Originally published on the Betkyo Journal. Drafted with AI assistance; every figure was checked against the game engine source and approved by a human editor.
Walk in with $100 and leave with $200 or nothing: a single all-in bet at ×1.98 gets you to $198 just under half the time. The same game at $1 a bet reaches $200 11% of the time, and at Chinchiro’s 2.6% edge, half a percent. Here is the whole table — why small bets lose more often than big ones, why a 1-in-100 long shot doubles you more often than a coin flip at the same stake, and what the house edge really buys the house.
In short: With a 1% edge even-money bet (our dice at 50%, ×1.98) one all-in bet reaches $198 49.995% of the time; betting to reach $200 at a fixed stake, the chance is 42.2% at $10 a bet, 25.9% at $2, 11.2% at $1 and 1.6% at 50 cents. The house edge is paid per bet, so the more bets a session takes, the more of it you pay: at $1 a bet the session lasts about 7,600 bets on average. At a 2.6% edge (Chinchiro) $1 bets double you 0.55% of the time; at 2.78% (Sic Bo Big/Small) 0.41%. Odds matter too: at $1 a bet on dice, a 1-in-100 shot at ×100 doubles you 41% of the time against the coin flip’s 11%, because it settles the question in far fewer bets. The only number that does not change is the average: every path returns 99 cents on the dollar wagered.
The question
Most sessions have an unspoken target: double it, or go home. Put a number on it and the question becomes exact — with $100, a fixed stake and a known edge, what is the chance of reaching $200 before reaching $0? This is the gambler’s-ruin problem, and because our games publish their win chances and multipliers, it can be answered for each of them without a single assumption.
Engine-verified. Win chances and payouts are read from the engines. Dice (OriginalBaseDiceService.kt): 9,999 equally likely results, multiplier = (1 − house edge) ÷ win chance floored to two decimals, so “over 50.00” wins 4,999 of 9,999 (49.995%) and pays ×1.98, “over 66.67” wins 33.32% at ×2.97, “over 90.00” wins 9.99% at ×9.90 and “over 99.00” wins 0.99% at ×100.00. Koban Flip pays ×1.96 on a fair coin. Sic Bo Big and Small (SicboEngine.kt) pay ×2 on 105 of 216 rolls. Chinchiro (ChinchiroDerivation.kt) returns 97.38% and is treated as an even-money bet won 48.69% of the time. Doubling chances come from replaying 200,000 sessions per cell with the engine’s exact steps — a win adds stake × (multiplier − 1), a loss removes the stake — until the bankroll is $200 or more, or too small for the next bet (±0.1 point). The fair coin and the Chinchiro model use the even-money gambler’s-ruin closed form, (1 − (q/p)ᴺ) ÷ (1 − (q/p)²ᴺ), which the replay reproduces.
The stake is the lever
Take the simplest case: dice at a 50% target, ×1.98, a 1% edge. Bet the whole $100 once and you are at $198 or $0 with the chance of winning, 49.995% — as close to doubling as a ×1.98 bet can get in one step. Bet smaller, aiming for $200, and two things happen — the session takes more bets, and every bet hands over 1% of the stake on average. The edge is a toll per bet, and small stakes pay it more often.
Dice at 50% (×1.98, 1% edge): $100, bet until $200 or $0
| STAKE | STAKE AS % OF $100 | CHANCE OF DOUBLING | BETS ON AVERAGE |
|---|---|---|---|
| $100, one bet | 100% | 49.995% (to $198) | 1 |
| $10 | 10% | 42.18% | 100 |
| $5 | 5% | 38.62% | 399 |
| $2 | 2% | 25.92% | 2,343 |
| $1 | 1% | 11.22% | 7,634 |
| $0.50 | 0.5% | 1.64% | 19,137 |
Target $200 or more; bust when the bankroll can no longer cover the stake. On a fair coin paying ×2 every row would read 50%. The gap between 50% and each figure is what the 1% edge costs over the number of bets the session takes to resolve.
Read the last two rows twice. At $1 a bet, $100 doubles about one time in nine; at 50 cents, about one time in sixty. Nothing about the game changed between the rows — only how many times you let the house take its 1%. “Play small to make it last” is true: the session lasts 7,600 bets at $1. It just almost never ends at $200.
The edge compounds through the bets
A bigger edge does the same thing faster. Here are our even-money-style games at two stakes, with the chance of doubling $100.
Doubling $100, by game and stake
| GAME | EDGE | $10 A BET | $1 A BET |
|---|---|---|---|
| Fair coin (for reference) | 0% | 50.00% | 50.00% |
| Dice at 50%, ×1.98 | 1.00% | 42.18% | 11.22% |
| Koban Flip, ×1.96 | 2.00% | 37.63% | 1.51% |
| Chinchiro (97.38% return) | 2.62% | 37.28% | 0.55% |
| Sic Bo Big / Small, ×2 | 2.78% | 36.53% | 0.41% |
Chinchiro’s payouts are not all even money (×3, ×4, ×6 for specials); it is modelled here as an even-money bet with the same return, which is slightly pessimistic for the long-shot payouts and does not change the picture.
