Bankroll and Swings
How far blackjack results swing over an hour, a session and a year, and how much to bring, calculated from the house edge and variance.
Blackjack has a small house edge and a lot of short-term luck. Knowing how big the swings are is the difference between a session budget that makes sense and one that runs out after an hour of ordinary bad cards.
This page takes the two numbers that describe the game, the house edge of 0.57 percent and a standard deviation of 1.13 bets per hand, both calculated by our engine for perfect basic strategy in a standard shoe game, and turns them into dollars. The examples use a $25 bet at 60 hands an hour, a typical pace at a full table.
Results over time at $25 a hand
The range column is where 90 percent of players finish; one in twenty does better than the top of it and one in twenty does worse than the bottom.
| Playing time | Hands | Average result | Typical swing (1 SD) | 90% of results | Chance of being ahead |
|---|---|---|---|---|---|
| 1 hour | 60 | -$9 | $219 | -$369 to +$351 | 48.4% |
| 4 hours | 240 | -$34 | $438 | -$754 to +$686 | 46.9% |
| 20 hours | 1,200 | -$171 | $979 | -$1,781 to +$1,439 | 43.1% |
| 100 hours | 6,000 | -$855 | $2,188 | -$4,455 to +$2,745 | 34.8% |
| 1,000 hours | 60,000 | -$8,550 | $6,920 | -$19,933 to +$2,833 | 10.8% |
Why the swings dwarf the edge in the short run
Over a four hour session the average loss is about $34, but the typical swing is about $438. Luck is roughly 13 times larger than the edge at that length. That is why a good night and a bad night say almost nothing about whether you played well, and why a winning session is common even though the game favours the house.
As the hours pile up, the average loss grows in a straight line with the number of hands, while the swing grows only with its square root. Eventually the edge wins. After a few hundred hours, the chance of being ahead has fallen a long way, and over a lifetime of steady play it heads toward zero. No betting pattern changes that, because every bet carries the same edge.
How much to bring for a session
A simple way to size a session budget is to cover the bottom of the 90 percent range. For four hours at $25, that is about $754. With that amount, about 19 sessions in 20 will end before the money does, on these assumptions. Doubles and splits mean you occasionally need two or three times your base bet on the table at once, so keep a little in reserve beyond that.
The figures scale directly with the bet. At $10 a hand, divide every dollar figure by 2.5; at $50, double them.
The rules matter more than the budget
The edge in these tables is for a good game. At a table that pays 6 to 5 on blackjack the edge roughly triples, as shown on the house edge by rules page, and every average loss above roughly triples with it. Mistakes do the same: the cost of mistakes page shows how quickly a few habits outweigh the entire edge of a well played game.
What the swings cannot do
Progressive betting systems, such as doubling your bet after a loss, rearrange the swings without changing the edge. They turn many small wins into an occasional large loss, and the large loss arrives exactly when a table limit or your budget stops the progression. The average result per dollar bet stays where the rules and your play put it.
Set the session budget before you sit down, treat it as the cost of the entertainment, and stop when it is gone.
Session budget by bet size and length
This table extends the same calculation to other bets and session lengths. Each figure covers the bottom of the 90 percent range, so about 19 sessions in 20 finish before the budget does.
| Bet per hand | 1 hour budget | 2 hour budget | 4 hour budget |
|---|---|---|---|
| $10 | $147 | $210 | $302 |
| $25 | $369 | $526 | $754 |
| $50 | $737 | $1,052 | $1,508 |
| $100 | $1,474 | $2,105 | $3,017 |
The budget does not double when the session doubles in length. Swings grow with the square root of the number of hands, so a four hour session needs well under four times the budget of a one hour session.
Frequently asked questions
What are my chances of leaving a one hour session ahead?
About 48 percent, on these assumptions. The house edge barely matters over an hour; luck decides nearly everything.
Why use 1.13 for the swing of a hand?
It is the standard deviation of one round in units of your bet, calculated by our engine. It is a little above 1 because doubles and splits sometimes put two or more bets at stake.
How accurate are these ranges?
They use the normal approximation, which is very good over hundreds of hands and reasonable over an hour. Real sessions have slightly heavier tails because of doubles, splits and blackjack payouts.
Does a bigger bankroll improve my odds?
No. It only lets you ride out more swings. The expected loss per hand stays the same, and playing longer increases the total you expect to lose.
How these numbers were made: every figure on this page is calculated, not quoted. Our blackjack engine works out the exact expected value of every hand for an infinite deck, which lands within about a tenth of a percent of a 6 to 8 deck shoe. It assumes the dealer checks for blackjack, one split per hand, and split aces receiving one card each.
A note on risk. Basic strategy reduces the house edge to roughly half a percent. It does not remove it. Nothing here is gambling advice or a prediction of results. If gambling has stopped being entertainment, the National Problem Gambling Helpline is 1-800-522-4700, or ncpgambling.org.