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Royal or Bust
Introduction
This page is designed to address questions like, 'With a bankroll of $2,000, what are my odds of hitting a royal flush before depleting my funds?' While this information won't enhance a player's chances, it can assist them in budgeting effectively if their aim is to achieve a royal or exhaust their funds in the process.
Alongside the 'royal or bust' table, we will also examine the bankroll required to achieve four deuces or a superior hand in two deuces wild scenarios. Additionally, we have a table outlining the likelihood of bankruptcy correlated with bankroll size if the objective is to secure a win of 25 or greater, which represents four of a kind or better in non-wild card games, and a wild royal or superior hand in deuces wild games.
In the provided tables, bankroll is represented in terms of full bets. For instance, a bankroll of 100 in a $1 game equates to $500, as the player should be wagering five coins or $5 at a time.
Games
Below is a compilation of games included in this analysis.
Game Summary
| Abbreviation | Full Name | Full Pay Table | Royal Probability | Return |
|---|---|---|---|---|
| 9-6 DDB | Double Double Bonus | 1,1,3,4,6,9,50,80,160,160,400,50,800 | 1 in 40799 | 98.98% |
| 9-6 JoB | Jacks or Better | 1,2,3,4,6,9,25,50,800 | 1 in 40391 | 99.54% |
| FPDW | Full pay Deuces Wild | 1,2,2,3,5,9,15,25,200,800 | 1 in 45282 | 100.76% |
| NSUD | Not so ugly ducks ( Deuces Wild ) | 1,2,3,4,4,10,16,25,200,800 | 1 in 43456 | 99.73% |
| 10-7 DB | Double Bonus | 1,1,3,5,7,10,50,80,160,50,800 | 1 in 48048 | 100.17% |
| 8-5 BP | Bonus Poker | 1,2,3,4,5,8,25,40,80,50,800 | 1 in 40233 | 99.17% |
| FPJ | Full pay Joker Wild | 1(kings),1,2,3,5,7,20,50,100,200,800 | 1 in 41214 | 100.65% |
| FPA8 | Full pay Aces and Eights | 1,2,3,4,5,8,25,50,80,50,800 | 1 in 40233 | 99.78% |
Royal or Bust
It appears that casual players often set a weekend goal of achieving a royal flush, after which they typically stop playing. The subsequent table attempts to determine the probability of success based on different bankroll sizes and common game types.
For illustration, imagine a player with a $2,000 bankroll playing a 9-6 Jacks or Better on a 25¢ machine. The optimal bet, which is recommended for video poker players, is five quarters, amounting to $1.25. This results in a calculated bankroll of $2,000 divided by $1.25, equaling 1,600 total bets. The table indicates there is a 78.03% likelihood that the player will hit a royal flush before running out of funds.
Royal or Bust
| Bankroll | 9-6 DDB | 9-6 JoB | FPDW | NSUD | 10-7 DB | 8-5 BP | FPJ | FPA8 |
|---|---|---|---|---|---|---|---|---|
| 100 | 6.26% | 9.05% | 12.08% | 8.52% | 9.10% | 7.89% | 11.72% | 9.51% |
| 200 | 12.12% | 17.27% | 22.73% | 16.32% | 17.34% | 15.16% | 22.13% | 18.11% |
| 300 | 17.62% | 24.78% | 32.08% | 23.46% | 24.86% | 21.85% | 31.29% | 25.88% |
| 400 | 22.78% | 31.59% | 40.25% | 29.96% | 31.70% | 28.04% | 39.35% | 32.91% |
| 500 | 27.62% | 37.77% | 47.50% | 35.93% | 37.93% | 33.69% | 46.51% | 39.29% |
| 600 | 32.15% | 43.37% | 53.84% | 41.36% | 43.56% | 38.92% | 52.82% | 45.03% |
| 700 | 36.40% | 48.48% | 59.41% | 46.38% | 48.69% | 43.74% | 58.39% | 50.26% |
| 800 | 40.38% | 53.12% | 64.34% | 50.95% | 53.38% | 48.17% | 63.27% | 54.96% |
| 900 | 44.10% | 57.34% | 68.64% | 55.15% | 57.61% | 52.26% | 67.57% | 59.24% |