At $10 a bet the games are a few points apart. At $1 a bet a 1% game gives you one chance in nine and a 2.8% game one in 240. The difference between a 1% and a 2.8% edge looks like 1.8 points on a payout table; over a session of a thousand bets it is the difference between a long shot and no shot. This is also why the question “which game has the lowest edge?” matters far more to a small-stakes player than to someone making one bet.
The odds change the answer
Everything above is even money. Dice lets you pick the odds at the same 1% edge, and that changes the doubling chance in a way most players would not guess.
Dice at a 1% edge: doubling $100 at different odds
| TARGET | WIN CHANCE | PAYS | $10 A BET | $1 A BET |
|---|---|---|---|---|
| Over 50.00 | 49.995% | ×1.98 | 42.18% | 11.22% |
| Over 66.67 | 33.32% | ×2.97 | 43.47% | 25.86% |
| Over 90.00 | 9.99% | ×9.90 | 40.76% | 42.93% |
| Over 99.00 | 0.99% | ×100.00 | 9.54% | 41.47% |
Replayed with the engine’s multipliers; at $1 a bet the 1% target reaches $200 with two hits (the second one landing before 100 straight misses) and busts after 100 misses in a row.
At $1 a bet the coin flip doubles you 11% of the time and the 1-in-100 shot 41% of the time — nearly four times as often, at the same edge. The reason is the same toll: a long shot settles the question in far fewer bets, so the house collects its 1% far fewer times before you are at $200 or $0. At $10 a bet the order flips, because ten misses at ×100 is a bust before the first hit is likely.
None of this moves the average. Every row of every table returns 99 cents per dollar wagered; the long shot only changes how the loss is distributed — many sessions that end at $0 and a few that end at $200, instead of a slow grind to the same place. If the goal is “double or nothing”, the long shot is the better tool. If the goal is time at the table, it is the worst.
What this is not
It is not a strategy. There is no stake, odds or game in these tables that reaches 50%, because the edge is paid on every bet and no sequence of bets avoids it — the martingale and its cousins only move the loss into a rare large one. What the tables do is make the trade visible: betting bigger buys a better chance of the target at the cost of a shorter session; betting a long shot buys the same thing at the cost of a wilder one.
The honest use of the numbers is to pick the session you actually want before it starts. A player who wants an hour of play at $1 should know that the hour is the product and $200 is not; a player who wants to double should know that one bet at 49.995% to $198 is the best price on the board and anything slower is paying for the privilege of waiting. Our risk of ruin piece covers the same trade in prose; this one puts the figures on it, game by game, from the engines that pay them.
FAQ
What are the odds of doubling $100 at a casino?
At a 1% edge on dice (×1.98 at 50%): one all-in bet reaches $198 49.995% of the time; betting to $200 at a fixed stake, 42% at $10 a bet, 11% at $1, 1.6% at 50 cents. The edge is paid per bet, so the more bets the session takes, the lower the chance. At a 2.6–2.8% edge the $1-a-bet chance falls below 1%.
Is it better to bet big or small to double my money?
To reach a target, bigger: one bet at 49.995% beats any sequence of smaller bets at the same edge, because every extra bet pays the house again. Smaller bets buy time at the table, not a better chance of the target.
Do long-shot bets give a better chance of doubling?
At small stakes, yes. On dice at $1 a bet from $100, a 1-in-100 target at ×100 doubles you 41% of the time against 11% for the 50% target, because it settles in far fewer bets. At $10 a bet the order reverses. The average return is 99% either way.
How many bets does a session take?
On dice at 50% with $100: one bet all in, about 100 bets at $10, about 7,600 at $1 and about 19,000 at 50 cents before the bankroll reaches $200 or can no longer cover a bet.
Which game gives the best chance of doubling?
The lowest edge at the stake you intend to use: our 1% games (dice, limbo) ahead of Koban Flip at 2%, Chinchiro at 2.6% and Sic Bo Big/Small at 2.8%. At $1 a bet the gap is one chance in nine against one in 240.
Sources
- Betkyo engine sources for the win chances and multipliers: OriginalBaseDiceService.kt (9,999 results; multiplier = (1 − edge) ÷ chance floored to 2dp), Koban Flip (×1.96), SicboEngine.kt (Big/Small ×2 on 105 of 216 rolls), ChinchiroDerivation.kt (97.38% return)
- Calculation written for this article: 200,000 replayed sessions per cell with the engine’s exact win chances and multipliers (win +stake × (multiplier − 1), loss −stake; stop at ≥ $200 or when the next bet cannot be placed), giving the doubling chance to ±0.1 point and the mean session length; the even-money gambler’s-ruin closed form for the fair coin and the Chinchiro model (Sic Bo: closed form 36.45% / 0.38% vs replay 36.53% / 0.41%)
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