Jacks or Better, over the long run.
The paytable changes the odds. Luck changes the session. See how often 100,000 simulated sessions finish ahead—and how widely their results spread.
Precomputed Monte Carlo · 6 exact paytable models · Optimal play · Updated October 5, 2026
Where sessions finish
Net profit or loss after 100,000 hands. Each step is an observed histogram bin.
All 100,000 sessions per selected paytable are included, including the tails. Curves may overlap. Changing the wager scales dollars only; it does not resample the experiment.
A closer look at 9/6
99.5439% theoretical RTP · 100,000 observed sessions
- Expected net
- -$570Theoretical long-run mean
- Observed median
- -$703Half finished above, half below*
- Finished with a profit
- 34.866%34,866 of 100,000 sessions
The middle 90% of sessions
-$3,186 to +$2,5315th to 95th empirical percentiles. This describes the sample, not a guarantee for your next session.
Worst observed-$5,949
Best observed+$8,845
Observed mean-$563
Dollar summaries are rounded to the nearest dollar. Best and worst are extrema of this finite sample, not possible limits. The 95% Wilson interval for the profitable-session rate is 34.571%–35.162%; rare profitable sessions carry more relative sampling uncertainty. *Discrete ties can straddle the median.
Every paytable, side by side
Dollar results at $1.25 per hand; each row is a separate set of 100,000 sessions.
| Paytable / RTP | Expected net | Median | Middle 90% | Observed worst / best | Profitable |
|---|---|---|---|---|---|
| 9/699.5439% | -$570 | -$703 | -$3,186 to +$2,531 | -$5,949 +$8,845 | 34,866 / 100,00034.866% |
| 9/598.4498% | -$1,938 | -$2,074 | -$4,566 to +$1,151 | -$7,185 +$7,791 | 13,684 / 100,00013.684% |
| 8/698.3927% | -$2,009 | -$2,155 | -$4,615 to +$1,073 | -$7,493 +$7,190 | 12,753 / 100,00012.753% |
| 8/597.2984% | -$3,377 | -$3,505 | -$5,981 to -$290 | -$8,881 +$5,316 | 3,738 / 100,0003.738% |
| 7/596.1472% | -$4,816 | -$4,959 | -$7,421 to -$1,733 | -$9,870 +$5,296 | 834 / 100,0000.834% |
| 6/594.9961% | -$6,255 | -$6,404 | -$8,831 to -$3,225 | -$11,333 +$3,183 | 119 / 100,0000.119% |
Session results, by decile
At least X% of sampled sessions finished at or below the Xth-percentile result. Ties can make the actual share slightly larger. These columns follow the chart’s selected paytables.
| Percentile | 9/6 · net USD | 8/5 · net USD |
|---|---|---|
| 10th | -$2,703 | -$5,500 |
| 20th | -$2,066 | -$4,863 |
| 30th | -$1,575 | -$4,379 |
| 40th | -$1,134 | -$3,939 |
| 50th | -$703 | -$3,505 |
| 60th | -$253 | -$3,061 |
| 70th | $251 | -$2,561 |
| 80th | $863 | -$1,948 |
| 90th | $1,761 | -$1,058 |
Nearest-rank percentiles from 100,000 sessions per column, 100,000 hands each, at $1.25 per hand. The median is the 50th percentile. Observed extrema remain in the separate comparison table.
How often does a session cross your threshold?
Exact empirical counts from the retained endpoints. These are end-of-session results, not the chance of crossing a level along the way.
Endpoint counts load only when requested. Once loaded, thresholds update immediately. A new horizon or additional paytable may need another load. Wager changes scale the dollar-loss threshold, while RTP stays wager-independent.
Enter an RTP from 0% to 80,000%, with at most four decimal places.
| Paytable | Finish ahead (net > $0) | Lose over $5000.00 | RTP ≥ 99% |
|---|---|---|---|
| 9/6 | Not loaded | Not loaded | Not loaded |
| 8/5 | Not loaded | Not loaded | Not loaded |
Intervals describe Monte Carlo uncertainty, not uncertainty in real-world strategy or conditions. Zero observed does not mean impossible; 100% observed does not mean certain. For zero or all observations we show exact one-sided 95% bounds; otherwise, two-sided 95% Wilson intervals. Exploring many thresholds does not give simultaneous 95% coverage across all of them.
