size_t DfpnSolver::MID(const DfpnBounds& maxBounds, DfpnHistory& history)
{
    maxBounds.CheckConsistency();
    SG_ASSERT(maxBounds.phi > 1);
    SG_ASSERT(maxBounds.delta > 1);

    ++m_numMIDcalls;
    size_t prevWork = 0;
    SgEmptyBlackWhite colorToMove = GetColorToMove();

    DfpnData data;
    if (TTRead(data)) 
    {
        prevWork = data.m_work;
        if (! maxBounds.GreaterThan(data.m_bounds))
            // Estimated bounds are larger than we had
            // anticipated. The calling state must have computed
            // the max bounds with out of date information, so just
            // return here without doing anything: the caller will
            // now update to this new info and carry on.
            return 0;
    }
    else
    {
        SgEmptyBlackWhite winner = SG_EMPTY;
        if (TerminalState(colorToMove, winner))
        {
            ++m_numTerminal;
            DfpnBounds terminal;
            if (colorToMove == winner)
                DfpnBounds::SetToWinning(terminal);
            else
            {
                SG_ASSERT(SgOppBW(colorToMove) == winner);
                DfpnBounds::SetToLosing(terminal);
            }
            TTWrite(DfpnData(terminal, SG_NULLMOVE, 1));
            return 1;
        }
    }
    
    ++m_generateMoves;
    DfpnChildren children;
    GenerateChildren(children.Children());

    // Not thread safe: perhaps move into while loop below later...
    std::vector<DfpnData> childrenData(children.Size());
    for (size_t i = 0; i < children.Size(); ++i)
        LookupData(childrenData[i], children, i);
    // Index used for progressive widening
    size_t maxChildIndex = ComputeMaxChildIndex(childrenData);

    SgHashCode currentHash = Hash();
    SgMove bestMove = SG_NULLMOVE;
    DfpnBounds currentBounds;
    size_t localWork = 1;
    do
    {
        UpdateBounds(currentBounds, childrenData, maxChildIndex);
        if (! maxBounds.GreaterThan(currentBounds))
            break;

        // Select most proving child
        std::size_t bestIndex = 999999;
        DfpnBoundType delta2 = DfpnBounds::INFTY;
        SelectChild(bestIndex, delta2, childrenData, maxChildIndex);
        bestMove = children.MoveAt(bestIndex);

        // Compute maximum bound for child
        const DfpnBounds childBounds(childrenData[bestIndex].m_bounds);
        DfpnBounds childMaxBounds;
        childMaxBounds.phi = maxBounds.delta 
            - (currentBounds.delta - childBounds.phi);
        childMaxBounds.delta = delta2 == DfpnBounds::INFTY ? maxBounds.phi :
            std::min(maxBounds.phi,
                     std::max(delta2 + 1, DfpnBoundType(delta2 * (1.0 + m_epsilon))));
        SG_ASSERT(childMaxBounds.GreaterThan(childBounds));
        if (delta2 != DfpnBounds::INFTY)
            m_deltaIncrease.Add(float(childMaxBounds.delta-childBounds.delta));

        // Recurse on best child
        PlayMove(bestMove);
        history.Push(bestMove, currentHash);
        localWork += MID(childMaxBounds, history);
        history.Pop();
        UndoMove();

        // Update bounds for best child
        LookupData(childrenData[bestIndex], children, bestIndex);

        // Compute some stats when find winning move
        if (childrenData[bestIndex].m_bounds.IsLosing())
        {
            m_moveOrderingIndex.Add(float(bestIndex));
            m_moveOrderingPercent.Add(float(bestIndex) 
                                      / (float)childrenData.size());
            m_totalWastedWork += prevWork + localWork
                - childrenData[bestIndex].m_work;
        }
        else if (childrenData[bestIndex].m_bounds.IsWinning())
            maxChildIndex = ComputeMaxChildIndex(childrenData);

    } while (! CheckAbort());

    // Find the most delaying move for losing states, and the smallest
    // winning move for winning states.
    if (currentBounds.IsSolved())
    {
        if (currentBounds.IsLosing())
        {
            std::size_t maxWork = 0;
            for (std::size_t i = 0; i < children.Size(); ++i)
            {
                if (childrenData[i].m_work > maxWork)
                {
                    maxWork = childrenData[i].m_work;
                    bestMove = children.MoveAt(i);
                }
            }
        }
        else
        {
            std::size_t minWork = DfpnBounds::INFTY;
            for (std::size_t i = 0; i < children.Size(); ++i)
            {
                if (childrenData[i].m_bounds.IsLosing() 
                    && childrenData[i].m_work < minWork)
                {
                    minWork = childrenData[i].m_work;
                    bestMove = children.MoveAt(i);
                }
            }
        }
    }
    
    // Store search results
    TTWrite(DfpnData(currentBounds, bestMove, localWork + prevWork));
    return localWork;
}
void DfpnSolver::LookupData(DfpnData& data, const DfpnChildren& children,
                            std::size_t childIndex) const
{
    const SgMove move = children.MoveAt(childIndex);
    LookupChildData(move, data);
}