Bankroll basics, and why betting systems do not beat the house edge
How to set a gambling budget and limits, what play costs on average, and why the Martingale and other betting systems cannot change the house edge.
By Alexander Jeff Lange
- Level
- Beginner
Key takeaways
- A bankroll is money you can afford to lose completely. Set loss, deposit and time limits before you start.
- Expected loss is total wagered times house edge. 1,000 wagered at a 4% edge costs 40 on average.
- Bet size changes how bumpy the ride is. It does not change the expected cost of each unit you bet.
- The Martingale swaps many small wins for a rare big loss. The average result is still the house edge.
- If your balance is held in a coin whose price moves, a price change can cost more than the bets do.
Every casino game is built so that the casino keeps a small share of all the money bet on it. Nothing in this guide changes that. It covers how to decide what you can afford to lose, how to work out what play costs on average, and why no way of sizing your bets turns that cost into a profit.
What is a bankroll?
A bankroll is the money you set aside for gambling and nothing else. The one rule that matters is that it must be money you can afford to lose completely.
That rules out:
- money for rent, bills, food or debts
- money you have borrowed
- savings you will need later
- money you would feel you had to win back
Treat the bankroll as the price of entertainment, already spent. If losing all of it would cause you a problem, it is too big.
How do you set limits before you play?
Set your limits before you deposit, while you are calm. Do not change them during a session.
Loss, deposit and time limits
- Loss limit. The most you are willing to lose in a session, a week or a month. When you reach it, you stop.
- Deposit limit. The most you will pay in over a set period. This stops a top-up after a loss.
- Time limit. How long you will play. The longer you play, the more you bet in total, and the casino's share is taken from every bet.
What tools do casinos offer?
Look in the account settings for tools that hold you to a limit, and check which ones a casino offers before you deposit. Not every crypto casino has all of them.
| Tool | What it does | Useful for |
|---|---|---|
| Deposit limit | Blocks deposits above an amount you set for a day, week or month | Keeping to a budget |
| Cool-off, also called a time-out | Locks your account for a short period you choose | Taking a break after a bad session |
| Self-exclusion | Locks your account for a long period, or for good | When gambling is causing harm |
| Session reminder | Shows how long you have been playing | Keeping to a time limit |
Self-exclusion at one casino usually covers only that casino. For a wider block, free software such as BetBlocker, from a charity registered in Scotland, blocks gambling sites and apps on your own devices.
Tip
Set limits in your everyday currency, not in coin amounts. A limit of 0.01 of a coin can be a different amount of money next month.
How much does gambling cost on average?
The house edge is the share of every bet that the casino keeps on average. RTP, short for return to player, is the share paid back. The two add up to 100%, so a game with a 96% RTP has a 4% house edge.
The average cost of play is called the expected loss:
Expected loss = total wagered × house edge
Total wagered is your average bet times the number of bets. Here is the example that the house edge calculator opens with. A slot has an RTP of 96%, so its house edge is 4%. You place 500 bets of 2 each.
- Total wagered: 2 × 500 = 1,000
- Expected loss: 1,000 × 4% = 40
Total wagered can be far more than your bankroll, because winnings you bet again count again. If you started with 100, that 1,000 wagered is ten times your money, and, if your money lasts for all 500 bets, the expected loss of 40 is 40% of it.
Note
Expected loss is an average over a very large number of sessions. It is not a forecast for yours. In one session you can finish ahead, or you can lose the whole bankroll.
In maths terms, every bet has a negative expected value: on average it returns less than it costs. For more on these numbers, see house edge and RTP.
Does bet size change what you lose?
Bet size changes the ride. It does not change the expected cost of each unit you bet. Here are three ways to wager 1,000 on a game with a 4% house edge.
| Plan | Number of bets | Bet size | Total wagered | Expected loss |
|---|---|---|---|---|
| Many small bets | 500 | 2 | 1,000 | 40 |
| Fewer, larger bets | 100 | 10 | 1,000 | 40 |
| One large bet | 1 | 1,000 | 1,000 | 40 |
What differs is how far a real result can land from that average. This spread is called variance. With one large bet, everything rides on a single result. With many small bets, the total tends to land closer to the average, though it still swings.
Expected loss only falls if you bet less in total or play a game with a lower house edge. Neither turns it into a profit.
Can a betting system beat the house edge?
No. A betting system is a rule for changing your bet size after wins or losses. The best known is the Martingale: double your bet after every loss, so that the first win covers all the earlier losses and leaves you one unit up.
A Martingale example with the numbers
Take a simple dice game that pays 2× your stake and wins 49.5% of the time. Its RTP is 49.5% × 2 = 99%, so the house edge is 1%.
You start with a bet of 1 unit and double after each loss. Your bankroll, or the table's maximum bet, allows six bets in a row: 1, 2, 4, 8, 16 and 32. That is 63 units in total.
A win at any step leaves you 1 unit up, and you start again at 1. For example, if you win on the fourth bet, you have lost 1 + 2 + 4 = 7 and the win pays a profit of 8. Six losses in a row cost all 63.
| Bet | Stake | Total staked so far | Chance you get this far | Stake × chance |
|---|---|---|---|---|
| 1 | 1 | 1 | 100% | 1.0000 |
| 2 | 2 | 3 | 50.50% | 1.0100 |
| 3 | 4 | 7 | 25.50% | 1.0201 |
| 4 | 8 | 15 | 12.88% | 1.0303 |
| 5 | 16 | 31 | 6.50% | 1.0406 |
| 6 | 32 | 63 | 3.28% | 1.0510 |
The working:
- Chance of losing all six bets: 0.505 × 0.505 × 0.505 × 0.505 × 0.505 × 0.505 = 0.016586, or about 1.66%. That is roughly once in every 60 rounds.
