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Category: Effects
Type: A reinforcer after a varying number of responses, around a stated average. A fixed count, a wait, and a constant chance on every try are neighboring arrangements
Origin: C. B. Ferster and B. F. Skinner, Schedules of Reinforcement (Appleton-Century-Crofts, New York, 1957), the variable-ratio chapter. Gambling sentences used here are B. F. Skinner Foundation excerpts of Cumulative Record (p. 138), About Behaviorism (p. 67), and Science and Human Behavior (p. 104). Those three books were not re-read
Also known as: Variable-ratio schedule. Intermittent reinforcement is the family of schedules that do not pay every response. It is not a second title
Quick Answer — Variable Ratio Reinforcement delivers a reinforcer after a varying number of responses, around a stated average. Ferster and Skinner specified that schedule in 1957, mostly with pigeons pecking a key. A fixed count tends to leave a pause after the reinforcer. A 2018 loot-box survey links spending categories to problem-gambling bands and does not show which way the link runs.

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What is Variable Ratio Reinforcement?

Variable Ratio Reinforcement is a schedule that delivers a reinforcer after a varying number of responses, with that number moving around a stated average.
Reinforcement is contingent on a given average number of responses but the numbers are allowed to vary roughly at random.
That sentence is B. F. Skinner, in the B. F. Skinner Foundation’s excerpt of Cumulative Record, chapter 10, page 138. The book was not re-read. A reinforcer is an event that follows a behavior and makes that behavior more likely later. The count is responses since the last reinforcer, not minutes on a clock. VR 100, in the 1957 book’s notation, names the average. It does not promise that the hundredth response is the one that pays. A prize on every try is a different schedule, and so is a prize that never comes. While every try is still paid, the try is maintained. The fast drop shows up after that pay stops. Illusion of Control is a person’s expectancy rising above the chance once a skill cue sits on a chance task. A claw machine can add that cue. This page counts the varying number of tries.

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Variable Ratio Reinforcement in 3 Depths

  • Beginner: The next prize depends on a count of tries, and the count changes. Write the try before you treat a mood, a wait, or a near miss as the same event.
  • Practitioner: Write three lines. Is the payoff a count of responses or a wait? Is an average stated? If the payoff stops, what do the next tries do? Only the first line is this schedule.
  • Advanced: At the same average, a fixed count and a varying count can share an overall rate and still differ in the pause after reinforcement. A loot-box spending link does not assign a cause.

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Origin

Variable Ratio Reinforcement is specified in C. B. Ferster and B. F. Skinner, Schedules of Reinforcement, published by Appleton-Century-Crofts in New York in 1957. The title page places Ferster at the Indiana University Medical Center and Skinner at Harvard. The acknowledgments say most of the work was done under Office of Naval Research contracts N5ori-07631 and N5ori-07656 with Harvard, from 1 September 1949 to 30 June 1955. Most of the experiments are pigeons pecking a key. Chapter numbers in later printings do not share one page for the variable-ratio chapter, so this page does not print a page. The book sorts schedules by two choices. The reinforcer can depend on responses since the last reinforcer, or on time since the last reinforcer. The requirement can be fixed, or it can vary. Those choices give four basic schedules: fixed ratio, variable ratio, fixed interval, and variable interval. In a fixed ratio, the response that completes a set count is reinforced. FR 100 is the hundredth response after the previous reinforcer. A variable ratio is like that fixed ratio, except the book schedules reinforcement on a series of ratios with a stated mean, between arbitrary bounds. The mean is written as a number, as in VR 100. Skinner’s later sentences treat gambling devices as this schedule. The same Cumulative Record excerpt says the schedule is the heart of all gambling devices and systems, and that the confirmed or pathological gambler shows the result: a very high rate of activity from a relatively slight net reinforcement. That sentence is his illustration. It is not a count of gamblers, and it is not a machine’s return. The foundation’s excerpt of About Behaviorism, page 67, says all gambling systems are based on variable-ratio schedules, although their effects are usually attributed to feelings. The excerpt then skips, with an ellipsis this page does not fill, to a second claim: the same schedule affects people who explore, prospect, invent, do scientific research, and compose art, music, or literature, and in those fields a high level of activity is usually attributed to dedication rather than compulsion. The foundation’s excerpt of Science and Human Behavior, page 104, says the long-term net gain or loss is almost irrelevant in accounting for the effectiveness of this schedule. The excerpt marks the schedule, in brackets, as variable ratio. The brackets are the excerpt’s, and the 1953 book was not re-read. An earlier, different procedure is Lloyd G. Humphreys, Journal of Experimental Psychology 25(2), August 1939, pages 141–158. The abstract was read. The article was not. Sixty-six college students were conditioned to a light followed by a puff of air to the cornea. One group had the puff on every trial for 96 trials. A second had the puff on half the trials for 96 trials. A third had the puff on every trial for 48 trials, with 48 rest intervals of the sort used for the unpaid trials in the half-puff group. Each group then had 24 extinction trials, with the light and no puff. The abstract reports no difference in acquisition, by frequency or by magnitude, and a significantly higher level of responding across those 24 extinction trials after the half-puff training. The abstract does not print a p value or the cell means. This is a light and a puff, on a share of trials. It is not a pigeon completing a listed ratio.

