In the diced Go-Geared game, rolling has a less than 50/50 chance of success, but in the face of a losing position, it is obviously correct to roll before your opponent wins. In theory, one can recursively assign probabilities to each position and know whether rolling or not is the correct decision. (Whether that calculation can actually be carried out, however....)

In the absence of "the absolute truth", I keep debating myself over one heuristic question: If a player is losing, is it better to roll the dice early or stay as close to tied as possible and then start rolling at the end? The answer is not clear to me. In one hypothetical situation I created, it seemed better to roll early. It's hard to fully analyze when the right time to roll is.

Since there is a "money" tournament (http://www.wargear.net/tournaments/view/1492) coming up, I don't expect any secrets to be spilled, but it seems like a safe enough question where everyone can agree that they have an opinion and reasons for the opinion, but no rock-solid analysis.

Lately I've been leaning towards "roll early if losing, but find a good roll".

Seeing as I'm the one giving away the "money," I don't mind 'spilling' my theories.

First, I think that the perceived strength of you opponent is actually part of the calculus of it all. In the face of a bone-head move, a close game from behind against a significantly weaker opponent is probably worth waiting on. The implied corollary to this is that if your opponent is perceived to be stronger, there should more of an urgency to roll.

That said, I don't just agree with Hugh's 'leaning' opinion that the right position is important, I feel somewhat strongly about it.

Just as there are good moves and bad moves, there are good rolls and poor rolls - and though that could easily be the subject of another thread, I would posit that the intersection of an 'early' and 'good' roll is not uncommon. Specifically, I'm thinking of a position where your opponent has surrounded you on three sides. Generally speaking it is unwise to pull back from such a position, and the advantages of rolling your way out are often significant. Not only do you not lose a piece, but your opponent loses a piece as well.  While the space you have fled from is now a blank (0) and a potential liability, your opponent will not capture that space.  It is my experience that a winning 'good' roll from this type position almost always puts your opponent on his heels.

Do you feel lucky? ...punk. Well, do ya?

I mean, part of the fun is that it's not clear at all. I would never favor rolling over a good strategic approach - or position. Nor would I ever compromise a good strategic position for the dice. 

But if you don't have a good strategy, or position... well... it makes things decisive.

I once beat M57 at go geared, purely on the dice.  Statistically, what happened was VERY improbable.  Over many games, it's a bad approach. You will always win more games by being good at Go, and never having to use the dice (imo).

ratsy wrote:

You will always win more games by being good at Go, and never having to use the dice (imo).

I believe that the extra set of skills needed to optimize play with 8-sided dice is significant. Let's take the hypothetical example of two opponents who are equally skilled at the 1-sided 100% deterministic scenario - where there are effectively no dice; I.e., over 100 games they will go 50-50.

Let's further assume the extreme example where one player refuses to roll, but his opponent will always roll as soon as he believes he is behind. Let's further assume that they are so evenly matched that a one roll advantage is all that is necessary to win.  The 'roller' will win half of the games outright - and because he rolls on all of the other games, he will win 43% of the remaining games, winning 72% of all the games.

I liken it in an upsides-down inverted way to the doubling cube in backgammon.  Whereas in backgammon the player who is ahead uses the cube to assure victory, the Go-Geared player uses dice to avoid certain defeat.

I think the player who refuses to roll would never play the W8Dice-Mode

To really answer this question you have to divide the game into Early/Mid/Late-Game.

Early vs " weak " opponent.

There is no point in rolling the dice cause you  should beat the shit out of him anyway ^^

Early vs " strong " opponent.

I think its very hard to answer this one.

I played a few games VS M57 and i had a good position and forced him to roll.

Now you have 2 outcomes

He looses the rolls and i take over the world or he wins and he is 2 pieces ahead.

http://www.wargear.net/games/player/407019  ; Turn212
Its a very agressiv early game and i forced him to roll the dice
He had to roll or he would have lost to mutch to early

In this game he lost his roll
http://www.wargear.net/games/view/398279

It is safe to say that if you are in a positon like this you have to roll the shit out of your opponent or you are dead.

As the player with the upper Hand you can just wait and hope that he looses the roll.
I came to the conclusion that if you have the better positon on the board you should try to expand without forcing your opponent to roll.

In the early game there is to mutch at stake for me to depend on my luck :-)

Thats me for now

Merry X-MAS from Germany

One other consideration that I have been thinking of while discussing and teaching game play and tactics to newer players..

I believe many situations arise where a player only needs to win one roll in two tries in order to improve or save a position, and there's a better than 67% chance of winning at least one of these rolls. Moreover, if the first roll is successful (43% of the time), often the second roll can be skipped and a stone played or moved with devastating effect.

When it comes to this tactical approach, deciding on which type of roll to execute first involves some sophisticated considerations.  For instance, starting with a 'moving' attack from an established line (such that the blank left is replenished on the next turn) is often a preferred way to extricate a threatened stone.  Whether or not the move wins, the player now still has his most powerful weapon available - the stone played from the bowl - to either make a second attempt at rescue or inflict damage elsewhere.

