Guide 8 of 8 / 7 min read
Turn $1,000 Into $5,000? Here's What the Odds Actually Say
$1,000 chasing $5,000
- Bet
- $1,000
- Reach
- 16.0%
- Lose
- 84.0%
At $1,000 a bet on red or black, the $1,000 stake reaches $5,000 in 16.0% of attempts and is lost in 84.0%. Stopping at $2,000 instead: 47.4% reach it, 52.6% lose the stake.
"How do I turn $1,000 into $5,000" is one of the most common real questions a player asks, and every honest answer it gets online is a moral one: don't chase, set a budget, walk away. All true, and none of it is the actual answer to the question that was asked. This page gives the mathematical one instead.
Written and reviewed by Alexander Korsager · last reviewed October 6, 2026 · corrections
The short version
The two goals are opposed
Reaching the target and keeping the stake pull in opposite directions: the staking pattern that helps one the most hurts the other the most.
Smaller bets lower the odds
Spreading the same stake across more, smaller bets makes the target less likely, because it exposes the stake to the house edge over far more bets.
Ask about risk of ruin
A fixed stake cannot answer how to hit a number. It can answer what bankroll keeps the risk of ruin under a threshold you accept.
The maths turns out to say something sharper than "the odds are against you." It says the two things a target-chasing player wants at once, reach the target and don't lose the stake, are not merely hard to balance. They are mathematically opposed: the staking pattern that gives you the best chance at one is the staking pattern that most reliably destroys the other. That is a provable statement about the game, not advice about how to play it.
01 / 05
What "reaching a target" actually asks
Strip the question to its bones: a fixed stake, a fixed bet size, a negative-edge even-money wager, played until the stake is gone or a stated target is reached, whichever comes first. That is exactly the two-outcome gambler's-ruin problem this site's own Risk of Ruin Calculator computes in its quit-at-goal mode, and every figure on this page is that same formula, coinRuin, evaluated at different bet sizes for the same $1,000 stake.
- Stake gone
- $0
- Start
- $1,000
- Target
- $5,000
Play stops at whichever end comes first.
The answer depends on exactly three things: the probability of winning one bet, how many bet-sized units the stake is divided into, and how many more units away the target sits. Nothing else moves it, not confidence, not a system, not how the money is spread across different games. For a fixed target expressed in dollars, shrinking the bet size only does one thing to those three numbers: it turns the same $1,000 into more, smaller units, and turns the same distance to the target into more of them too.
$1,000 bets1 unit of stake, 4 to go
$250 bets4 units of stake, 16 to go
$100 bets10 units of stake, 40 to go
The $1,000 stake Still to win to reach $5,000
02 / 05
Grinding it out is close to hopeless
Take the plainest version of the question: turn $1,000 into $2,000, doubling the stake, on an even-money outside bet at American roulette. Red and black pay even money and win 18 times in 38 (a 5.26% house edge), so a single spin has a 47.4% chance of doubling the money outright.
- Wins, 18 of 38
- 47.4%
- Loses, 20 of 38
- 52.6%
- House edge
- 5.26%
The table below runs that same $1,000 stake through both targets this page discusses, side by side: the $2,000 double above and the page's own $5,000 target, at progressively smaller bet sizes, so the money is spread across more spins instead of fewer.
Chance of reaching the target before losing the $1,000 stake
| Bet size | Reach $2,000 | Reach $5,000 |
|---|---|---|
| $1,000 bets | 47.4% | 16.0% |
| $500 bets | 44.8% | 12.6% |
| $250 bets | 39.6% | 7.3% |
| $100 bets | 25.9% | 0.97% |
| $50 bets | 10.8% | 0.02% |
| $25 bets | 1.5% | < 0.0001% |
| $10 bets | 0.0027% | < 0.0001% |
| $5 bets | < 0.0001% | < 0.0001% |
† Not a rounded-down small number: at this bet size the arithmetic itself returns exactly zero, because the true chance is smaller than the smallest difference from 1 a computer’s floating-point numbers can represent. It is not literally impossible to reach the target, only indistinguishable from impossible at this precision.
Same $1,000 stake, same American roulette even-money bet (47.4% win probability per spin) for every row. Reaching $5,000 means covering four times the distance from the stake that $2,000 does, so ruin sits nearer than the goal at every bet size, and the $5,000 column starts lower and disappears faster as bets shrink. Methodology and sourcing below.