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Key Points

Four readings keep the counter, the pause, the extinction procedure, and the spending survey apart. A mood of surprise is not a schedule.
1

Count responses since the last reinforcer

The 1957 schedule pays after a series of ratios with a stated mean. VR 100 names that mean. It does not name the next try. A timer that makes the next payoff due after a changing wait is a variable-interval schedule. Waiting out a quiet stretch can bring that interval payoff due. Waiting does not finish a ratio. A notification that arrives with time is the timer case until someone writes the count of checks.
2

Look for the pause after a fixed count

Edward K. Crossman, Elliott J. Bonem, and Brady J. Phelps, at Utah State University, compared fixed-ratio, variable-ratio, and random-ratio schedules in pigeons. Journal of the Experimental Analysis of Behavior 48(3), November 1987, pages 395–406. The abstract was read. The article’s tables were not. Within each type, the ratio size moved irregularly through 5, 10, 40, and 80. Overall rate, the pause after reinforcement plus the running rate, did not differ by type at those sizes. The pause after reinforcement was relatively longer on the fixed ratio. They read the size of the ratio as the control on overall rate, and the type of ratio as the control on that pause. Skinner’s excerpt on page 137 of Cumulative Record calls a fixed ratio piecework. The high running rate he describes for gambling sits next to this pause result. It is not a second overall-rate table.
3

Keep partial extinction in its own procedure

Humphreys’s half-puff group kept responding at a higher level across 24 extinction trials than the groups trained with a puff on every trial. Acquisition did not differ. The popular line that people quit when every try is paid mixes the paid phase with the stop. During the paid phase, a reinforcer on every response maintains the response. The faster drop is what the abstract reports after that reinforcer is removed. Gambler’s Fallacy is the belief that a miss makes the next hit due. A series with a mean still allows a long run of misses. The belief and the schedule are two readings of one dry stretch.
4

Keep a spending grade off the key peck

A survey can show that people in higher problem-gambling bands report a higher loot-box spending code. That grade is not a listed ratio, and it is not an extinction curve. House Money Effect is a greater willingness to take a bet after a gain that the person would have refused otherwise. A prior win is not the average count until the next reinforcer.

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Applications

Write the response, the reinforcer, and the count. Then decide whether the note in front of you is a schedule, a survey category, or a story.

Mark a counter before a timer

Before a habit is called this schedule, write what is counted. Checks of a mailbox can be responses. If the message becomes available because time passed, the schedule in Skinner’s split is the timer. A ratio needs the number of responses since the last reinforcer, and an average if one is known.

State the average when people can hear it

A practice set can confirm every answer, or confirm after a changing number of answers. A household can thank every finished chore, or thank after a changing number of chores. State the average when the people in the task can hear it. A hidden count, used so someone will not stop, is a description of the schedule turned into pressure. This page does not recommend that pressure.

Read a spending code as a code

The 2018 means below are category codes for monthly loot-box spend, from never bought through greater than 300.A6.47isnot300. A 6.47 is not 6.47. It is not a shop’s week, and it is not a blind-box receipt. A paid box with a randomized content has the shape of the survey’s object. The code still does not name a mean ratio.

Split a near miss from the count

A claw machine can pay on a changing number of paid tries and also show a near miss, or a grip that looks like skill. The near miss is an extra cue. Sunk Cost Fallacy is staying because of what was already spent. The next unpredictable prize is a different reason to continue. Write both if both are present. Neither one is a diagnosis of a partner.