In fact, I'm beginning to wonder that (against a similarly skilled opponent), there are times when even the player with the lead is better off rolling in certain situations where the tactic offers statistically favorable results, else his opponent will do the same.

I don't doubt there are some who will disagree with me, and I will have to do some work researching specific positions, but I'm tempted to liken the phenomenon to the one where Simulgear players attack with less than favorable odds. On the surface, it doesn't seem to be tactically correct, yet apparently it is.  Now I suspect the analogy won't hold up to scrutiny; I don't want SG players jumping down my throat, but I'm simply making the point that all may not be what it seems on the surface with the less-than-favorable Go-Geared dice.

Good thoughts all. The more I play, the more subtle I think this question is. Once tournaments end, I will post some analyses I've done of a few situations.

I am approaching this from the assumption of a really strong opponent. Since it is a diced game, if rolling maximizes your winning chances, then as with any duel with dice, I see no reason to cling to some "purist" non-rolling perspective. (On the other hand, the games I've played indicate a certain positional resiliency for the non-roller, so I have no issues if the real answer is "don't roll early!!")

There's an idea that if a person rolls, then the opponent can roll back, so initiating rolling is to unnecessarily resort to luck. But there's asymmetry in the results, so that's not the right perspective.

One other thing that is apparent to me - and this has to do with perceived opponent strength ..and with a somewhat different perspective than my post #2 of this thread - GG is a game where a slight lead is difficult to overcome.  Tempo is critical.

Take the case where one player is marginally better than the other.  In such a game with 1-sided die (i.e. non-diced), I will conjecture that even with a marginal advantage skill-wise, the stronger player is likely to win a great majority of the time, certainly much better than 57% of the time. However, when a position arises where a single throw of the dice can turn the game on its head (and such positions are quite frequent) the weaker player can take the opportunity to turn those odds solidly in his favor - losing his bet 57% of the time.

Yes, he can further improve on those odds by winning a series of successive rolls after the initial loss, but we've all been down that rabbit hole before - the slope gets steep quickly - Winning three in a row is a .43^3 proposition = 8%  Nonetheless, there's no reason not to try when behind.  This should be intuitive for all reasonably skilled players.

More significantly, if the stronger opponent decides to roll back and let the dice decide the outcome -from here on out we are talking about geometric sequence that approaches 50/50.

There are some players (OK, a certain player) who complain when I roll "too early," in effect calling on the dice to dictate the outcome of the game.  Now I know this player is much stronger than I, and I'm fairly confident that I would lose to this player 9 out of 10 times in a dice-less game.

Of course, I fair significantly better when I throw the dice against this player; certainly winning more than 10% of my games against him.  I don't know how this impacts the early/late debate, but it definitely suggests that the dice are a skill-level equalizer and that opponent strength (perceived or real) should impact decision making.

M57 wrote:

However, when a position arises where a single throw of the dice can turn the game on its head (and such positions are quite frequent) the weaker player can take the opportunity to turn those odds solidly in his favor - losing his bet 57% of the time.

This is actually the part of the discussion that I find the most fascinating, because it subtly but fundamentally changes the heart of the struggle. In a diceless scenario, Hugh is going to beat me at this game far more frequently than 57% of the time. So if I'm offered a chance to guarantee a win with 43% probability, I should take that bet. This is trivial.

Where it gets interesting is when I'm not playing Hugh. M57, to take another example, is better than me at this game. How much better? How about the next person I play? Where do I draw the line? The most important single factor in a given match becomes, not what is my best theoretical play, but what I believe to be the relative skill levels of myself and my opponent, and perhaps as relevantly, what does my opponent believe about our relative skill levels?

Then you get into the possibility of altering my play with the intention of creating the most leveraged possible situation for the dice roll that I'd always intend to attempt against Hugh. How does that affect strategy?

Anyway. Interesting.

asm wrote:

Then you get into the possibility of altering my play with the intention of creating the most leveraged possible situation for the dice roll that I'd always intend to attempt against Hugh. How does that affect strategy?

Anyway. Interesting.

Indeed.  ..and an interesting corollary - how does it affect Hugh's strategy? I know for a fact that he has in the past considered NOT making a decisive play because he suspected (ok, knew) I would roll against it.

M57 wrote:

More significantly, if the stronger opponent decides to roll back and let the dice decide the outcome -from here on out we are talking about geometric sequence that approaches 50/50.

Though the discussion is at the opinion/heuristics level for now, I can't condone numerical sloppiness ;)

Probabilities based on geometric series DO NOT go to 50/50. Consider the case where both players are contesting a single spot with a single roll. The initiator just wants sequence of turns to be a win followed by an opponent loss. This has probability (.43)(.57) ~ .245... Rolling indefinitely till someone wins: .245 / (1 - .245) ~ .32 ~ 1/3 for the initiator who knows the strong player will roll back. One-third is not 50/50.

Intuitively, you shouldn't expect that probability to be higher than 43% because you need the 43% and you also need the person rolling back to fail.

Hugh wrote:

M57 wrote:

More significantly, if the stronger opponent decides to roll back and let the dice decide the outcome -from here on out we are talking about geometric sequence that approaches 50/50.

