout, then if another player gets that snake you won't be winning any more. If you suppose a three player game, that's a 2/3 chance someone else will get it. So...
If you are winning: To stay ahead, you want equally sized snakes on the layout, small enough that no one snake can give another player the lead. You are more likely to get your share of what's on offer, and if someone gets one more than you it won't matter.
If you are losing: To maximise your chances of catching up, you want there to be a single large snake you can grab to make a comeback.
If you want to quietly help your kids win: Play the reverse... when you're winning make a huge killer snake. When you're losing, even out the snake sizes when you have a chance.
Would You Care To Join Us?
A similar thought as above applies to joining snakes-under-construction.
If you are winning: To stay ahead avoid joining them up. It'll give you more short snakes to distribute your tiles around.
If you are losing: To maximise your chances of catching up, link snakes together to make fewer of them, which will (a) be longer and (b) get longer faster.
If you want to quietly help your kids win more often: Play the reverse. Link up when you're winning, avoid joins when you're losing.
Let's End This?
There's only one each of the head and tail colours, and the one each rainbow ends. Once they're used, a snake end of that colour isn't immediately available for completing the snake and will at least one more body tile before it can be finished. That means (a) the snake is harder to finish but (b) if it does get finished it'll likely be longer.
For example, suppose there's a snake YG/GB/BG. You draw a YG tile and can play it to either end. Play at one end, you'll be left with a snake with Yellow at both ends. Play at the other end, it'll be Green at both ends. Which should you do? If the Yellow head and/or tail pieces are already used, but the Green are still to come out, obviously your choice will make some sort of difference.
I'm not exactly sure where the best option is here.
It seems likely the decision of which colour ends to leave available is influenced both by whether you are ahead/behind and also whether it's early/late in the game.
Winning and Early: The snake will likely get finished eventually. It seems you want to leave easily-completed ends so this final snake will be shorter. Tiles that might have got played to this snake will end up somewhere else.
Winning and Late: At some point it'll switch that if you leave hard-to-complete ends then the snake won't get finished at all.
Losing and Early: Make the ends hard to finish so the snake has more chance to grow before you collect it.
Losing and Late: Better set up the opportunities to finish the snakes off. (Hmmm. What if there's already one huge snake that would be enough to let you take the lead? Then adding an easily-finished snake that won't make you win would probably be a bad idea.)
Of course you could card count and know even more accurately whether YY or GG will be more/less likely to be longer/shorter/unfinished by game's end. But who'd go that far for a game with no strategy?
Let's End This? - II
In general, it seems plausible that you could nudge the game to finish with seven very short snakes and lots of leftover body tiles, or encourage longer snakes and have very few leftovers. If you are ahead, you presumably want there to be shorter subsequent snakes in total. If you are behind, you want some chances at longer snakes.
This is very much like the question above, but thought from a different angle.
If you are winning: You may want there to be many options for finishing short snakes becuase then everyone's additional points from here to the end of the game will be less. I'm not sure if trying to do this just makes lots of options for joining snakes-under-construction.
If you are losing: You want fewer straggling individual pieces by the end of the game.
If you want to quietly help your kids win: Play the reverse. You got the idea by now.
Monochrome?
If all the available end colours are different, no matter what piece is drawn it can grow a snake. In particular, if the long snakes are all the same end colours, then only those one or two colours can be used to extend the long snakes and every other tile will have to go by itself or onto the shorter snakes.
I'm still in a mental quandry as to whether, if you're losing, you want more than one large snake available for finishing. This question aside, just in terms of controlling the opportunity for the losing player to pick up the score in a single snake.
There may be snakes long enough to push a loser into first place. There may be snakes that are almost that long.
If you are winning: Try to leave similar end colours on the snakes that are almost long enough to make a difference. Thus most tiles won't make these snakes longer.
If you are losing: Try to leave those "almost enough" snakes having different end colours.
If you want to quietly help your kids win: ... reverse.
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Joe Grundy
Australia
Sydney
NSW
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Ok so above was the expectation.
What do I get after setting a system learning which decisions led to victories over a couple of million games? So far I only have it chosing based on the snake lengths given a range of circumstances. Should you join to the longest snake? The shortest snake? Something in between?
The answer is a resounding "meh". The decisions do affect the outcome probabilities, but you can only effect your total overall win probability by a couple of percent by looking at snake lengths.
Progress Report - Basics of a game simulation
Firstly, I can tell you you are about 35% more likely to win the game if you notice and collect the longest snake you can, when there is an option, instead of choosing one of your play options at random. "At random" to the extent of sometimes completely missing claiming snakes. (eg if you saw the first option and never checked for more.) So observation forms the most important factor in this game. For example between two players you go from 50% to 85% chance to win, with three you go from 33% to 66%.
Secondly, turn order has a minor but measurable effect. The player who goes first (ie first once there's already one tile flipped up on the table) gets about 5% more chance to win than anyone else.
What Choice Have I Got?
Assuming you'll always claim the longest snake you can when available and assuming you won't set the tile out individually when you could have extended an existing snake, about a quarter of your turns you have a choice where to play your new tile. Many of those choices only change what colour ends are left on display, but not the available lengths of snakes. That's about one quarter of your choices ie about 6% of your turns. About three quarters of your choices do make a difference to the available snake lengths ie about 18% of turns.
25% of turns, 49 turns in the game, about 12 turns per game that have choices.
In 2P that's about 6 choices each per game
In 3P that's about 4 choices each
The rest of the time, you have only one way to make a longest snake, or the tile only joins to zero or one existing snake/s.
Progress Report - Choosing Snake Lengths
The AI I built so far only learns about biasing the available snake length. It doesn't card count or bias the mix of colours available to match on the table.
How much leverage can you get out of biasing your 3 to 6 choices to deliberately change the available snake lengths?
Not enough worth thinking about. You can increase or decrease your chance to win by about 2% in a two player game, or by about 1% in a three player game.
There are categories of situations in the late game where you can change your chance of winning by maybe 5%. There are really specific (very rare) circumstances where a choice can guarantee you a win or loss. In aggregate, even if you know all the details their application is rare and overall you can only swing your win / loss ratio by a couple of percent this way.
Progress Report - What Colours?
I would like, at some point, to look at allowing the AI to remember which heads and tails have been used and choose which colours to leave showing based on that. Since the choices of biggest impact is in the late game I suspect that you can choose to leave snakes which are likely/unlikely/impossible to complete and would do that if you were winning (or avoid doing that if you were losing).
Alas, this exercise may have to wait a long time. Sorry.
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Posted Fri Jan 2, 2009 4:25 am