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Dice Gambling Explained: You Pick the Odds, Not the Edge

In June 2013 one dice game generated an estimated 51% of all Bitcoin transactions by count — and about 5% of the value moving across them. Reading the first number as though it were the second is the error everyone repeats, and the same class of error is still inside the game today: the modern slider dice that descends from it runs a roll with 10,001 possible outcomes while its win-chance display divides by 10,000. Dice has been mis-measured twice, once by history and once by its own interface, and it is the only casino game that hands you the tools to check both.

What is dice gambling, and who sets the odds?

Dice is the crypto-casino game where the player chooses their own win probability before every roll: you drag a slider to a target number, the interface shows you the win chance that target implies, and the payout multiplier is derived from that chance rather than chosen by the house. One roll settles it. There is no cash-out decision, no board to clear, no curve to watch.

That makes dice structurally unique among common casino games. On a slot the paytable is fixed. On roulette the numbers are fixed. On crash you pick when to leave, and on Mines you pick how many bombs to hide — but only on dice do you type in a probability and have the machine quote you a price for it. Two decimal places of slider travel is the whole product.

Which is why dice is the cleanest available demonstration of a result the rest of this cluster asserts: you can choose your variance freely, across roughly three orders of magnitude, and the house edge will not move by a hundredth of a percent. Not because we ran a simulation, but because it falls out of one line of algebra you can check in your head. The game also has something none of its siblings has — a documented and consequential history — so we start there.

2012: how did one dice game come to generate half of all Bitcoin transactions?

Because SatoshiDice settled every bet on the Bitcoin blockchain itself, and by June 2013 it was doing that about 12,400 times a day — two transactions per bet, on a network then handling roughly 48,400 transactions a day in total. The arithmetic is not subtle: 12,400 bets generating 24,800 transactions out of 48,400 is 51%, as Lightspeed Venture Partners set out on 23 August 2013.

The mechanic was as simple as the numbers. You sent bitcoin directly to one of a set of vanity addresses, each carrying its own fixed odds — send between 0.001 and about 20 BTC to 1dice7fUk, Blockworks records, and you had 24.4% odds of instantly quadrupling your coins. The site combined your wager transaction’s hash with a secret it held, ran a 512-bit SHA-2, and turned the result into a “lucky number” between 0 and 65,535; you won if the number fell under your address’s threshold. The Bitcoin Wiki records the house edge as 1.90%, i.e. payouts of 98.1%. Losers were sent a single satoshi back, Blockworks notes, so they could see the bet had settled.

A footnote for anyone auditing that description, and it is on theme. The Bitcoin Wiki says the “first four bytes” of the hash become the lucky number, and also that the lucky number runs 0 to 65,535. Both cannot be true: four bytes span 0 to 4,294,967,295, while 0 to 65,535 is exactly two bytes. The wiki does not reconcile it, and we are not going to guess which half is the typo. The 0–65,535 range is the figure every account of the game uses and the one the odds tables are built on, so that is the one we carry. Flag it anyway, because it is the same habit this whole page is about: a range and a count of outcomes quoted past each other, in the primary reference, about the game’s own random number.

That last detail is the one that mattered historically. Every losing bet generated an outbound transaction of one hundred-millionth of a bitcoin. The service was, by design, a machine for writing very small transactions to a shared public ledger very quickly.

It also had the numbers to make that a network-scale problem. The Bitcoin Wiki states that within weeks of launch the site “became responsible for more Bitcoin transactions than all other uses of Bitcoin combined.” By 16 May 2013 CoinDesk was reporting the site’s own running totals at over 4.6 million bets and more than 3.6 million bitcoins wagered. Blockworks puts the first fifteen months at over 5.3 million bets, of which around 3.9 million won.

Two of those cumulative counters can be differenced, and doing so corroborates the June rate independently. Between CoinDesk’s 4.6 million bets on 16 May 2013 and Blockworks’ 5.3 million at the fifteen-month mark in late July, the site added roughly 700,000 bets in about 69 days — on the order of 10,000 bets a day, against the 12,400 Lightspeed measured for June (16Best analysis; both source totals are reported as “over” a rounded number, so read this as an order of magnitude, not a rate). The service did not spike and fade. It ran at a five-figure daily rate for more than a year.

Was SatoshiDice really half of Bitcoin?

