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August 4th, 2009

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End Game Advice

One of the more unintuitive principles in endgame play is that you usually play gote moves before reverse sente moves (of the same value). This principle is illustrated quite nicely with this diagram:

In this position, black to move, a play on the first line (reverse sente) gains one point, and a play on the third line (gote) also gains one point (note: using miai counting). Which way should black play (assuming these are the last moves before dame)?

If black plays gote:

for a gain of +6 points.

If black plays reverse sente:

for a gain of +5 points!

Source: www.godiscussions.com

Posted by Chris Welsh in Uncategorized

10 Comments »

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10 Responses to “End Game Advice”

  1. konrad says:

    But this is true only because of your assumption that these are the last moves before dame (so that sente is worthless). If we assume there is another 1-point gote move available, the two lines are equivalent; or if we assume there is another 2-point gote move available the reverse sente move wins out.

    The usual assumption is that the next largest move after the exchange under consideration will be the same as or just slightly less than the value of the currently biggest move (2 points here). Certainly most endgame decisions do not happen in a last-move-before-dame context. In which case the reverse sente move is at least as good as the gote move.

  2. Chris says:

    Actually, after I posted this, I realized it was probably a mistake. End game theory, especially miai counting, gets really complex. However, I believe you are incorrect in your statement. In moves of the same value, you play sente first, then gote, then reverse sente.

    Consider an example, where there are is a gote move and a reverse sente move, each gaining y points, and then another gote move, gaining x points, where y > x.

    If you play reverse sente first, gaining y points, your opponent takes the gote point, also gaining y points, and then you take the next gote move, for a net gain of y – y + x/2 = x/2.

    If you play the gote move first, your gain is y points. Your opponent plays the sente move, gaining 0 points, and then plays the gote move worth x, for a total gain of y – x/2, which is typically greater than x/2. Again, this is using miai counting, and ignoring ko’s. It’s worth remembering the point that “sente gains nothing”.

    This is all rather hard to grasp, which is why I hoped that rather contrived example helped illustrate the point. Also, it’s not clear how much practical application this has at our level.

  3. konrad says:

    I agree this counting approach is very confusing – perhaps more of a hinderance than a help. Why are you counting a gain of y for the first gote move but only x/2 for the second? I would have thought the choice is between gaining x (and losing sente) for the reverse sente move and gaining y-x (retaining sente) for the gote move. In the multi-point stage of the endgame y-x is usually much smaller than x, so it comes down to how much sente is worth.

    Or alternatively (more simply, stopping the analysis before considering x): reverse sente gains nothing but retains sente, while gote gains y at the cost of losing sente. The value of sente is always hard to judge, but is usually assumed to be around y and can be either smaller or larger than y.

  4. Chris says:

    Reverse sente does not retain sente, it ends in gote, and is evaluated like a gote move.

    With regard to why y is y and x is x/2, my understanding is that you are estimating a fixed sequence of plays. By going first, black would gain x, but may also gain 0, hence you divide x by 2.

  5. Steve says:

    Perhaps this is because I don’t know what miai counting is – but isn’t the gote play on the third line worth 2 points? (1 prisoner+1 point)?

  6. konrad says:

    Chris: Who has sente simply depends on where you stop the analysis. In the paragraph where I said reverse sente retains sente, the sequence was: player 1 plays reverse sente, player 2 responds with a gote move. The effect of this sequence (considered all together) is that player 1 has retained sente.

    I’m afraid I don’t understand your 2nd paragraph.

    Steve: you are correct, the move is worth 2 points in ordinary counting (which calculates the difference between the result when black plays first and when white plays first, i.e. two moves difference between the positions being compared), and correct again that this is different from miai counting.

    In miai counting the aim is to evaluate the value of only a single move, i.e. the difference between the score if one player plays and if nobody plays. The simplest case is a move which is gote for both sides, where the miai count is simply the ordinary count divided by two – two moves making a difference two points is one point per move.

    In the example you refer to: black can make two points by playing; white can prevent black from making any points by playing. As it stands, we don’t know who will get to play here first, so we evaluate it as if black has made half of the available points. (E.g. if there are two such situations on the board, they are miai so that black will score a total of two points from both situations combined – we therefore value them as one each.) Now: the argument behind miai counting is that on playing one move, the position is transformed from being worth 1 point to black to being worth either 0 or 2 points to black – hence the value of the move played is 1 point.

    For one-sided sente moves: these are worth nothing in miai counting, because the move is your privilege anyway – taking what is already yours doesn’t change the score. Also, the net nr of moves expended is zero, so it doesn’t cost you anything either.

    For reverse sente: these are worth full value – the difference between a sente and its corresponding reverse sente has to equal the ordinary count. So the miai counts of the moves being compared in the original example are the same.

    For double sente: well, these are just so urgent that you have to take them before stopping to count. Actually, I have no idea how they are normally evaluated in miai counting, but one argument would be that you should take their value and divide by the net nr of moves expended (zero). Double sente gives you something for nothing (“profit gained in sente is profit gained free”).

    Chris – did I get that right?

  7. Chris says:

    Sensei’s library has some articles, but they lack detailed examples and in my opinion are more confusing than helpful: http://senseis.xmp.net/?MiaiCounting

    Sometimes I feel as though I understand it, other times, like this morning, I feel they are talking gibberish. For instance, they define the miai value as C/T, where C is the net count and T the net number of moves. But in a gote move, the net number of moves is 1, not 2.

  8. konrad says:

    No, the net nr of moves is 2 because you are considering the difference between a position resulting from black playing and a position resulting from white playing.

  9. Steve says:

    So do you need miai counting for anything if you (think you) understand the “normal” way of counting?

  10. konrad says:

    Not really. I suppose it could be useful for evaluating ko situations, but those are even more complicated than anything we discussed here.

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