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Ganabul
Last seen 2 days ago
Overall
Super Star
Overall
Record
20/17/18
Win Percentage
52%
Archive

2010

2010-08-19 05:13:38
rating 4.6
2010-03-30 08:10:55
rating 5
2010-02-11 17:14:44
rating 5.2

2009

2009-08-14 18:06:14
rating 3.6
2009-08-10 18:30:36
rating 4.3
2010-03-30 08:10:55
28 votes, rating 5
Orders of magnitude
An interesting little titbit came up in the recent AI thread in General Chat. Including staying where he is, a 6 MA player has 169 possible moves, excluding any dice rolling. With 11 players on the team, the number of possible moves is upwards of 1800; add in different setups and the dice rolls, and the number of possible moves and consequences expands again. Multiply this by the next 7 turns, and before half time, the number of potential outcomes has exploded.

I'm prompted to consider this by some of the ongoing strategy discussions in the forum, because it seems to me questions of general strategy revolve around picking the best possible route through these branching possibilities; a brute force consideration of every option is impossible, pro-elf players in the last turns of a particularly rough match aside. Instead, we have to choose goals for the turn, for the half, for the game: these help us narrow down the moves from the possible to the manageable. In most situations, this still leaves a staggering range of possibilities, made more complex by skills & races, so we have to add in a consideration of what is plausible from our opponent: what limitations their set of possibilities has, and what guides we think they're using to narrow down their choices.

Yet even this process leaves us, usually, with more possible moves, all of which could apparently serve to advance us towards the goal at the end of the probabilities, than we can accurately evaluate. How do we decide which ones should be abandoned, and which are worth pursuing? It's clear that some players are more adept at pruning the probability tree. Somewhere, experience and talent allows better players to select optimal routes, while worse players are overloaded with choice and end up in cul-de-sacs. The actual moves that occur to players in-game are only the conscious result of a much more complex and instinctive process.

I think the point is probably three-fold.

First, the sheer mass of possibilities involved in every turn mean that few games will ever truly turn on a single dice roll; this is an illusion based on a bottleneck in the probabilities. Back up, and there are multiplying routes to and around this point; go forward, and the possibilities will expand again.

Second, experience is important; although few coaches consciously consult their memories of every single match they have played for early boundaries on the probability forest, games clearly lay down some instinctive sense of it: my own record is proof of that, in a move from very to merely bad that cannot just be explained by knowing the client better. We could take a stab at defining the prerequisites for bloodbowl talent, but these are given; the best we can hope for is that experience teaches us to use them to our best advantage.

The third is one which was touched on in the AI thread: BB is flat out hard. I seem to remember reading somewhere that top level go-players suffer a disproportionate number of cerebral haemorrhages. Win or lose, perhaps we should be more amazed that we play without our brains exploding from our ears.
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Comments
Posted by pythrr on 2010-03-30 08:22:19
pish

hit stuff, if it falls over,.kick it. if it doesn't squeal, it's probably the ball.
Posted by Ganabul on 2010-03-30 08:22:57
:)

You're on fire today, sunshine.
Posted by f_alk on 2010-03-30 13:45:16
Isn't even more than 169?
The first step has 8 possibilities, the second and each subsequent has 7 (if he does not have the ball, then walking backwards is a waste). And who knows if he goes all 6 MA or less - or even GFIs (I will ignore those)?
So we have 8*7*7*7*7*7 + 8*7*7*7*7 ... + 8 = 156864 !

169 is the number of possible end-positions, but not the number of possible ways.

And the AI should not only decide where to go, but also how to go :)
Posted by Hitonagashi on 2010-03-30 14:18:14
The difference is, that the options are dramatically reduced.

We don't say "I want that player to go there, then there, then there". We say "Okay, I want to mark that guy with this player, hence I want a path that takes him from there to there with the minimum number of dodges/rrs."

That's a dramatically smaller number of possibilities, and is usually reasonably intuitive.

The hard bit for me of BB is caging. I want to protect the ball carrier. How do I set up my defense of the ball carrier such that he cannot be blitzed? Just running figures won't do, and that I believe is where experience comes in, in the completely risk free positional moves.

The best BB coaches I think can look at a position and think "A lino there, there and there, and another cover there" and my ball carrier is safe for a turn. That's how it always appears to me.
Posted by Ganabul on 2010-03-30 16:33:49
@ falk

6 MA player has 169 possible moves, excluding any dice rolling.

I started with just moves to point up the scale of the problem, but actual route leads into Hitonogahsi's comment.

For an individual player, yes, the choice is reasonably intuitive - but you also have to decide which player; the optimal order; and what to do with the other 10 players.
Posted by princevaliant on 2010-03-30 19:38:01
tl; dr

;-)

Really interesting, quasi-academic look at blood bowl. Thanks
Posted by pythrr on 2010-03-30 20:58:06
"completely risk free positional moves"

-

hito - no such thing. BB is about managing risk, not removing it. In fact, one wishes to leave a small chance of the opp succeeding, in order to tempt him in, watch him fael, then boot him to death. Sucker-trap tactics rock.
Posted by f_alk on 2010-03-31 22:18:21
To get to the space 6 spaces "up", you can go:
(a) six spaces straight up or
(b) 4 straight up, one diagonal left-up, one right-up or
(c) 4 up, 1 right-up, 1 left up or
(d) 3 up, 1 right-up, 1 up, 1 left-up ....
etc. etc.
So, to get to one space (of the 169 possible reachable spaces) you have several ways (imagine to run around an opponent to the left or right).
So a player with MA 6 has more than 150000 moves to reach the 169 spaces.
The problem with Hitonagashi's comment is:
Computers have no intuition whatsoever - so even "reasonable intuitive" is incredibly hard for them for the above reasons: Computers must calculate each possible move and will assign numbers of merit to it.