Half of Bitcoin’s transactions, yes, for a period in 2013. About a twentieth of Bitcoin’s money. Those are different claims and the histories routinely merge them. This is the single most repeated error about dice, and it is worth pulling apart properly, because the confusion had real consequences for the Bitcoin protocol.

The Lightspeed figures give both sides. June 2013: SatoshiDice averaged 10,500 BTC a day of bet volume against a network-wide 213,800 BTC a day of transaction value.

Federal Reserve economists Anton Badev and Matthew Chen reached the same place from the other direction. Their FEDS working paper 2014-104 — dated 7 October 2014 and published that December — studies Satoshi Dice specifically as the largest online gambling service using Bitcoin, and reports that about half of all Bitcoin transactions in the period involved less than the equivalent of US$100, with most of those small-value transactions related to the gambling service.

Our own arithmetic corroborates that from the operator side, on precisely the Fed’s basis: per transaction, not per bet.

2013: how did dice become a flashpoint in the block-size argument?

Because a service producing half the network’s transactions and a twentieth of its value looks, from a node operator’s seat, exactly like spam — and some miners started refusing to mine it. The Bitcoin Wiki’s article on the service still states flatly that it “spams the p2p network and blockchain with useless data.” That is not neutral encyclopedic language, and it is a fair record of how contested this was.

The pressure was structural, not merely rhetorical. Luke Dashjr’s Eligius mining pool ran a transaction test it called “is notorious” on top of the standard checks; Mike Hearn’s contemporaneous write-up defines a notorious transaction as one paying an address the pool operator regarded as “non-transactional data spam,” and the pool simply ignored those transactions rather than mining them. We have not found a primary source that puts SatoshiDice’s addresses on that list, so read it as the climate the site operated in rather than a documented act against it. What is on the record is Blockworks’ account of the same months: some miners briefly enforced smaller block size limits, which it says has been suggested may have been to avoid handling relatively large volumes of SatoshiDice data. A single game had become an argument about what the ledger was for, and that argument became the scaling debate.

The service moved out from under the pressure in stages. It closed to US players in May 2013, citing legal concern (CoinDesk, 16 May 2013). Erik Voorhees sold his stake on 18 July 2013 for 126,315 BTC. In October 2013 the new owner launched a session-based game called Tribute, played off the blockchain; CoinDesk’s report of that launch is where the “between a quarter and a half of all block chain transactions” description comes from. By 2014 SatoshiDice itself offered off-chain, session-based bets, which the Bitcoin Wiki describes as a response to longstanding calls to stop abusing the blockchain.

The regulatory coda arrived on 3 June 2014, when the SEC announced a settled action against Voorhees for offering unregistered securities in SatoshiDice and FeedZeBirds: full disgorgement of $15,843.98 in profits plus a $35,000 penalty, and a five-year bar on crypto securities offerings. The first large crypto-gambling business and the first crypto securities enforcement were the same company.

The dice timeline, 2012 to 2026

Fourteen years took dice from a set of Bitcoin addresses with fixed odds to a continuous slider with 10,001 outcomes — and shrank the house edge from 1.90% to about 1.01%. Everything else about the game is unchanged: you still pick a probability and the house still prices it.

Table: compiled from Bitcoin Wiki, Lightspeed Venture Partners (23 Aug 2013), CoinDesk (16 May, 18 Jul and 31 Oct 2013), Bitcoin Magazine (28 Jul 2013), the SEC’s 3 June 2014 announcement, Badev & Chen (FEDS 2014-104), Blockworks, and current Stake and Wolfbet game listings. USD conversions are the figures the contemporaneous reports used, not restatements at a single FX date. The 2026 row is the only one not tied to a dated event: the multiplier endpoints come from third-party listings of Stake’s game and from one documented settled bet, discussed below.

What is the one formula behind every dice multiplier?

Pick a win chance p and the game offers you a multiplier m = RTP ÷ p, so your expected return is p × m = RTP — the same number at every setting. That cancellation is the entire economics of the game, and unlike almost every claim in gambling coverage it can be verified against published figures rather than taken on trust.

Readers of our crash gambling explainer will recognise the shape immediately, and we want to be explicit that this is not a new discovery. On crash the probability of reaching a multiplier is P = RTP ÷ m and the payout is m, so P × m = RTP and every cash-out target returns an identical 0.970 of stake on a 97% game. Dice is the same identity read from the other side: there you choose m and the game computes p, here you choose p and the game computes m. Mines reaches it through a hypergeometric survival probability, Plinko through a binomial one. Four games, one algebraic fact.