Though the discussion is at the opinion/heuristics level for now, I can't condone numerical sloppiness ;)

Probabilities based on geometric series DO NOT go to 50/50. Consider the case where both players are contesting a single spot with a single roll. The initiator just wants sequence of turns to be a win followed by an opponent loss. This has probability (.43)(.57) ~ .245... Rolling indefinitely till someone wins: .245 / (1 - .245) ~ .32 ~ 1/3 for the initiator who knows the strong player will roll back. One-third is not 50/50.

Intuitively, you shouldn't expect that probability to be higher than 43% because you need the 43% and you also need the person rolling back to fail.

mea culpa - of course the probability for the initial roller is worse than 43% when you consider the rollback opportunities, but I was referring to the case where the first roll is successful and the next roller has the option of continuing the series..  From here I suppose the convergence is likely to be 1/3  is favor of the original roller.  I was trying to point out (with the unwisely chosen aid of mathematical sloppiness) that because both players are rolling back and forth - there's an evenness at play.  Of course, the first to roll does so at a significant disadvantage.

There is a master equation for any roll: 7/16 * (Probability of winning after hitting the roll) + 9/16 * (Probability of winning after missing the roll) is the probability of winning the game by rolling. If this is higher than the probability of winning without rolling, the roll is correct. 

If the decision in question is "Roll. If hit, then move, if miss, roll again," then the equation is .44*P(hit,move) + .23*P(miss,hit) + .33*P(miss twice). If this beats not rolling, it is correct.

Realistically, I think there's only a few positions where the probability can be reliably calculated. But it can always be estimated, and through experience, your estimates are likely to improve, leading to more accurate decisions in the long term. And yes, the opponent should be accounted for, but within reason. Good players do not overcome terrible positions very often.

Two extreme opinions that can be taken in the debate are:

1) You've got a 67% chance of hitting at least one roll. Early rolls dramatically affect the position and can save you from losing by a little bit. Do it!

2) If you initiate a roll and hit, the opponent can roll back. If it comes down to who wins the roll-off, the person initiating the roll is at a disadvantage to win the roll-off. Better to save the rolls until they are necessary at the end of the game.

While maybe it's a straw man to attach names to these two ideas, there are specific people who sound a lot like this :)

For opinion #1, I believe you have to consider all three results, including the ~1/3 of the time where a miss occurs. Sometimes the hit-and-move is great but no guarantee of winning, the miss-and-hit is mediocre, and the miss-miss is awful for the roller. How does this compare to losing by just a little bit?

Assume your opponent is winning 41-40 (or 42-39 where your hit does extra damage). Also assume that all you need is to stay up by one hit at the end with your 2 rolls. My calculations (worth checking) indicate that the person initating the roll wins ~44% of the time. (Sadly, needing 2 rolls at the end is only around 11%.) If your early rolling decision falls below this, it's probably best to accept that you'll be down by 1 or 2 stones at the end or that a better rolling opportunity will arise.

Extreme opinion #2 is harder to counter.  The assumption being made is symmetry in the resulting position - that only the result of the roll-off matters. This is not always the case.

I believe white can justify an early roll here:

http://www.wargear.net/rest/GetBoardImage?gameid=417488&turnid=218&setbgcolor=1&territory0=

(Gah! I can't get the image thingy to work, so I leave it as a link. Grrr.)

White rolls at the center, shutting down Black's factories. It doesn't come down to the roll-off. If White hits and moves, Black's return hit doesn't come with a particularly good move. Thus if White hits and Black recaptures, White has gained at least a move. It's not necessarily about who wins the roll-off.

Furthermore, with White's hit, White can set up a capture if Black re-hits. So, it's just not symmetric. You can't make the argument that by initiating rolling, White made it all about who wins two rolls in a row first. If Black misses the re-hit or fails to roll, it's practically over whereas White is very much alive if he misses. I think it's a justifiable early roll.

Hugh wrote:

Realistically, I think there's only a few positions where the probability can be reliably calculated. But it can always be estimated, and through experience, your estimates are likely to improve, leading to more accurate decisions in the long term. And yes, the opponent should be accounted for, but within reason. Good players do not overcome terrible positions very often.

 Adding my thoughts here.. Assuming, it's correct to roll in a certain situation, one not too inconsequential aspect of the decision then becomes how to roll. Options include attacking from the bowl first or attacking from the board first.  Often the success or failure of the first impacts the second decision, so plans must be made for both cases. Related considerations:

The attack from the bowl is generally more powerful (in terms of its discretion) - but for the same reason it can be the most costly when it loses.

Board attacks, on the other hand, have a range of potential costs. If the resulting blank from a loss 'refills' immediately at the beginning of the next turn, the costs are mostly tempo related.  However, depending on where the resulting blank is (even when the roll wins), the cost may possibly be greater than the roll considered from the bowl.

Because in many cases a winning first roll nullifies the need for a follow-up roll, the nature of this part of the decision is paramount.  How may be just as, if not more important than when.

M57 wrote:  How may be just as, if not more important than when.

True. There can be competing rolling (and non-rolling) options in any position. The evaluation process is about comparing them. "How" is implicitly part of that process.