Money Management & Position Sizing: Martingale, Anti-Martingale, Kelly and Risk of Ruin

Two traders can take exactly the same trades and end the year in opposite places. The entries, the stops and the targets are identical; the only difference is how much each one puts on every trade. That decision — money management, or position sizing — controls how fast an account grows, how deep its drawdowns go and, above all, whether it survives the losing streaks every strategy eventually runs into.

The reason is that losses and gains are not symmetric. After losing a fraction L of an account, the gain needed to get back to where you started is:

• Recovery gain = L ÷ (1 − L)

A 10% loss needs an 11.1% gain to recover, a 25% loss needs 33.3%, a 50% loss needs 100% and a 75% loss needs 300%. The deeper the hole, the steeper the climb — which is why every sizing method in this guide is, at heart, a way of keeping drawdowns shallow enough to climb out of. The Drawdown Calculator shows the recovery gain for any loss.

This guide compares the four sizing families traders and bettors actually use — fixed fractional, Kelly, martingale and anti-martingale — with the formulas behind each, worked examples you can reproduce in our calculators, and the risk-of-ruin numbers that are usually left out of the sales pitch.

Fixed fractional sizing risks the same percentage of the current balance on every trade. It is the default for professional traders because it automatically shrinks positions during a drawdown and grows them as the account grows.

• Dollar risk = Balance × Risk %
• Position size = Dollar risk ÷ Distance to stop (as a fraction of entry)
• Balance after n straight losses = Balance × (1 − Risk %)ⁿ

Worked example

A $10,000 account risking 1% has $100 of risk per trade. With a stop 2% below entry, the position is $100 ÷ 0.02 = $5,000. If the stop is hit ten times in a row, the account is $10,000 × 0.99¹⁰ = $9,044 — a 9.6% drawdown that needs a 10.6% gain to recover. Risk 5% per trade instead and the same streak leaves $5,987 (−40.1%); at 10% per trade it leaves $3,487 (−65.1%), which needs a 187% gain to recover.

How long can you survive a losing streak?

The number of consecutive losses that takes the account to a 50% drawdown is ln(0.5) ÷ ln(1 − Risk %): about 69 losses at 1%, 35 at 2%, 14 at 5% and just 7 at 10%. That matters because long streaks are not rare. A useful rule of thumb is that the longest losing streak you should expect over N trades is about ln(N × p) ÷ ln(1 ÷ q), where p is the win rate and q the loss rate. With a 55% win rate over 500 trades that is ln(275) ÷ ln(2.22), about 7 losses in a row — survivable at 1–2% risk, crippling at 10%.

The Position Size Calculator turns a risk percentage and stop distance into a lot size, and the Bankroll Management Calculator projects a fixed-percentage plan against fixed stakes and Kelly over many bets.

No sizing rule can turn a losing strategy into a winning one. Before choosing how much to risk, check that the trades have a positive expectancy. Measured in multiples of the amount risked (R):

• Break-even win rate = 1 ÷ (1 + R), where R = reward ÷ risk
• Expectancy per trade = p × R − (1 − p)

With a 2:1 reward-to-risk ratio the break-even win rate is 33.3%; at 1.5:1 it is 40%; at 1:1 it is 50%. A strategy that wins 45% of the time at 2:1 earns 0.45 × 2 − 0.55 = +0.35 R per trade — at 1% risk on $10,000, about $35 per trade on average. Run your own numbers in the Risk Reward Calculator.

Expectancy tells you whether to trade; sizing tells you how much. Every method below assumes the first answer is yes. If it is no, the only correct position size is zero.

John Kelly showed in 1956 that, for a repeated bet with a known edge, there is a single fraction of the bankroll that maximises long-run growth. For a bet that pays b-to-1 and wins with probability p:

• Kelly fraction f* = p − (1 − p) ÷ b

Worked examples

Trading: a setup that wins 45% of the time at 2:1 (b = 2) gives f* = 0.45 − 0.55 ÷ 2 = 17.5% of the account at risk per trade. Betting: a bet at decimal odds 2.10 (b = 1.10) that you believe wins 50% of the time gives f* = 0.5 − 0.5 ÷ 1.1 = 4.55% — $91 on a $2,000 bankroll. The Kelly Criterion Calculator does this for any odds format.

Why almost nobody bets full Kelly

Full Kelly maximises growth but is brutally volatile. In Thorp's continuous approximation, the chance that a full-Kelly bettor's bankroll ever falls to a fraction x of its starting value is x itself: a 50% chance of being cut in half at some point. Betting a fraction c of Kelly changes that to x^{(2/c − 1)} — at half Kelly the chance of ever halving drops to 0.5³ = 12.5%, while the growth rate is still c × (2 − c) = 75% of the full-Kelly rate. Betting more than Kelly is strictly worse: at twice Kelly the expected growth rate falls to zero even with a real edge.

The biggest practical problem is that p is an estimate. Overestimate your edge and "full Kelly" is really over-betting. That is why half or quarter Kelly is the common choice, and why Kelly is best used as a ceiling on position size rather than a target.