What dice adds is legibility. On the other three the probability is a consequence of a setting you chose for other reasons — a mine count, a risk level, a cash-out nerve. On dice the probability is the setting, printed on screen in percent, before you commit. If the flat-edge result were ever going to fail, this is the game where you would catch it.

Does moving the slider change the house edge?

No. A 98% win chance and a 0.01% win chance both return 0.990 of stake at a stated 99% RTP — while the standard deviation of that return moves by a factor of 700. Read the table below across, not down: the expected-return column never changes, and the last column changes by nearly three orders of magnitude.

Variance is the honest definition of “riskier” here, and it has a closed form. A roll returns RTP ÷ p with probability p and nothing otherwise, so the standard deviation of return per unit staked is SD = RTP × √((1 − p) ÷ p) — the same expression we use on Mines, because it is the same two-outcome bet.

Table: 16Best analysis. Offered multiplier = 0.99 ÷ p; standard deviation = 0.99 × √((1−p)/p); volatility indexed to the 98% row. Win chances shown are the figures a Stake-style interface displays; the 1.0102x and 9,900x endpoints match published Stake Dice limits. The next section explains why the true expected return is very slightly below 0.990.

Set that against the rest of the cluster and dice sits in the middle of a wide family. High-risk Plinko carries about 19.8x the standard deviation of low risk at the same 99% RTP; Mines spans 11,172x between its tamest and wildest settings. Dice’s 700x sits between them, and it is the only one of the three where the dial is labelled in the currency that actually matters — probability — rather than in bombs or risk tiers.

One consequence worth stating because the language obscures it: on dice there is no such thing as a “safer” bet in the sense players mean. A 98% win chance loses 1% of every dollar staked. A 0.01% win chance loses 1% of every dollar staked. What the 98% setting buys is the near-certainty of losing that 1% slowly and the near-impossibility of a large win; what the 0.01% setting buys is the reverse. Neither is cheaper.

Is a 99% RTP dice game really 99%?

Not quite — on the Stake-lineage roll it is 98.9901%, because the roll has 10,001 equally likely outcomes while the win-chance display divides the range by 10,000. This is a one-outcome discrepancy that survives every provably-fair check, applies uniformly at every slider position, and is worth about two cents an hour. It is also the reason the dice house edge is not the round number every guide prints.

The mechanism is documented, not inferred. The published game-event translation for a Stake-style dice roll is Math.floor(float × 10001) ÷ 100, which maps the interval onto the integers 0 to 10,000 and then onto the roll values 0.00 to 100.00 in steps of 0.01. Shuffle’s help centre spells out the count — the values with up to two decimal places, plus zero, give 10,000 + 1 = 10,001 possible outcomes — and ProvablyFair.me documents the same 10,001 constant for the Primedice implementation. Our own provably fair explainer records the same 10,001-outcome mapping.

Not every operator has this problem, and the comparison is the cleanest way to see it. Wolfbet states a 1% house edge and a roll range of 0.00 to 99.99 — exactly 10,000 outcomes — and quotes 50% at 1.98x, 20% at 4.95x, 10% at 9.90x and 2% at 49.50x, all of which are 0.99 ÷ p to the digit. On that grid a displayed 50% really is 50%.

Table: roll ranges and outcome counts from the operators’ own published material (Shuffle’s provably-fair game-events documentation for the 10,001-outcome formula; Wolfbet’s dice page for the 0.00–99.99 range and 1% house edge). The RTP and house-edge columns are 16Best analysis, computed as offered multiplier × true probability. Both operators advertise the same 1% edge.

What happens at the far end of the slider?

At the minimum 0.01% win chance the game pays 9,900x on a genuine 1-in-10,001 roll — about 50 hours of continuous play between expected wins at 200 rolls an hour. Every row below has the same expected return, and the “true chance” column is where the widely quoted 1-in-10,000 goes wrong.

Table: 16Best analysis, computed on the 10,001-outcome roll grid. Winning outcomes = 10,000 − 100t; true chance = outcomes ÷ 10,001; offered multiplier = 0.99 ÷ displayed chance; rolls between wins = 1 ÷ true chance. Rolls-per-hour is our assumption, not a measured or published play rate.