03 / 05
The play that maximizes your odds is the play that risks the most
This is not a coincidence of roulette specifically. It is a proven result: on a negative-expectation game, the staking strategy that maximizes the probability of reaching a target before going broke is bold play, staking as much as possible on as few bets as possible (Lester Dubins and Leonard Savage, How to Gamble If You Must: Inequalities for Stochastic Processes, 1965). Small, careful bets feel like the patient route to a target. They are the route that makes the target least likely.
The clean case in the table above proves it exactly: a single all-in bet reaches the target with probability equal to the bet's own win probability, 47.4% here, because reaching a $2,000 target from $1,000 in one spin simply is winning that one spin. No staking pattern spread across more bets does better than that, and every one of them shown above does worse, in proportion to how many bets it spreads the money across.
The spin itself
18 ÷ 3847.4%
The formula at 1 unit of stake, 1 to go
$1,000 to $2,00047.4%
The formula returns the spin's own chance exactly, with nothing added.
State plainly what this is not: it is not advice to bet everything on one spin. It is the opposite kind of statement, a reductio. The bet that best serves "reach the target" is the bet that leaves the least room for anything to go right if it doesn't land, which is exactly the trade the next section makes explicit.
- Reach $2,000
- 47.4%
- Lose all $1,000
- 52.6%
A fact about the formula, not a way to play: the larger share is the whole stake gone.
04 / 05
Why the two goals are mathematically opposed
A target-chasing player is really holding two goals at once: reach the target, and don't lose the stake getting there. The table above shows those two goals move in opposite directions as the same dial turns. Fewer, bigger bets push the probability of reaching the target up and leave a total loss one or two unlucky spins away. More, smaller bets feel safer because no single spin threatens much, but they push the probability of reaching the target toward zero, and they do it by exposing the stake to the house edge over far more trials, not fewer. Grinding does not trade a worse shot at the target for a better shot at keeping the money. On a negative-edge game played out this way, it is closer to guaranteeing neither: even at 47.4%, the best case on the table, roughly one in two single-spin attempts still fail to double, and every finer split fails far more often than that, while still eventually losing the stake if the target is never hit.
$1,000 bets
47.4% reach52.6% lose
$250 bets
39.6% reach60.4% lose
$100 bets
25.9% reach74.1% lose
$25 bets
1.5% reach98.5% lose
Every run ends one way or the other, so the two shares always fill the bar.
The shape does not change for a harder target, and the table's own two columns show why it changes something else instead: how fast. Turning $1,000 into $5,000 needs four net wins at a fixed $1,000 bet rather than one, so its column starts lower than the $2,000 column at every bet size in the table, not just the small ones, and it disappears faster as bets shrink: by the bet size where chasing $2,000 is still very much alive, chasing $5,000 already reads as close to zero. A steeper target does not change which direction the dial points. It only moves how quickly grinding it out reaches practically zero.
$1,000 bets, chance of reaching
$2,00047.4%$5,00016.0%$100 bets, chance of reaching
$2,00025.9%$5,0000.97%
$5,000 sits 4 stakes away from $1,000. $2,000 sits 1.
There is no point on this dial, no bet size between the two extremes, that gets a better shot at the target and a better shot at keeping the stake at the same time. Every step toward one is a step away from the other.
05 / 05
The honest version of the question
If the real goal is protecting a bankroll rather than hitting a number, the mathematically sound move is to flip the question around. Instead of asking what gets me to a target, ask what minimum bankroll keeps my risk of ruin under a threshold I'm willing to accept, at the bet size and edge I'm actually playing. The Risk of Ruin Calculator solves exactly that version, and the Bankroll Calculator sizes a session against it. Both answer a question a fixed stake can actually satisfy. "How do I turn $1,000 into $5,000" is not that question, and no staking pattern answers it for you.
Check yourself
Can any bet size get you there?
1 / 3
One all-in $1,000 bet on red or black at American roulette reaches $2,000 how often?
2 / 3
The same $1,000 is split into $100 bets instead. What happens to the chance of reaching $2,000?
3 / 3
Which bet size gives a better chance at the target and a better chance of keeping the stake?
Pick an answer to see the working. Nothing is scored or saved.
Try it
Put your own numbers through it
- Risk of Ruin Calculator Find the odds of going broke
- Bankroll Calculator Size your stake per bet
- House Edge Comparison The house edge on every common casino bet, side by side, and what it costs you per hour.
- Prediction Market Exit-Cost Calculator See what closing a Kalshi or Polymarket position pays right now, after the spread and trading fee.
- Gambling Loss Tracker Turn a loss into real turnover
FAQ
- Is there any bet-sizing strategy that reaches a target and protects my stake?