The martingale increases the stake after every loss so that one win recovers all previous losses plus the original profit. In trading it appears as averaging down: adding a larger position each time price falls by a set step. With a base size s and multiplier m:

• Size at level n = s × mⁿ⁻¹
• Capital required through level n = s × (mⁿ − 1) ÷ (m − 1)

Worked example — roulette

Start at $10 on red (18 of 38 pockets win, so a single spin loses 52.6% of the time) and double after each loss. Eight straight losses need $10 + $20 + … + $1,280 = $2,550. That run happens only 0.59% of the time per sequence — but each successful sequence wins just $10. The expected value per sequence is 0.9941 × $10 − 0.0059 × $2,550, about −$5.07. The small, frequent wins hide a rare loss that is 255 times larger, and the house edge never goes away. Over 100 sequences the chance of at least one wipe-out is 44.6%; over 200 it is 69.3%.

Worked example — averaging down a crypto position

Buy $100 of BTC at $40,000, then double the position every 5% drop for four levels: $100 at $40,000, $200 at $38,000, $400 at $36,100 and $800 at $34,295. Total capital required: $1,500. The average entry falls to $35,570, so a bounce of only 3.7% from the last level gets you back to break-even — that is the appeal. But a 15% stop below the final average sits at $30,234, a 24.4% fall from the first entry, and costs $225 — more than twice the size of your first position. If your account holds only $1,000, you cannot place the fourth entry at all: the plan runs out of money exactly when it needs the most.

The Martingale Calculator shows the size, capital required and exposure at every level and, once you enter your account balance, flags the first level you cannot fund.

The honest verdict

A martingale does not change the expected value of the underlying bets; it only reshapes the distribution into many small wins and one catastrophic loss. With a negative or zero edge, ruin is certain given enough sequences — this is the classic gambler's ruin result. With a positive edge you would do better simply sizing up the edge directly. If you use any averaging-down plan, fix the maximum number of levels in advance, make sure the balance covers every one of them, and accept the stop at the last level.

The anti-martingale does the opposite: it increases size after wins and returns to the base size after any loss. Losses therefore always happen at the smallest size or, deeper in a streak, are partly paid for by profit already banked. Trend followers use the same idea when they pyramid into a position that is working.

• Size at streak level n = s × mⁿ⁻¹
• Profit banked before level n = the sum of (size_i × average win %) for i = 1 … n − 1
• Chance of reaching level n = pⁿ⁻¹

Worked example

Base $100, 2× after each win, four levels, 5% average win, 3% average loss, 55% win rate. Sizes run $100, $200, $400, $800. Before the fourth trade you have banked $5 + $10 + $20 = $35, so losing the $800 position (−$24) still leaves the streak $11 in profit. You reach the fourth level only 0.55³ = 16.6% of the time — the big positions are rare, and they are funded by the market.

The house-money cushion breaks if the multiplier is too aggressive. At 3× the third position is $900; a 3% loss costs $27 against only $20 banked, so the streak now dips into your own capital. It also breaks without enough capital: with a $400 account the fourth position ($800) is bigger than the $435 you would hold at that point. The Anti-Martingale Calculator shows the banked profit and capital required at each level and flags the first one your balance cannot cover.

Anti-martingale is not a free lunch either: it cannot create an edge, and if wins do not cluster, the extra size mostly adds variance. It is, however, the only one of the two "progression" systems that keeps the worst-case loss bounded by design.

Risk of ruin is the probability of losing so much that you can no longer continue. For a simple game where every trade wins or loses the same fixed dollar amount, the classic formula is:

• Risk of ruin = ((1 − A) ÷ (1 + A))^U
• A = edge = p − q (win probability minus loss probability)
• U = number of risk units in the account (balance ÷ amount risked per trade)

With a 55% win rate (A = 0.10) the base is 0.9 ÷ 1.1 = 0.818. Risking 10% of the starting balance per trade (U = 10) gives a 13.4% chance of ruin — roughly one trader in seven goes bust with a genuine edge. Risking 5% (U = 20) cuts it to 1.8%; risking 2% (U = 50) to 0.004%. Halving the bet size squares the risk of ruin (0.134² is about 0.018), which is why small risk per trade is the cheapest insurance in trading.

Two caveats keep the formula honest. First, it assumes even-money trades of fixed size; with fixed fractional sizing an account never literally reaches zero, so "ruin" is better defined as a drawdown you could not tolerate — say 50%. Second, when A is zero or negative the result is 1: ruin is certain given enough trades. That is the mathematical core of every warning about martingale systems on negative-edge games. For a fuller picture of path risk, run your trade statistics through the Monte Carlo Simulator.

1. Prove the edge first. Estimate win rate and reward-to-risk from a meaningful sample, and check the break-even win rate in the Risk Reward Calculator.
2. Cap risk per trade. 0.5–2% of the balance for trading; 1–3% of the bankroll per bet for sports betting. Use the Kelly Criterion Calculator as an upper bound and bet a fraction of it.
3. Plan the bad streak. Know how many losses take you to a 20% and a 50% drawdown, and what gain recovers each — the Drawdown Calculator answers both.
4. Compare staking plans before you commit. The Bankroll Management Calculator projects fixed stakes, fixed percentage and Kelly side by side.
5. Fund every level of a progression. If you scale in or out, enter your balance in the Martingale Calculator or the Anti-Martingale Calculator and never plan a level the account cannot pay for.
6. Write the rules down and stop changing them mid-streak. Most blow-ups come from raising size to win back losses — an unplanned martingale.

None of these numbers predict the market. They describe what your account can survive, which is the one part of trading you fully control.