The bottom row happened. On 9 August 2024 a Stake player rolled over 99.99, the result came up 100.00 — the single winning outcome — and the bet paid 9,900x for $24,004.13 from a stake reported as $2.42 in XRP. Note that $24,004.13 ÷ 9,900 = $2.4247, so the stake was a shade above the rounded figure; that is a crypto-to-USD conversion artefact, and the multiplier is the part that reproduces exactly.

There is a design point buried in that row that separates dice from its siblings. Dice imposes its ceiling on the input: the slider will not go below a 0.01% win chance, so the identity holds all the way to the edge and the top setting still returns 98.99%. Mines does the opposite where a cap applies — it lets you configure a 5,148,297x outcome and then truncates the payout, which is what collapses the effective RTP of its headline settings to a fraction of a percent. Capping the input preserves the edge; capping the output destroys it.

What would a maximum-payout cap do?

Wherever a site limits the payout per bet to fewer times the stake than the slider can offer, the probability stops cancelling and the effective RTP collapses on exactly the settings the game markets hardest. This is a conditional calculation — it applies only where such a limit binds — but the mechanism is worth having, because it is the same trap as a bonus max-cashout cap, which our no-deposit bonus analysis models in detail.

Table: 16Best analysis, computed as true probability × min(0.99 ÷ displayed chance, 1,000) on the 10,001-outcome grid. This is illustrative and conditional: the 1,000x limit is a stated assumption, not a figure published by any operator named on this page. Stake’s Dice has demonstrably paid 9,900x, so no limit of this kind binds there. Always read the specific game’s maximum-payout term.

The practical reading matches what we found on Mines: a payout limit is harmless at ordinary settings and severe at the extreme ones, and it never shows up in the advertised RTP figure. On dice the arithmetic is unusually easy to run yourself, because you can read your win chance straight off the interface.

Does Martingale work on dice?

No — and on dice the doubling ladder stops working three steps earlier than on Mines, because the coin-flip setting pays 1.98x rather than 2.00x. A 1% shortfall sounds trivial. Compounded against a bet that doubles every round, it turns the recovery win negative at the 7th consecutive loss.

Table: 16Best analysis, doubling from a $1 base at a displayed 50% win chance paying 1.98x. True loss probability on the 10,001-outcome grid is 0.50005, so the chance a doubling sequence reaches N straight losses is 0.50005^N. Cumulative staked is 2^N−1; the net column is 1 − 0.02 × 2^N−1. The $1,023 at the tenth loss is deliberately the same figure as on our crash page — the doubling sequence does not care which game you attach it to.

One further note specific to dice, and it undercuts the appeal directly. The reason players reach for a 50% win chance is that it feels like a coin flip. It is not: the true chance is 49.995% and the payout is 1.98x. If you want an actual doubling of your stake you have to set the win chance to 49.5%, because 0.99 ÷ 0.495 = 2.00 exactly. The slider will happily give you either. Neither changes the expected return by a hundredth of a cent.

How much does dice cost per hour?

Expected loss per hour = stake × rolls per hour × house edge — about $2.02 an hour at $1 a roll and an assumed 200 rolls an hour. There is no published figure for how many dice rolls players complete per hour, so 200 is our stated assumption: a roll is one click with no round timer, which puts it faster than crash and slower than a turbo Plinko drop. Treat the hourly numbers as scaling, not measurement.

Table: 16Best analysis, computed as stake × decisions × edge. Decisions-per-hour rates are assumptions consistent with our crash, Plinko, Mines and RTP pages, not measured play rates. The blackjack and slot rows reproduce the $5-stake figures published on our RTP page ($1.75/hour and $120/hour). Comparisons hold only at equal stake per decision.

Make it physical. At $1 a roll and 200 rolls an hour you are pushing $200 of turnover through the edge every hour from a stake that never once exceeds a dollar. Three hours a night, four nights a week works out at about $105 a month at that stake and about $525 a month at $5 a roll — and that is the average, arriving as a long grind of small results interrupted by swings whose size depends entirely on where you left the slider.

What does provably fair prove about a dice roll?

It proves the roll was fixed before you bet and can be reproduced from the seeds — and it proves nothing whatsoever about the multiplier the roll is settled against. Dice is the game where that gap is easiest to see, because we have just measured it.

The mechanism is short. The casino commits to a hashed server seed in advance; you supply a client seed; a nonce increments with each bet. HMAC-SHA256 over those inputs produces bytes, the first four become a float, and the float becomes a roll via floor(float × 10001) ÷ 100. Rotate your seed, get the original server seed revealed, and you can regenerate every roll you played. Our provably fair gambling explainer walks the verification through with real HMAC output rather than an illustration, so we will not re-derive it here.

