# Integrated Bounds and Values

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**Integrated Bounds and Values** (IBV) were proposed 1995 by Don Beal ^{[1]}. 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:

- negating a bound yields in the corresponding bound from opponent's point of view (Negamax)
- a lower bound at n (>= n) is greater than an exact n
- 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

- ↑ Don Beal (
**1995**).*An Integrated-Bounds-and-Values (IBV) Numeric Scale for Minimax Searches*. ICCA Journal, Vol. 18, No. 2