Deeper statistics: means and the worst 5%
The worst-5% average uses exactly the lowest 5,000 of 100,000 net results. If the 5th-percentile cutoff has ties, only enough tied outcomes to fill 5,000 are included. Equal-valued ties make that ordering immaterial. This is a tail average, not a drawdown or a worst-case bound.
| Paytable | Theoretical mean net | Empirical mean net | Median net | 5th-percentile cutoff | Worst-5% average net |
|---|---|---|---|---|---|
| 9/6 | -$570 | -$563 | -$703 | -$3,186 | -$3,673 |
| 8/5 | -$3,377 | -$3,369 | -$3,505 | -$5,981 | -$6,460 |
Take the samples with you
Each CSV contains the original 100,000 session endpoints for one selected paytable and the current 100,000-hand horizon: session ID, paytable, hands, net wager units and RTP percent. Multiply net wager units by the current $1.25 wager to get USD. CSVs are wager-neutral and download only when clicked.
The accompanying JSON captures the current paytables, horizon, wager, thresholds, seed, stream keys, conventions and source. Raw CSVs preserve original session order. No new random draws were made for these tools.
Accessible chart data: histogram counts
Bins include their lower endpoint and exclude their upper endpoint. Zero-count bins are retained. Each selected column sums to 100,000 sessions.
| Net result bin (USD) | 9/6 sessions | 8/5 sessions |
|---|---|---|
| -$9,000 to <-$8,875 | 0 | 1 |
| -$8,875 to <-$8,750 | 0 | 1 |
| -$8,750 to <-$8,625 | 0 | 0 |
| -$8,625 to <-$8,500 | 0 | 0 |
| -$8,500 to <-$8,375 | 0 | 1 |
| -$8,375 to <-$8,250 | 0 | 6 |
| -$8,250 to <-$8,125 | 0 | 3 |
| -$8,125 to <-$8,000 | 0 | 5 |
| -$8,000 to <-$7,875 | 0 | 11 |
| -$7,875 to <-$7,750 | 0 | 20 |
| -$7,750 to <-$7,625 | 0 | 31 |
| -$7,625 to <-$7,500 | 0 | 39 |
| -$7,500 to <-$7,375 | 0 | 58 |
| -$7,375 to <-$7,250 | 0 | 90 |
| -$7,250 to <-$7,125 | 0 | 104 |
| -$7,125 to <-$7,000 | 0 | 180 |
| -$7,000 to <-$6,875 | 0 | 188 |
| -$6,875 to <-$6,750 | 0 | 274 |
| -$6,750 to <-$6,625 | 0 | 362 |
| -$6,625 to <-$6,500 | 0 | 478 |
| -$6,500 to <-$6,375 | 0 | 568 |
| -$6,375 to <-$6,250 | 0 | 667 |
| -$6,250 to <-$6,125 | 0 | 792 |
| -$6,125 to <-$6,000 | 0 | 977 |
| -$6,000 to <-$5,875 | 2 | 1,035 |
| -$5,875 to <-$5,750 | 0 | 1,219 |
| -$5,750 to <-$5,625 | 1 | 1,378 |
| -$5,625 to <-$5,500 | 0 | 1,505 |
| -$5,500 to <-$5,375 | 3 | 1,633 |
| -$5,375 to <-$5,250 | 4 | 1,833 |
| -$5,250 to <-$5,125 | 5 | 2,029 |
| -$5,125 to <-$5,000 | 13 | 2,052 |
| -$5,000 to <-$4,875 | 24 | 2,231 |
| -$4,875 to <-$4,750 | 35 | 2,487 |
| -$4,750 to <-$4,625 | 72 | 2,527 |
| -$4,625 to <-$4,500 | 89 | 2,590 |
| -$4,500 to <-$4,375 | 108 | 2,691 |
| -$4,375 to <-$4,250 | 133 | 2,739 |
| -$4,250 to <-$4,125 | 182 | 2,952 |
| -$4,125 to <-$4,000 | 279 | 2,863 |
| -$4,000 to <-$3,875 | 345 | 2,794 |
| -$3,875 to <-$3,750 | 429 | 2,925 |
| -$3,750 to <-$3,625 | 535 | 2,922 |
| -$3,625 to <-$3,500 | 608 | 2,839 |
| -$3,500 to <-$3,375 | 750 | 2,810 |