What matters on this page is the boundary of the proof:

• What it guarantees: the roll was determined before your bet and could not be moved once your stake was in. Every roll is independent, and no sequence of previous results shifts the next one — which disposes of every “the site is due” and “switch sides after three losses” heuristic in one line.
• What it does not guarantee: that the win chance printed next to the slider is the true probability, or that the multiplier next to it is 99 ÷ that probability. The verification inspects the roll, never the paytable wrapped around it. The 10,001-versus-10,000 discrepancy in the section above is a fully verifiable roll settled against a slightly generous displayed probability — and it passes every fairness check the operator offers, because there is nothing wrong with the roll.

Our provably-fair page puts the general form of this well: the proof verifies the dice, not the croupier. Dice gives that sentence a number.

Why do dice numbers disagree?

Because six different things get quoted under the same words, and every conflict we hit while researching this page falls into one of them. Learn the six and you can audit any dice page — this one included — in about a minute.

• Share of transactions versus share of transaction value. The headline that made dice famous is a count. In June 2013 SatoshiDice was 51% of Bitcoin transactions and about 4.9% of Bitcoin value. Blockworks writes “more than half of all bitcoin transactions by volume”; the figure is a transaction count, and “volume” in Bitcoin discussion usually means value. CoinDesk’s October 2013 formulation — “between a quarter and a half of all block chain transactions” — is the more defensible one because it is a range and it names the basis. There is a second trap one level down, which we walked into before we re-read the source: Lightspeed’s 10,500 BTC is stated as including both the bet and the payout leg, so grossing it up for payouts a second time double-counts, and sets a two-legged numerator over a network total that is already counting every leg. The tell is that it roughly doubles the answer. If a page tells you a dice game was half of Bitcoin without saying half of what, it has copied the claim rather than checked it.
• Win chance quoted inclusive or exclusive of the target number. The off-by-one that changes every multiplier. A roll of 0.00 to 100.00 has 10,001 outcomes; a roll of 0.00 to 99.99 has 10,000. On the first grid a displayed 50% is really 49.995% and a stated 99% RTP is really 98.9901%. On the second it is exact. Both operators advertise a 1% house edge. The number to check is the roll range, not the RTP claim.
• RTP published by the operator, assumed by a writer, or estimated by a tracker. Wolfbet publishes a 1% house edge on its dice page. Stake’s Dice is widely listed at 99% RTP, and we corroborate the listing structurally rather than on trust: the multiplier limits of 1.0102x and 9,900x are 0.99 ÷ p at both ends of the slider. Be careful even so, because the third-party listings do not agree with each other about where the slider stops — SportsGambler describes Stake’s range as a 2% to 98% win chance topping out at 49.50x, while other guides list 0.01% and 9,900x. The documented 9 August 2024 payout settles that one: a roll-over-99.99 bet paid 9,900x, so the slider does reach 0.01%, and the listing that stops at 49.50x is describing something narrower than the live game. Trackers can also read low — one comparison places Roobet’s dice around 96% against Stake’s 99% — and we cannot settle that from outside. Where a tracker and an operator disagree, believe the operator’s own game-info panel on the day you look. The historical figure is different again: SatoshiDice ran a 1.90% edge per the Bitcoin Wiki, which Blockworks reports as a 1% to 1.9% range because different wager addresses carried different odds.
• Multipliers quoted gross or net of the stake. A 1.98x payout returns 1.98 units on a 1-unit stake — a profit of 0.98. Dice calculators and strategy pages mix “payout” and “profit on win” freely, and the two differ by exactly 1.00x. If a chart shows 0.98x at a 50% win chance rather than 1.98x, it is a profit chart, and every expected-value sum built on it will be wrong by one stake.
• House edge quoted per roll or per hour. The ~1% is a property of a single roll, charged once at settlement. It is not a rate per hour, and it is not charged per unit of slider travel. Turning it into an hourly figure requires a rolls-per-hour rate that nobody publishes — ours is an assumption of 200, stated every time we use it.
• Maximum win quoted as a multiplier or as a currency amount. A 9,900x ceiling and a fixed maximum payout in dollars are different constraints. The first is the end of the slider and leaves the edge intact; the second truncates the payout and, as the cap table above shows, can cut effective RTP to a tenth of the advertised figure on the extreme settings.