- No. The maths shows the two are opposed, not just hard to balance. The staking pattern that gives the best chance of reaching a target is the same one that puts the whole stake at risk on the fewest possible bets, and the pattern that spreads the stake over many small bets is the one that makes reaching the target least likely. Every point between those two extremes trades one for the other; none escapes the trade.
- Does this mean I should bet everything on one spin to reach a target?
- No, and that reading is exactly what this page exists to head off. Bold play maximizing the probability of reaching a target is a mathematical fact about that one narrow question, not a recommendation. Reaching a target is only half of what a player actually wants; the other half is not losing the stake, and the bet that best serves the first goal serves the second worst.
- Why does grinding it out in small bets feel safer if the odds are worse?
- Because it spreads the risk over enough decisions that variance can look kind for a long stretch, and each individual bet is small enough that any single loss barely registers. Neither of those changes the destination. More decisions at a fixed negative edge means more total exposure to that edge, which is why the probability of ever reaching a stated target falls as the bet size shrinks, however a given session happens to feel while it's underway.
Where these figures come from
Every reachGoal figure in the bet-size table (both the $2,000 and $5,000 columns) is derived at render time by src/guides/figures/target-chasing-data.ts, which computes 1 - coinRuin(p, B, G) from this site's own Risk of Ruin Calculator (coinRuin, src/tools/risk-of-ruin/math.ts), the same function that tool's quit-at-goal panel calls and math.test.ts pins against the textbook two-barrier gambler's-ruin identity. Nothing in the table is hand-typed: target-chasing-data.test.ts re-derives every cell independently against coinRuin on every build, so the printed figures cannot drift from the formula that produces them. The win probability p = 18/38 = 47.368% for American roulette red/black is the complement of the 5.26% edge this site's House Edge tool and the casino house edge guide both publish for the same bet (edge = 1 - 2p on an even-money wager). Both columns set B = 1000/unit for each bet size in the table (a $100 bet is 10 units of stake); the $2,000 column sets G = 1000/unit and the $5,000 column sets G = 4000/unit, at the same unit sizes. The single-bet bold-play case (B = G = 1) returning exactly p, rather than an approximation of it, follows directly from the formula: a one-barrier-away two-outcome random walk is the same event as the single bet itself. Cells the table marks with a dagger are not rounded down: at those bet sizes 1 - coinRuin(...) computes to exactly 0 in double-precision arithmetic, because the true value is smaller than the gap between 1 and the next representable number below it, not because the chance is mathematically zero. The bold-play optimality theorem in 'The play that maximizes your odds is the play that risks the most' is a cited published result, not something this site's code derives: Lester E. Dubins and Leonard J. Savage, How to Gamble If You Must: Inequalities for Stochastic Processes (McGraw-Hill, 1965), the standard reference for the result that bold play maximizes the probability of reaching a goal before ruin on a sub-fair game.
Verification
Checked against this site's own coinRuin function and math.test.ts (risk-of-ruin) for every reachGoal figure in this guide's table; Dubins and Savage (1965) for the bold-play optimality theorem, cited rather than re-derived: agrees on the bet-size table's sixteen reachGoal values across both columns, the $5,000-target figures (16.0% at $1,000 bets, 0.97% at $100 bets, computing to exactly zero by $10 bets), and the single-bet case returning exactly p (0.473684...) rather than an approximation of it (verified by target-chasing-data.test.ts, which re-derives every cell independently against coinRuin in src/tools/risk-of-ruin/math.ts on every build, cross-checked for the underlying formula by math.test.ts's existing pins of the same function, 2026-09-27).
Know the risk
- Reading "bold play maximizes your odds" as a recommendation to bet everything at once. It is a reductio, stated to show why the target-chasing impulse is self-defeating, not a strategy to adopt: the same bet that raises the probability of reaching a target the most is the bet that leaves the least room for anything to go right if it doesn't land.
- Reading the falling table as meaning smaller bets are riskier in general. For stake preservation over a bounded number of trials, smaller bets are the calmer ride. The claim here is narrower and different: smaller bets make reaching a stated target less likely, not more, because they multiply how many times the stake is exposed to the same negative edge.
- Treating this page's exact percentages as universal. They are computed for one specific game, bet and target (American roulette, an even-money outside bet, $1,000 to $2,000 or $5,000); the shape of the result (fewer bigger bets favor the target, more smaller bets favor neither) holds generally on any negative-edge even-money game, but the numbers themselves change with the edge, the bet size and the target, and are reproducible for other inputs on the Risk of Ruin Calculator's quit-at-goal panel.
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