| -$3,375 to <-$3,250 | 885 | 2,916 |
| -$3,250 to <-$3,125 | 1,015 | 2,792 |
| -$3,125 to <-$3,000 | 1,130 | 2,719 |
| -$3,000 to <-$2,875 | 1,358 | 2,543 |
| -$2,875 to <-$2,750 | 1,419 | 2,488 |
| -$2,750 to <-$2,625 | 1,593 | 2,442 |
| -$2,625 to <-$2,500 | 1,746 | 2,282 |
| -$2,500 to <-$2,375 | 1,877 | 2,175 |
| -$2,375 to <-$2,250 | 2,102 | 2,143 |
| -$2,250 to <-$2,125 | 2,203 | 1,985 |
| -$2,125 to <-$2,000 | 2,317 | 1,856 |
| -$2,000 to <-$1,875 | 2,496 | 1,707 |
| -$1,875 to <-$1,750 | 2,501 | 1,681 |
| -$1,750 to <-$1,625 | 2,679 | 1,522 |
| -$1,625 to <-$1,500 | 2,688 | 1,495 |
| -$1,500 to <-$1,375 | 2,789 | 1,355 |
| -$1,375 to <-$1,250 | 2,924 | 1,245 |
| -$1,250 to <-$1,125 | 2,836 | 1,191 |
| -$1,125 to <-$1,000 | 2,881 | 1,013 |
| -$1,000 to <-$875 | 2,916 | 942 |
| -$875 to <-$750 | 2,934 | 968 |
| -$750 to <-$625 | 2,899 | 811 |
| -$625 to <-$500 | 2,765 | 784 |
| -$500 to <-$375 | 2,763 | 618 |
| -$375 to <-$250 | 2,706 | 606 |
| -$250 to <-$125 | 2,562 | 537 |
| -$125 to <$0 | 2,499 | 532 |
| $0 to <$125 | 2,496 | 414 |
| $125 to <$250 | 2,374 | 425 |
| $250 to <$375 | 2,293 | 334 |
| $375 to <$500 | 2,150 | 314 |
| $500 to <$625 | 2,001 | 279 |
| $625 to <$750 | 1,907 | 244 |
| $750 to <$875 | 1,846 | 201 |
| $875 to <$1,000 | 1,780 | 190 |
| $1,000 to <$1,125 | 1,605 | 161 |
| $1,125 to <$1,250 | 1,437 | 168 |
| $1,250 to <$1,375 | 1,364 | 152 |
| $1,375 to <$1,500 | 1,252 | 127 |
| $1,500 to <$1,625 | 1,210 | 105 |
| $1,625 to <$1,750 | 1,085 | 82 |
| $1,750 to <$1,875 | 1,116 | 90 |
| $1,875 to <$2,000 | 886 | 69 |
| $2,000 to <$2,125 | 838 | 50 |
| $2,125 to <$2,250 | 772 | 59 |
| $2,250 to <$2,375 | 709 | 41 |
| $2,375 to <$2,500 | 630 | 27 |
| $2,500 to <$2,625 | 553 | 29 |
| $2,625 to <$2,750 | 472 | 31 |
| $2,750 to <$2,875 | 479 | 19 |
| $2,875 to <$3,000 | 435 | 20 |
| $3,000 to <$3,125 | 420 | 15 |
| $3,125 to <$3,250 | 311 | 9 |
| $3,250 to <$3,375 | 283 | 12 |
| $3,375 to <$3,500 | 272 | 16 |
| $3,500 to <$3,625 | 275 | 10 |
| $3,625 to <$3,750 | 210 | 11 |
| $3,750 to <$3,875 | 185 | 1 |
| $3,875 to <$4,000 | 166 | 7 |
| $4,000 to <$4,125 | 145 | 5 |
| $4,125 to <$4,250 | 140 | 3 |
| $4,250 to <$4,375 | 99 | 9 |
| $4,375 to <$4,500 | 92 | 2 |
| $4,500 to <$4,625 | 86 | 4 |
| $4,625 to <$4,750 | 82 | 1 |
| $4,750 to <$4,875 | 64 | 4 |
| $4,875 to <$5,000 | 53 | 0 |
| $5,000 to <$5,125 | 48 | 0 |
| $5,125 to <$5,250 | 37 | 1 |
| $5,250 to <$5,375 | 33 | 1 |
| $5,375 to <$5,500 | 29 | 0 |
| $5,500 to <$5,625 | 25 | 0 |
| $5,625 to <$5,750 | 20 | 0 |
| $5,750 to <$5,875 | 20 | 0 |
| $5,875 to <$6,000 | 19 | 0 |
| $6,000 to <$6,125 | 11 | 0 |
| $6,125 to <$6,250 | 9 | 0 |
| $6,250 to <$6,375 | 12 | 0 |
| $6,375 to <$6,500 | 9 | 0 |
| $6,500 to <$6,625 | 7 | 0 |
| $6,625 to <$6,750 | 9 | 0 |
| $6,750 to <$6,875 | 3 | 0 |
| $6,875 to <$7,000 | 11 | 0 |
| $7,000 to <$7,125 | 5 | 0 |
| $7,125 to <$7,250 | 3 | 0 |
| $7,250 to <$7,375 | 3 | 0 |
