How to read a dice simulation

The panel next to the chart updates while the run is going. In order:

• Rolls: the number of bets placed so far, with the total you asked for underneath. A run can stop early when the script calls stop() or the next bet is larger than the balance.
• Win rate: wins divided by rolls, with the win and loss counts and the chance the script was betting at. Compare it with that chance. At 49.5% over 10,000 rolls the win rate has a standard deviation of about 0.5 percentage points, so a gap of that size is ordinary luck and says nothing about the strategy.
• Net profit: balance plus vaulted funds minus the starting balance, with the same figure as a percentage of the start (ROI). If the script calls resetstats(), profit is re-based to 0 at that point.
• Balance and Vaulted: the funds still in play, and the funds moved out of play with vault().
• Wagered: the sum of every stake. It is the volume the house edge works on, so wagered × edge / 100 is the expected loss of the run.
• Max drawdown, max win streak, max loss streak and current streak: covered below.
• Elapsed and Speed: wall-clock time and rolls per second. They describe your machine, not the strategy.

The engine tracks equity, which is the balance plus everything vaulted. Max drawdown is the largest drop in equity from any earlier peak to a later low point, shown as a negative number and as a percentage of the starting balance. Because vaulted funds count toward equity, moving money to the vault is not a drawdown, and a loss of the active balance after vaulting is measured against the full peak.

Drawdown shows how bad the run got on the way, which the final profit does not. A run that ends +5% after being down 60% at one point needed most of its bankroll to get there. With slightly different rolls it would have gone bankrupt.

Max loss streak is the longest run of consecutive losing bets. For progressions it is the most important number on the panel, because ruin comes from one streak longer than the bankroll can pay for. Compare it with the max survivable streak N from the calculator.

The longest losing streak in n rolls is typically close to log(n · p) / log(1 / q), where p is the win chance and q = 1 − p (Schilling, "The Longest Run of Heads", The College Mathematics Journal, 1990). At 49.5% over 10,000 rolls that is about 12.5 losses. The classic martingale with a base bet of 1/10,000 of the balance survives N = 13, which is why its risk of ruin over 10,000 rolls is about 49.7%. A run whose max loss streak stayed well below N never met the streak that ends the strategy.

The current streak shows positive numbers for wins and negative numbers for losses. The max win streak matters for positive progressions such as Paroli, which raise the bet after wins.

Efficiency appears on logged runs, the dashboard and the leaderboard. It is net profit divided by the size of the max drawdown:

A value of 2 means the run made twice its worst peak-to-trough drop. A value below 1 means it went through a drop larger than its final profit. Negative values are runs that lost money. It rewards smooth equity curves and penalizes runs that got lucky after a deep hole.

The Auto-Tuner ranks parameter sets with a related fitness score, efficiency multiplied by the natural log of the rolls survived, so that a run which lasts longer scores higher at the same efficiency.

Every simulation uses a server seed, a client seed and a nonce, and the rolls follow from them. When you submit a run to the leaderboard, the server replays the script with the same seeds and settings and checks that the numbers match. A run that matches is marked verified.

The server replays runs of up to 250,000 rolls. Longer runs are still saved to your account but cannot be verified or ranked. A verified run shows that the numbers are real for those seeds. It does not show that the strategy will do the same on other seeds.

One run is one sample from a wide distribution. The expected value and variance guide shows that a flat bettor at 49.5% is still ahead after 10,000 rolls in a noticeable share of cases, purely by chance. Any strategy will produce some winning runs.

A smooth, rising balance chart can hide several things. Check these before trusting it:

• The run was shorter than the expected wait for a fatal streak, so the streak never had a chance to appear.
• The max loss streak was below the survivable streak, which means the strategy was never tested at its weak point.
• The max drawdown was close to the starting balance, so the run nearly ended before it recovered.
• The wagered amount was large, so the expected loss was large too and the profit came from luck on top of it.
• Other seeds give different results. One seed is one draw, and the stress test shows the others.

The risk of ruin guide shows how to estimate the chance of the streak that the run did not meet.

All guides are listed on the Learn hub. Other articles on dice math:

• Risk of Ruin Explained: Formula for Dice Betting
• Dice House Edge Explained: Payout & Expected Loss
• Expected Value and Variance in Dice Betting
• Dice Bankroll Management: Bet Sizing & Stop Loss