| 1000 | 47.61% | 61.21% | 72.42% | 58.99% | 61.49% | 56.03% | 71.38% | 63.12% |
| 1100 | 50.89% | 64.73% | 75.76% | 62.50% | 65.00% | 59.51% | 74.72% | 66.63% |
| 1200 | 53.96% | 67.91% | 78.69% | 65.67% | 68.19% | 62.70% | 77.70% | 69.79% |
| 1300 | 56.84% | 70.81% | 81.25% | 68.59% | 71.08% | 65.66% | 80.34% | 72.67% |
| 1400 | 59.55% | 73.46% | 83.51% | 71.26% | 73.73% | 68.36% | 82.64% | 75.24% |
| 1500 | 62.09% | 75.86% | 85.49% | 73.69% | 76.13% | 70.89% | 84.70% | 77.59% |
| 1600 | 64.46% | 78.03% | 87.23% | 75.90% | 78.29% | 73.20% | 86.50% | 79.74% |
| 1700 | 66.69% | 80.01% | 88.74% | 77.97% | 80.27% | 75.31% | 88.08% | 81.68% |
| 1800 | 68.77% | 81.81% | 90.10% | 79.83% | 82.05% | 77.23% | 89.48% | 83.42% |
| 1900 | 70.72% | 83.46% | 91.29% | 81.54% | 83.67% | 79.04% | 90.71% | 84.99% |
| 2000 | 72.56% | 84.95% | 92.33% | 83.11% | 85.15% | 80.68% | 91.79% | 86.43% |
| 2100 | 74.28% | 86.30% | 93.26% | 84.52% | 86.49% | 82.23% | 92.77% | 87.72% |
| 2200 | 75.88% | 87.54% | 94.08% | 85.85% | 87.70% | 83.62% | 93.61% | 88.89% |
| 2300 | 77.39% | 88.67% | 94.79% | 87.06% | 88.81% | 84.91% | 94.37% | 89.94% |
| 2400 | 78.80% | 89.69% | 95.42% | 88.17% | 89.84% | 86.11% | 95.03% | 90.89% |
| 2500 | 80.13% | 90.63% | 95.97% | 89.17% | 90.76% | 87.21% | 95.61% | 91.75% |
| 2600 | 81.38% | 91.49% | 96.47% | 90.10% | 91.59% | 88.22% | 96.13% | 92.54% |
| 2700 | 82.54% | 92.26% | 96.90% | 90.95% | 92.35% | 89.15% | 96.59% | 93.25% |
| 2800 | 83.63% | 92.96% | 97.26% | 91.71% | 93.04% | 90.00% | 96.99% | 93.88% |
| 2900 | 84.65% | 93.59% | 97.59% | 92.41% | 93.67% | 90.78% | 97.34% | 94.45% |
| 3000 | 85.61% | 94.16% | 97.88% | 93.06% | 94.25% | 91.51% | 97.66% | 94.98% |
| 3100 | 86.51% | 94.68% | 98.13% | 93.65% | 94.78% | 92.18% | 97.93% | 95.46% |
| 3200 | 87.36% | 95.16% | 98.35% | 94.20% | 95.26% | 92.80% | 98.17% | 95.90% |
| 3300 | 88.15% | 95.60% | 98.55% | 94.70% | 95.69% | 93.37% | 98.39% | 96.29% |
| 3400 | 88.89% | 96.00% | 98.73% | 95.15% | 96.09% | 93.89% | 98.59% | 96.65% |
| 3500 | 89.58% | 96.36% | 98.88% | 95.57% | 96.43% | 94.38% | 98.75% | 96.96% |
| 3600 | 90.23% | 96.69% | 99.02% | 95.95% | 96.76% | 94.83% | 98.90% | 97.25% |
| 3700 | 90.84% | 96.99% | 99.14% | 96.30% | 97.05% | 95.24% | 99.03% | 97.51% |
| 3800 | 91.42% | 97.26% | 99.25% | 96.61% | 97.32% | 95.61% | 99.15% | 97.75% |
| 3900 | 91.96% | 97.51% | 99.34% | 96.90% | 97.57% | 95.96% | 99.25% | 97.96% |
| 4000 | 92.46% | 97.73% | 99.42% | 97.17% | 97.79% | 96.28% | 99.34% | 98.15% |
| 5000 | 96.04% | 99.13% | 99.84% | 98.85% | 99.14% | 98.37% | 99.81% | 99.32% |
| 6000 | 97.92% | 99.65% | 99.96% | 99.53% | 99.67% | 99.28% | 99.95% | 99.75% |
| 7000 | 98.92% | 99.86% | 99.99% | 99.81% | 99.88% | 99.68% | 99.99% | 99.91% |
| 8000 | 99.43% | 99.94% | 100.00% | 99.92% | 99.95% | 99.86% | 100.00% | 99.97% |
| 9000 | 99.70% | 99.98% | 100.00% | 99.97% | 99.98% | 99.94% | 100.00% | 99.99% |
| 10000 | 99.85% | 99.99% | 100.00% | 99.99% | 99.99% | 99.97% | 100.00% | 100.00% |
| 11000 | 99.92% | 100.00% | 100.00% | 99.99% | 100.00% | 99.99% | 100.00% | 100.00% |
| 12000 | 99.96% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% |
| 13000 | 99.98% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% |
| 14000 | 99.99% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% |
| 15000 | 99.99% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% | 100.00% |
Here is the average bankroll necessary to achieve a royal flush based on the game.
