Concept Architecture
Concept
Theoretically, Standard Gamble is a preference elicitation method based on expected utility theory used to measure the utility of a health state under conditions of uncertainty. Individuals are asked to choose between remaining in a specified health state with certainty or accepting a gamble with two possible outcomes: full health and immediate death. The probability at which the respondent is indifferent between these alternatives represents the utility of the health state.
Mathematically, the Standard Gamble is represented using expected utility theory. The utility of the health state is equal to the probability of achieving full health at the point of indifference, assuming utilities of 1 for full health and 0 for death. The method estimates cardinal utility values suitable for quality-adjusted life year (QALY) calculations and cost-utility analysis.
In practice, respondents are presented with a series of gambles in which the probability of full health is varied until an indifference point is reached. The resulting probability is recorded as the utility value for the health state. Standard Gamble has been widely used to derive preference weights for health state valuation and to develop preference-based measures used in health technology assessment.
Purpose
Used to elicit health state utility values under uncertainty for quality-adjusted life year estimation, preference measurement, and cost-utility analysis.
Mathematical Formulae
Primary Formula
U(H) = pU(FH) + (1 ? p)U(D)
With U(FH) = 1 and U(D) = 0:
U(H) = p
where:
- U(H) = utility of the health state
- p = probability of full health at the point of indifference
Supporting Formulae
Expected utility of the gamble:
EU = p ? 1 + (1 ? p) ? 0 = p
Related Mathematical Methods
- Expected utility theory
- Utility elicitation
- Cardinal utility measurement
- Health state valuation
- Preference weighting
- QALY estimation
Example
A respondent must choose between living with moderate arthritis for certain or accepting a treatment that offers an 85% probability of full health and a 15% probability of immediate death.
The respondent is indifferent between the two options when the probability of full health is 0.85.
U(H) = 0.85
The health state therefore has a utility value of 0.85.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =IF(B2=C2,B2,"""") | Identifies the probability at the respondent's point of indifference. |
| AVERAGE | =AVERAGE(B2:B101) | Calculates the mean utility across respondents. |
| SUMPRODUCT | =SUMPRODUCT(B2:B101,C2:C101) | Computes weighted average utilities for subgroup analyses. |
| DATA TABLE | =TABLE() | Performs sensitivity analyses by varying gamble probabilities. |
VBA (Optional)
Automate iterative adjustment of gamble probabilities until the respondent's indifference point is reached and record the resulting utility values.
Sources
- von Neumann J, Morgenstern O. Theory of Games and Economic Behavior. Princeton University Press.
- Torrance GW. Social preferences for health states: An empirical evaluation of three measurement techniques. Socio-Economic Planning Sciences. 1976;10(3):129?136.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes. Oxford University Press.
- Brazier J, Ratcliffe J, Salomon JA, Tsuchiya A. Measuring and Valuing Health Benefits for Economic Evaluation. Oxford University Press.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
1
Measuring and Valuing Health Benefits for Economic Evaluation — Brazier, Ratcliffe, Salomon & Tsuchiya, 2nd Edition ed., 2017 (Oxford University Press)
The comprehensive text on the measurement and valuation of health benefits for economic evaluation — defining health, valuation techniques (time trade-off, standard gamble), whose values to use, preference-based measures (EQ-5D, SF-6D), and the construction of QALYs.
BookView source →
Frequently Asked Questions (6)
What is the standard gamble?
A health state valuation method in which respondents choose between a defined health state with certainty or a gamble between full health and death.
Source: Torrance, Thomas & Sackett 1972
How are utilities calculated from a standard gamble?
The value of a health state is read from the probability at which a respondent becomes indifferent between remaining in that state for certain and taking a gamble that yields full health if it succeeds and death if it fails. If a person is indifferent when the chance of full health is nine tenths, the state is assigned a utility of nine tenths, since at that probability the expected value of the gamble equals the certain state. Adjusting the probability until indifference is reached yields the number. Torrance (1986) sets out this calculation.
Source: Torrance 1986
How does the standard gamble work?
The respondent is offered a choice between remaining in a described health state for certain and taking a gamble that yields full health with some probability or death with the remaining probability. The probability of full health is adjusted until the respondent finds the certain state and the gamble equally attractive. At that point of indifference, the probability of full health equals the utility of the state, on a scale where full health is one and death zero.
Source: Torrance, Thomas & Sackett 1972
Why is the standard gamble grounded in utility theory?
The standard gamble is grounded in expected utility theory because it derives the value of a state from a choice between a certain outcome and a risky prospect, which is exactly the kind of decision that theory concerns. The indifference probability that equates the certain state with the gamble is, under the theory's axioms, the utility of the state. This theoretical basis is why the standard gamble is regarded as a classical, valid method for eliciting utilities.
Source: Torrance, Thomas & Sackett 1972
What are the limitations of the standard gamble?
The standard gamble requires respondents to reason about probabilities and to contemplate a risk of death, which many find difficult or distressing, and its values are affected by attitudes to risk, so a risk-averse respondent may value states differently from a risk-neutral one. It can give different values from the time trade-off for the same state. These features complicate its use and interpretation, though it remains a foundational valuation method.
Source: Torrance, Thomas & Sackett 1972
How does the standard gamble differ from the time trade-off?
The standard gamble values a state through a choice under risk, varying a probability of death until indifference, so it reflects attitudes to risk, whereas the time trade-off values it through the sacrifice of length of life, asking how many years of full health equal a longer time in the state, so it reflects attitudes to time. Both are choice-based methods yielding utilities, but they draw on different trade-offs and can give different values.
Source: Torrance, Thomas & Sackett 1972
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 2 Sep 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/standard-gamble
- Term code
- HE-EE-HU-073
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