Key takeaways

• Dice was mis-measured twice, and both times it was a counting error. In 2013 the count of its transactions got read as a share of Bitcoin’s money — 51% versus about 4.9%, a 10.4-fold gap. Today the count of its roll outcomes gets read as 10,000 when it is 10,001.
• One formula runs the modern game: offered multiplier = RTP ÷ win chance, so expected return = win chance × multiplier = RTP at every setting. This is the same identity as crash’s P = RTP ÷ m, read from the other end — not a new discovery, but the clearest possible statement of it, because on dice the probability is the thing you choose.
• Stake’s published multiplier limits prove its own RTP constant. 1.0102x at 98% and 9,900x at 0.01% both equal 0.99 ÷ p to five significant figures.
• The true edge on the Stake-lineage roll is 1.0099%, not 1.00% — 9,900 ÷ 10,001 = 98.9901% RTP, uniform at every slider position. Two cents an hour at $1 a roll, and invisible to every provably-fair check, because the roll itself is honest.
• The slider buys volatility, not value: a 700-fold range in standard deviation, from 0.141 at a 98% win chance to 98.995 at 0.01%, at an identical expected return. Plinko’s dial is 19.8× wide, Mines’ is 11,172×.
• The 9,900x maximum is 1 in 10,001, not 1 in 10,000 — roll over 99.99 wins only on 100.00, about 50 hours of continuous play per expected win at 200 rolls an hour. A real payout at that exact multiplier was reported on 9 August 2024.
• Dice caps the input, not the output — which is why its top setting still returns 98.99%, where a payout limit would cut it to a tenth of that. That is the difference between a floor on win chance and a Mines-style ceiling on multiplier.
• Martingale fails earlier here than anywhere else in the cluster. The 1.98x coin-flip payout turns the recovery win negative at the 7th consecutive loss, having staked $127; by the 10th it has staked $1,023 and a win still leaves you $9.24 down.
• The one game that lets you set your own odds is the one that proves setting them changes nothing. Three orders of magnitude of choice, one unmoving edge. That is not a strategy problem to be solved; it is the reason there is no strategy.

Frequently asked questions

What is the dice game in a crypto casino?

Dice is a single-roll game in which the player sets a target number on a slider, the interface shows the win chance that target implies, and the payout multiplier is derived from that win chance. A number is then rolled once, typically between 0.00 and 100.00, and the bet is settled. It descends from SatoshiDice, launched on 24 April 2012, which settled bets directly on the Bitcoin blockchain.

How is the dice multiplier calculated?

The offered multiplier is the return-to-player divided by the win chance you selected. On a 99% RTP game a 50% win chance pays 0.99 divided by 0.50 = 1.98x, a 10% win chance pays 9.90x and a 2% win chance pays 49.50x. Because expected return is win chance times multiplier, the two terms cancel and every setting returns the same fraction of stake.

Does changing the win chance change the house edge in dice?

No. Every win chance returns the same fraction of stake, because the multiplier is derived directly from the probability you chose. What changes is volatility: the standard deviation of return per unit staked runs from about 0.141 at a 98% win chance to about 98.995 at 0.01%, a 700-fold range at an identical expected return. No slider position is a better or worse deal than any other.

Is a 99% RTP dice game really 99%?

Not quite, on the Stake-lineage roll. That roll runs from 0.00 to 100.00 in steps of 0.01, which is 10,001 equally likely outcomes, while the displayed win chance divides the range by 10,000. Since the multiplier is 99 divided by the displayed win chance, the true return is 9,900 divided by 10,001, or 98.9901%, and the house edge is 1.0099% rather than 1.00%. The discrepancy is uniform at every setting and worth about two cents an hour at $1 a roll. Wolfbet, whose roll runs 0.00 to 99.99 and therefore has exactly 10,000 outcomes, delivers its stated 1% edge exactly.

What is the maximum win on crypto dice?

On Stake the slider stops at a 0.01% win chance, which pays 9,900x. On the 10,001-outcome roll grid that setting is rolling over 99.99, which can only be beaten by 100.00, so the true odds are 1 in 10,001 rather than the commonly quoted 1 in 10,000. At an assumed 200 rolls an hour that is about 50 hours of continuous play between expected wins. A real 9,900x payout of $24,004.13 was reported on Stake on 9 August 2024, on a roll that came up 100.00.