| $7,375 to <$7,500 | 1 | 0 |
| $7,500 to <$7,625 | 3 | 0 |
| $7,625 to <$7,750 | 3 | 0 |
| $7,750 to <$7,875 | 1 | 0 |
| $7,875 to <$8,000 | 0 | 0 |
| $8,000 to <$8,125 | 2 | 0 |
| $8,125 to <$8,250 | 0 | 0 |
| $8,250 to <$8,375 | 0 | 0 |
| $8,375 to <$8,500 | 0 | 0 |
| $8,500 to <$8,625 | 1 | 0 |
| $8,625 to <$8,750 | 0 | 0 |
| $8,750 to <$8,875 | 3 | 0 |
What this experiment can—and cannot—tell you
A session is the experiment
Each result represents exactly 100,000 or 1,000,000 independent hands, with no bankroll limit or stopping rule. There are 100,000 sessions per paytable and horizon: 1,200,000 sampled session totals.
We used multinomial Monte Carlo to sample each session’s final-category counts, then multiplied those counts by the full payout schedule. This has the same distribution of final totals as independent hand-by-hand category sampling. It does not retain hand order, draw actual cards, or execute the production simulator.
The sessions represent 660,000,000,000 hand outcomes in aggregate; those hands were not individually generated. This cannot estimate ruin, drawdowns or the bankroll needed to reach the finish.
Exact sources, finite samples
Standard 52-card deck, no wild cards, jacks or better to pay. All models assume five coins and the 4,000-credit royal award. Five coins and the maximum royal award are assumed throughout. Perfect strategy is assumed; mistakes and different payouts change the answer.
Each paytable uses its own published integer weights divided by 19,933,230,517,200. The source 9/5 total-count cell is a typo; its category rows sum correctly. Published analysis is not an independent proof of every optimal hold. NumPy receives double-precision ratios derived from the integer weights; residual-category rounding is below 3 × 10⁻¹⁶.
Older simulator JoB presets use rounded probabilities. These separate exact-source research models do not silently change those models; displayed theory can differ slightly.
Reproducibility and uncertainty
NumPy 2.4.2, Generator.multinomial, PCG64DXSM. Master seed 2026100501; SeedSequence keys are (paytable index, horizon index). Paytables: 9/6, 9/5, 8/6, 8/5, 7/5, 6/5. Horizons: 100,000 then 1,000,000. First results are retained; no selection of favorable seeds.
Histograms are empirical, with bins of 100 total-wager units at 100,000 hands and 300 at one million. Percentiles use the inverse empirical CDF (nearest rank). Payout mean, category totals and session variance passed predeclared five-standard-error checks against the model. Probability intervals measure Monte Carlo sampling error, not uncertainty about strategy, availability or your future results.
The dashed reference lines are theoretical means, not fitted curves. A longer run narrows the spread of return percentages while increasing the size of dollar swings. Every schedule here has a negative theoretical expectation. No simulated outcome guarantees a real-world result.