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Case Study

The counted case is David Zendle and Paul Cairns, PLOS ONE 13(11), 21 November 2018, article e0206767. Zendle is in the Department of Computer Science at York St. John University. Cairns is in the Department of Computer Science at the University of York. They asked whether money spent on loot boxes lined up with problem-gambling severity. A loot box, in their paper, is a virtual item with randomized contents that can be paid for with real money. The survey was online, in English, unpaid, and limited to ages 18 and over. Recruitment used 29 links on Reddit gaming pages. The invitation said the study concerned links between loot boxes and gambling, and that a person could take part without having bought a loot box. They collected 14,182 responses. They removed 3,173 with no age, 872 listed as under 18, two ages above 120, two monthly gambling spends above $1,000,000, nine negative gambling spends, and 2,702 incomplete responses. The analyzed set is 7,422. In that set, 5,793 people (78 percent) had bought a loot box and 1,629 had not. Separate from that, 6,441 (87 percent) had bought some other in-game item with real money and 981 had not. Severity is the Problem Gambling Severity Index: nine questions about the past 12 months, each scored 0 to 3, summed from 0 to 27. Zendle and Cairns use bands of 0, 1 to 4, 5 to 7, and 8 or above, and they label those bands non-problem, low-risk, moderate-risk, and problem gambling. The scoring paper they cite was not re-read. Loot-box spend starts with whether the person had ever bought one. Buyers then answered, in the paper’s wording, approximately how much money in US dollars they spend on loot boxes each month. The choices run from less than 1throughgreaterthan1 through greater than 300, in 13 steps. Never bought is coded 0. The question prints no date range. The means below are mean category codes. The paper says so. A Kruskal-Wallis test on loot-box spend gives χ²(3) = 284.255, p < 0.001, η² = 0.054. The category means are 2.41 for non-problem, 3.67 for low-risk, 4.96 for moderate-risk, and 6.47 for problem gambling. The paper places 2.41 between the 1–1–5 and 5–5–10 labels, 3.67 between 5–5–10 and 10–10–15, 4.96 between 10–10–15 and 15–15–20, and 6.47 between 20–20–30 and 30–30–40. The same test on other microtransaction spend gives χ²(3) = 38.622, p < 0.001, η² = 0.004. The authors say each step up in the severity band comes with higher loot-box spending. Pairwise tests used a Bonferroni threshold of 0.008. Those six cells are not reprinted here. They also say the other-spend gap between the non-problem and problem bands is d = 0.046, more than five times smaller than the loot-box gap between those same bands. The loot-box d for that pair is not printed on this page. The lesson is a graded spending code in this Reddit sample. People in higher severity bands reported a higher loot-box category, and that grade is steeper than the grade for other in-game purchases. Zendle and Cairns say the design cannot show whether buying the boxes leads toward problem gambling, or whether people who already gamble in a harmful way spend more on the boxes. No ratio was programmed. The 6.47 is not a number of tries until a prize.

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Boundaries and Failure Modes