Did SatoshiDice really account for half of all Bitcoin transactions?

Half of the transactions, for a period, but not half of the money. Figures published by Lightspeed Venture Partners in August 2013 put SatoshiDice at about 12,400 bets a day in June 2013, generating roughly 24,800 of the network's approximately 48,400 daily transactions, or 51% by count. Its 10,500 BTC of daily bet volume against 213,800 BTC of daily network value was about 4.9%, and that 10,500 already includes both the bet and the payout leg, so there is no larger value share hiding behind it. CoinDesk described the service in October 2013 as having accounted for between a quarter and a half of all blockchain transactions at its peak. Federal Reserve economists documented the same pattern in working paper 2014-104: most small-value Bitcoin transactions in the period they studied were the gambling service, and SatoshiDice's average on-chain transaction was about 0.42 BTC, roughly a tenth of the network average that month.

Does Martingale work on dice?

No, and it fails earlier on dice than on the related games. The coin-flip setting pays 1.98x rather than 2.00x, so the net result of recovering on the next roll is 1 minus 0.02 times 2 to the power of the streak length minus one, which turns negative at the seventh consecutive loss. By the tenth loss a $1 base has staked $1,023 and a recovery win still leaves the sequence $9.24 down. A ten-loss run arrives about once every 10.2 hours for a player who resets on every win, at an assumed 200 rolls an hour.

Sources

• Bitcoin Wiki — Satoshi Dice (launch 24 April 2012; 1.90% house edge; lucky number 0–65,535; blockchain spam; 2014 off-chain bets)
• Lightspeed Venture Partners — At least half of all Bitcoin transactions are for online gambling (23 August 2013; June 2013 daily bets, BTC volumes and network transaction counts)
• Anton I. Badev and Matthew Chen, Board of Governors of the Federal Reserve System — Bitcoin: Technical Background and Data Analysis (FEDS Working Paper 2014-104, dated 7 October 2014, published December 2014; Satoshi Dice as the largest online gambling service using Bitcoin; about half of transactions under US$100 equivalent)
• CoinDesk — Gambling site SatoshiDice sells for $11.5 million (126,315 BTC) (18 July 2013)
• Bitcoin Magazine — SatoshiDice Sold For $12.4 Million (28 July 2013; the conflicting USD figure on the same 126,315 BTC)
• CoinDesk — Bitcoin gaming site SatoshiDice closes to US players (16 May 2013; “extensive legal counsel”; running totals of over 4.6 million bets and more than 3.6 million bitcoins wagered)
• CoinDesk — New SatoshiDICE owner launches Tribute game (31 October 2013; “between a quarter and a half of all block chain transactions”)
• US Securities and Exchange Commission — SEC Charges Bitcoin Entrepreneur With Offering Unregistered Securities (3 June 2014; 13 million shares for 50,600 BTC, ~$722,659; $15,843.98 disgorgement plus $35,000 penalty)
• Blockworks — Bitcoin gambling: How SatoshiDice picked up where Satoshi left off (5.3 million bets and ~3.9 million wins in 15 months; 1–1.9% edge; the 1dice7fUk address at 24.4% odds)
• Shuffle Help Center — Provably Fair — Game Events (dice roll = Math.floor(floats × 10001) ÷ 100; 10,001 possible outcomes)
• ProvablyFair.me — Dice (Primedice) verification (the same 10,001 constant)
• Wolfbet — Bitcoin Dice & Crypto Dice (1% house edge; roll range 0.00 to 99.99; 50% at 1.98x, 20% at 4.95x, 10% at 9.90x, 2% at 49.50x)
• SportsGambler — How to Play Stake Dice Game (99% RTP and 1% house edge; minimum multiplier 1.0102x at a 98% win chance; 100-sided roll. Note this listing describes the slider as stopping at a 2% win chance and 49.50x, which the documented 9,900x payout contradicts)
• HugeStakes — Stake Originals Dice max win pays out over $24K (9 August 2024; roll over 99.99, result 100.00, 9,900x, $24,004.13 from $2.42 in XRP; “the highest possible roll is 100.00”)
• Mike Hearn — Double spending, and how to make it harder (the Eligius pool’s “is notorious” transaction check and its “non-transactional data spam” definition)
• StatMuse Money — Bitcoin price, June 2013 (June 2013 closing prices ranging from about $94 to about $123, used as a range rather than a single conversion date)