Integrated Bounds and Values

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Integrated Bounds and Values (IBV) were proposed 1995 by Don Beal. It treats values and bound flags, typically stored as distinct items inside a transposition table, inside one scalar value as a single numeric scale, providing a convenient notion for coding and processing backed-up values, and might slightly simplify control structure for storing and retrieving TT scores.

=Representation=
 * Exact numbers (n) are represented as 4n
 * Upper bounds (<= n) are represented as 4n-1
 * Lower bounds (>= n) are represented as 4n+1

with following properties:
 * 1) negating a bound yields in the corresponding bound from opponent's point of view (Negamax)
 * 2) a lower bound at n (>= n) is greater than an exact n
 * 3) an exact value (n) is greater than an upper bound

=IBV in Alpha-Beta= Inside an alpha-beta search, for a beta-cutoff one has to compare with forceExact(beta), to return forceLB in that case.

int ibvSearch(int alpha, int beta, ...) { ...  int cut = forceExact(beta); for (all moves) { ...    score = -ibvSearch(-beta, -alpha, ...); ...    if ( score >= cut ) return forceLB(score); ...  }   ... } with int forceExact(int x) {return (x+1) &~ 3;} int forceLB (int x) {return forceExact(x) + 1;} =Publications=
 * Don Beal (1995). An Integrated-Bounds-and-Values (IBV) Numeric Scale for Minimax Searches. ICCA Journal, Vol. 18, No. 2

=Forum Posts=
 * Re: Quiescence search problems by David Blackman, rgcc, August 3, 1995 » Quiescence Search

=References=

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