- 9-6 Double Double Bonus: 1547.76
- 9-6 Jacks or Better: 1056.41
- Full pay Deuces Wild: 777.43
- Not so ugly ducks Deuces Wild: 1123.74
- 10-7 Double Bonus: 1049.43
- 8-5 Bonus Poker: 1216.61
- Full pay Joker Wild: 799.79
- 8-5 Aces and Eights: 1002.47
Win of 200 or Bust
The next table illustrates the probabilities of hitting four deuces or better, which awards 200 to 1, in two different Deuces Wild games. It also provides the same data for achieving a five of a kind or better in full pay Joker Wild (kings or better), which also pays out 200.
Win of 200 or More or Bust
| Bankroll | FPDW | NSUD | FPJ |
|---|---|---|---|
| 25 | 9.33% | 7.83% | 6.90% |
| 50 | 17.78% | 15.06% | 13.30% |
| 75 | 25.45% | 21.72% | 19.26% |
| 100 | 32.39% | 27.84% | 24.82% |
| 125 | 38.70% | 33.50% | 29.98% |
| 150 | 44.43% | 38.71% | 34.80% |
| 175 | 49.61% | 43.51% | 39.28% |
| 200 | 54.31% | 47.95% | 43.45% |
| 225 | 58.55% | 52.03% | 47.33% |
| 250 | 62.42% | 55.79% | 50.95% |
| 275 | 65.93% | 59.25% | 54.33% |
| 300 | 69.11% | 62.45% | 57.46% |
| 325 | 71.99% | 65.39% | 60.38% |
| 350 | 74.60% | 68.11% | 63.11% |
| 375 | 76.97% | 70.61% | 65.64% |
| 400 | 79.12% | 72.91% | 68.00% |
| 425 | 81.06% | 75.04% | 70.20% |
| 450 | 82.83% | 77.00% | 72.24% |
| 475 | 84.43% | 78.80% | 74.16% |
| 500 | 85.88% | 80.46% | 75.93% |
| 600 | 90.45% | 85.90% | 81.89% |
| 700 | 93.55% | 89.83% | 86.39% |
| 800 | 95.64% | 92.66% | 89.76% |
| 900 | 97.06% | 94.71% | 92.30% |
| 1000 | 98.01% | 96.18% | 94.22% |
| 1100 | 98.65% | 97.25% | 95.66% |
| 1200 | 99.09% | 98.01% | 96.73% |
| 1300 | 99.38% | 98.57% | 97.55% |
| 1400 | 99.58% | 98.96% | 98.15% |
| 1500 | 99.72% | 99.25% | 98.61% |
| 1600 | 99.81% | 99.46% | 98.96% |
| 1700 | 99.87% | 99.61% | 99.22% |
| 1800 | 99.91% | 99.72% | 99.41% |
| 1900 | 99.94% | 99.80% | 99.56% |
| 2000 | 99.96% | 99.85% | 99.67% |
| 2100 | 99.97% | 99.89% | 99.75% |
| 2200 | 99.98% | 99.92% | 99.81% |
| 2300 | 99.99% | 99.94% | 99.86% |
| 2400 | 99.99% | 99.96% | 99.89% |
| 2500 | 99.99% | 99.97% | 99.92% |
| 2600 | 100.00% | 99.98% | 99.94% |
| 2700 | 100.00% | 99.98% | 99.96% |
| 2800 | 100.00% | 99.99% | 99.97% |
| 2900 | 100.00% | 99.99% | 99.98% |
| 3000 | 100.00% | 99.99% | 99.98% |
Presented here is the average bankroll required to attain a payout of 200 or more according to each game.
- Full pay Deuces Wild: 255.90
- Not so ugly ducks Deuces Wild: 306.79
- Full pay Joker Wild: 351.40
Win of 25 or More or Bust
The following table reveals the probabilities of obtaining a win of 25 or higher for various bankroll sizes. I selected 25 because it typically represents the minimum payout for a four of a kind in non-wild card games. This figure also reflects a common win for a wild royal in deuces wild games.