- Chance of ending the round 1 unit up: 100% − 1.66% = 98.34%.
- Average result per round: (0.983414 × 1) − (0.016586 × 63) = 0.983414 − 1.044918 = −0.0615 units.
- Average amount staked per round: add up the last column. 1.0000 + 1.0100 + 1.0201 + 1.0303 + 1.0406 + 1.0510 = 6.1520 units.
- House edge on that amount: 6.1520 × 1% = 0.0615 units.
The two answers match. The system wins 1 unit about 98 times in 100, and it still loses, on average, exactly what the formula says: total wagered times house edge. The Martingale only changes the shape of the results. You get many small wins, paid for by a rare loss that is 63 times larger.
The doubling also grows fast. After ten losses in a row, 1,023 units are gone and the next bet is 1,024. No bankroll is endless, and tables have a maximum bet.
Why does no system fix this?
Every bet on a game with a house edge has a negative expected value. A system only decides how big each bet is and when you place it. Add up bets that each lose on average, and the total loses on average. That holds for the Martingale and for any other progression, including ones that raise bets after wins instead of losses.
Warning
A betting system cannot lower the house edge. A system that raises bets after losses also raises the total you wager, which raises your expected loss, and it can empty a bankroll in a few bets.
What is the gambler's fallacy?
The gambler's fallacy is the belief that a result is "due" because it has not happened for a while. In games where each bet stands alone, such as dice, roulette and slots, it is false. The game has no memory.
In the dice game above, six losses in a row are unlikely before you start: about 1.66%. But once five losses have happened, the chance of losing the sixth bet is still 50.5%, the same as the first. A losing run does not make a win more likely. A winning run does not make a loss more likely.
What do volatility and chasing losses have to do with it?
Volatility describes how much a game's results swing. A high-volatility game pays out rarely but in larger amounts. A low-volatility game pays small amounts more often. Two games can have the same house edge and feel very different. On a high-volatility game, long losing runs are normal. They are not a sign that a win is close.
Chasing losses means raising your bets, or depositing again, to win back what you have lost. It joins two mistakes. It treats a win as due, and it increases the total you wager, which increases the expected loss at the moment you can least afford it. This is what a loss limit is for. When you hit it, the session is over.
Why can the coin price matter more than your bets?
If your casino balance is held in a coin whose price moves, you carry a second risk on top of the games.
Say you deposit coins worth $1,000 and wager $1,000 in total on a game with a 4% edge. The expected loss from the bets is $40. If the coin's price falls 10% while the balance sits at the casino, its value drops by $100 before any bet is counted. A price rise works the other way, but that is not a gambling win. You would have had it without placing a bet.
A stablecoin is a coin designed to track a currency such as the US dollar. Holding your balance in one removes most of this price swing, though stablecoins carry risks of their own.
What are the warning signs of a gambling problem?
These signs are based on the self-check questions used by the support service Gambling Therapy:
- betting more than you can afford to lose
- needing to bet larger amounts to get the same feeling
- going back to try to win back money you lost
- borrowing money or selling things to gamble
- feeling guilty, stressed or anxious about your gambling
- other people telling you that you have a problem
- money problems at home caused by gambling
If any of these fit, stop and talk to someone. These services can help:
- Gambling Therapy: online advice, support forums and support groups for anyone affected by gambling, in many languages. It is a global service from Gordon Moody, a charity registered in England and Wales.
- Gamblers Anonymous: meetings in person, online and by phone, with no fees. You can search its international meetings.
- Gam-Anon: for people affected by someone else's gambling.
Look for a service in your own country too, because a local service knows what help exists near you. Gambling Therapy keeps a list of helplines by country.
Is gambling with crypto legal, and are winnings taxed?
It depends on where you live. Countries, and sometimes regions inside them, have different rules on online gambling, on gambling with crypto, on the minimum age and on tax. This guide is not legal or tax advice. Check the rules that apply to you before you deposit. For checks on the casino itself, see how to check a crypto casino is legit.
Questions
Does the Martingale system work?
No. It wins a small amount most of the time and loses a large amount now and then. In the example above it loses 0.0615 units per round on average, which is exactly the house edge on the money staked.
How big should my bankroll be?
There is no right size. The test is that you could lose all of it without it affecting your bills, your debts or the people who depend on you. If you are not sure, make it smaller.
Do smaller bets reduce my losses?
Only if they reduce the total you wager. Expected loss is total wagered times house edge. On the same game, 500 bets of 1 cost half as much on average as 500 bets of 2. But 1,000 bets of 1 cost the same as 500 bets of 2.
Where can I get help if gambling is getting out of control?
Gambling Therapy and Gamblers Anonymous both offer free support and both work across many countries. Also look for a helpline in your own country.
Keep reading
Guide
House edge and RTP: what the numbers really mean
RTP is the share of all bets a game pays back. House edge is the share it keeps. Here is how to turn either one into an expected loss, and why one session can look nothing like it.
Guide
How to check a crypto casino is legit before you deposit
A licence logo proves nothing by itself. How to check the licence, the company, the ID rules, the games and the terms before you send any money.
Guide
Wagering requirements explained, with the maths
What a wagering requirement is, how much you really have to bet to clear a bonus, what that betting costs on average, and the terms that change the answer.