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A new look at the 3:1 rule of combat through Markov Stochastic Lanchester models

Author

Listed:
  • M Kress

    (CEMA—Center for Military Analyses)

  • I Talmor

    (CEMA—Center for Military Analyses)

Abstract

The 3:1 rule of combat states that in order that for the attacker to win the battle, his forces should be at least three times the force of the defender. This somewhat vague statement has resulted in numerous interpretations and discussions from historical and military science points of view. In this paper we attempt to examine this rule by utilising a number of Markov Stochastic Lanchester models that correspond to various basic combat situations and to draw some conclusions from their implementations. We identify general combat situations where the 3:1 rule is reasonable as well as situations where the force ratio should be either smaller or larger. Since the analysis is performed in the formal and somewhat ‘sterile’ setting of (pure) mathematical modeling, the results should be appropriately interpreted as reasoning of a certain abstraction of the battlefield.

Suggested Citation

  • M Kress & I Talmor, 1999. "A new look at the 3:1 rule of combat through Markov Stochastic Lanchester models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(7), pages 733-744, July.
    • Handle: RePEc:pal:jorsoc:v:50:y:1999:i:7:d:10.1057_palgrave.jors.2600758
    DOI: 10.1057/palgrave.jors.2600758
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    Citations

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    Cited by:

    1. Brian L. Morgan & Harrison C. Schramm & Jerry R. Smith, Jr. & Thomas W. Lucas & Mary L. McDonald & Paul J. Sánchez & Susan M. Sanchez & Stephen C. Upton, 2018. "Improving U.S. Navy Campaign Analyses with Big Data," Interfaces, INFORMS, vol. 48(2), pages 130-146, April.
    2. Pettit, L. I. & Wiper, M. P. & Young, K. D. S., 2003. "Bayesian inference for some Lanchester combat laws," European Journal of Operational Research, Elsevier, vol. 148(1), pages 152-165, July.
    3. Michael J. Armstrong, 2005. "A Stochastic Salvo Model for Naval Surface Combat," Operations Research, INFORMS, vol. 53(5), pages 830-841, October.
    4. Kress, Moshe & Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Seidl, Andrea, 2018. "Lanchester model for three-way combat," European Journal of Operational Research, Elsevier, vol. 264(1), pages 46-54.
    5. Kyle Y. Lin, 2014. "New results on a stochastic duel game with each force consisting of heterogeneous units," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(1), pages 56-65, February.
    6. Michael P. Atkinson & Moshe Kress & Niall J. MacKay, 2021. "Targeting, Deployment, and Loss-Tolerance in Lanchester Engagements," Operations Research, INFORMS, vol. 69(1), pages 71-81, January.
    7. Ken R. McNaught, 2002. "Markovian models of three‐on‐one combat involving a hidden defender," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(7), pages 627-646, October.
    8. Chad W. Seagren & Donald P. Gaver & Patricia A. Jacobs, 2019. "A stochastic air combat logistics decision model for Blue versus Red opposition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 663-674, December.

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