For example, suppose a player using a 9-6 Jacks or Better strategy feeds a $100 bill into a 25¢ machine. What are the chances he will secure a payout of 25 bet units or more before running out of money? $100 will allow for 100 divided by 1.25, resulting in 80 full bets on that machine. The table displays that the probability of achieving a four of a kind or better before depleting the $100 is 83.86%.
Win of 25 or More or Bust
| Bankroll | 9-6 DDB | 9-6 JoB | FPDW | NSUD | 10-7 DB | 8-5 BP | FPA8 |
|---|---|---|---|---|---|---|---|
| 10 | 10.36% | 20.39% | 16.00% | 15.55% | 12.25% | 17.91% | 17.92% |
| 20 | 19.66% | 36.61% | 29.45% | 28.69% | 23.00% | 32.61% | 32.63% |
| 30 | 27.99% | 49.53% | 40.74% | 39.77% | 32.44% | 44.69% | 44.70% |
| 40 | 35.46% | 59.82% | 50.22% | 49.14% | 40.72% | 54.59% | 54.60% |
| 50 | 42.15% | 68.01% | 58.18% | 57.06% | 47.99% | 62.73% | 62.73% |
| 60 | 48.15% | 74.53% | 64.87% | 63.73% | 54.36% | 69.41% | 69.41% |
| 70 | 53.53% | 79.72% | 70.50% | 69.37% | 59.96% | 74.88% | 74.89% |
| 80 | 58.34% | 83.86% | 75.22% | 74.14% | 64.87% | 79.38% | 79.39% |
| 90 | 62.67% | 87.15% | 79.18% | 78.16% | 69.18% | 83.07% | 83.08% |
| 100 | 66.54% | 89.77% | 82.51% | 81.55% | 72.95% | 86.11% | 86.11% |
| 110 | 70.01% | 91.85% | 85.31% | 84.42% | 76.26% | 88.59% | 88.60% |
| 120 | 73.12% | 93.51% | 87.66% | 86.84% | 79.18% | 90.64% | 90.64% |
| 130 | 75.90% | 94.83% | 89.63% | 88.89% | 81.73% | 92.31% | 92.32% |
| 140 | 78.40% | 95.89% | 91.29% | 90.62% | 83.97% | 93.69% | 93.69% |
| 150 | 80.64% | 96.73% | 92.69% | 92.08% | 85.93% | 94.82% | 94.82% |
| 160 | 82.65% | 97.39% | 93.86% | 93.31% | 87.65% | 95.74% | 95.75% |
| 170 | 84.45% | 97.93% | 94.84% | 94.35% | 89.17% | 96.51% | 96.51% |
| 180 | 86.06% | 98.35% | 95.66% | 95.23% | 90.50% | 97.13% | 97.14% |
| 190 | 87.50% | 98.69% | 96.36% | 95.97% | 91.66% | 97.65% | 97.65% |
| 200 | 88.80% | 98.95% | 96.94% | 96.59% | 92.68% | 98.07% | 98.07% |
| 250 | 93.52% | 99.67% | 98.72% | 98.54% | 96.19% | 99.28% | 99.28% |
| 300 | 96.25% | 99.89% | 99.47% | 99.37% | 98.02% | 99.73% | 99.73% |
| 350 | 97.83% | 99.97% | 99.78% | 99.73% | 98.97% | 99.90% | 99.90% |
| 400 | 98.74% | 99.99% | 99.91% | 99.88% | 99.46% | 99.96% | 99.96% |
| 450 | 99.27% | 100.00% | 99.96% | 99.95% | 99.72% | 99.99% | 99.99% |
| 500 | 99.58% | 100.00% | 99.98% | 99.98% | 99.86% | 99.99% | 99.99% |
Here is the average bankroll needed to realize a win of 25 or more based on the game.
- 9-6 Double Double Bonus: 91.86
- 9-6 Jacks or Better: 44.37
- Full pay Deuces Wild: 57.85
- Not so ugly ducks Deuces Wild: 59.66
- 10-7 Double Bonus: 76.99
- 8-5 Bonus Poker: 51.17
- 8-5 Aces and Eights: 51.16
Methodology
For this analysis, a random simulation model was employed. As always, it is presumed that optimal player strategy is utilized.
External Links
Further discussion on this topic can be found in the section titled Bankroll Requirement to Hit a Royal at my forum at Wizard of Vegas.