Variable Ratio Reinforcement is the wrong summary in three retellings. Every surprise is called a ratio. A fixed count is said to produce a lower overall rate at the same average. A survey, a claw machine, or an unpredictable partner is treated as proof that the schedule is the most addictive mechanism in the laboratory. The first boundary is the procedure. Humphreys varied the share of trials with a puff. He did not list ratios around a mean. His abstract’s higher extinction level is that eyelid response, across 24 trials, in those students. It is not a classroom quiz, a chore chart, or a relationship. Crossman’s abstract, at ratio sizes 5, 10, 40, and 80, did not find an overall-rate difference among fixed, variable, and random ratios. The difference they report is the longer pause after reinforcement on the fixed ratio. A random ratio, in that comparison, is its own type. A constant chance on every try, such as a box that hits a rare item with a set probability, is closer to that random-ratio arrangement than to a prewritten list with a mean and bounds. Ferster and Skinner’s variable ratio is the list. Calling both by one name hides the pause result, which separated the fixed count from the other two. The second boundary is the loot box as a coded game, and as a receipt. Aaron Drummond and James D. Sauer, Nature Human Behaviour 2, August 2018, pages 530–532, was not re-read. Zendle and Cairns quote their conclusion that loot-box systems share structural and psychological similarities with gambling in the way they encourage and sustain engagement. Drummond and Sauer’s own account, in The Conversation on 28 June 2018 and in their written parliamentary evidence, says they reviewed 22 console and PC games published in 2016 and 2017. Ten of the 22, which they also write as 45 percent, met all five of Mark Griffiths’s criteria as they applied them: money or something of value changes hands, an unknown future event determines the exchange, chance plays a part, staying out avoids the loss, and winners gain at the expense of losers. They judged the fifth criterion by a competitive edge in later play, and they set aside the subjective value of a scarce cosmetic. A cosmetic box can fail that fifth test under their rule and still, in their account, pay the valued item on a varying count. They call that varying count a variable-ratio schedule. Their example of a 10 percent chance, success on average once every ten boxes, with the exact count changing, is an illustration. It is not a drop rate from a named game. Ten of 22 is a coding count. It is not η² = 0.054, and it is not a response rate. The third boundary is the use of the schedule on a person who cannot see the average. A lesson or a household can state the average and still be this schedule. Hiding the average so a student, a worker, or a partner will keep going is the schedule used as pressure. No study on this page counted a partner’s kind acts and cold acts against a mean ratio. Staying is not that count. Leaving does not require the name of a schedule. Overjustification Effect is a drop in later free choice after a promised reward for an activity the person already did. Learned Helplessness is a later drop in action after outcomes the person could not change. Those two rows are not a varying count until the next reinforcer. A correction by Zendle and Cairns, PLOS ONE, 14 March 2019, article e0214167, deletes one conclusions sentence. The sentence said a non-problem versus problem split accounted for 37.7 percent of the variance in loot-box spend. They say it referred to a parametric test in the preprint and was not used in the published paper. That percent is not a result here. The published η² values, 0.054 and 0.004, stay. The sample knew the topic, was recruited on Reddit, and answered in English. The severity window is 12 months. The spend question says “each month” and prints no dates. Those are not one window.

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Common Misconceptions

Three retellings travel with the name. One says steady pay makes people quit. One calls every surprise a ratio. One reads a spending link, or an unpredictable partner, as proof of the most addictive mechanism.
A reinforcer on every response maintains the response while it keeps arriving. Humphreys’s abstract found no acquisition difference between a puff on every trial and a puff on half the trials. The higher level was in extinction, across 24 trials with no puff, after the half-puff training. The paid phase and the stop are two phases. A chore that is thanked every time is not already in extinction.
Skinner’s split is a counter or a timer. A varying wait until the next payoff is available is a variable interval. A varying number of responses is a variable ratio. A constant probability on every try is the random-ratio neighbor in Crossman’s comparison. At the sizes in that abstract, overall rate did not split by type. The longer pause sat on the fixed count. A feed that updates with time has not yet been written as a ratio.
The 2018 category means rise with the severity band, and the authors refuse a direction. A correction removes the 37.7 percent sentence. Drummond and Sauer’s 10 of 22 is a count of games meeting five criteria, not a rate of play. An item in every box is compatible with a rare item on a varying count. Zendle and Cairns quote an ESRB comparison of loot boxes to baseball cards, where there is a surprise and you always get something. That sentence is not a ratio. No partner on this page has a counted mean.
Variable Ratio Reinforcement sits beside a skill cue on a chance task, a belief about the next miss, a promised reward, a prior gain, money already spent, and a later drop after outcomes that could not be changed.

Illusion of Control

Expectancy above the chance once a skill cue sits on a chance task. A grip that looks skillful is that cue. The varying count is a separate line.

Gambler's Fallacy

The belief that a miss makes the next hit due. A series with a mean still allows a long run of misses.

Overjustification Effect

Later free choice falls after a promised reward for an activity the person already chose. That row is not a varying count.

House Money Effect

A greater willingness to take a bet after a gain. The gain is prior. It is not the average number of responses until the next reinforcer.

Sunk Cost Fallacy

Staying because of what was already spent. The next unpredictable prize is a different reason to go on.

Learned Helplessness

Later action falls after outcomes the person could not change. A varying count until a reinforcer is the other direction.

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One-Line Takeaway

Before a habit is called Variable Ratio Reinforcement, write the response, the reinforcer, and the changing count, and do not read a loot-box category mean as proof that the count caused the spending.