On this page
Royal or Bust
Introduction
The purpose of this page is to answer such questions as, "If I have a bankroll of $2,000, what is my probability of hitting a royal flush before going broke?" The information in this page will not increase the player's odds, but it may be of use to the player in planning a budget if his goal is to hit a royal or go bust trying.
In addition to a "royal or bust" table, we will also look at the bankroll needed to hit four deuces or better in two deuces wild games. We also have a table for the probability of ruin by bankroll size if the goal is to hit a win of 25 or more, which is a four of a kind or better in non-wild card games and a wild royal or better in deuces wild games.
In all tables, the bankroll is measured in full bets. For example, a bankroll of 100 at a $1 game would be $500, because the player should be betting five coins, or in this case $5, at a time.
Games
Following is a list of games covered by 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 seems to me that recreational gamblers often have a weekend goal of hitting a royal, at which time they immediately quit playing. The following table strives to answer the question of the probability of success for various bankroll sizes and common games.
For example, consider a player has a bankroll of $2,000 and is playing a 9-6 Jacks or Better on a 25¢ game. A full bet, which video poker players should always make, is five quarters, or $1.25. That comes to a bankroll of $2,000/$1.25 = 1,600 bets. The table shows the player will have a 78.03% chance of hitting a royal before going bust.
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% |
Following is the average bankroll needed to hit a royal flush by 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 following table shows the probability of achieving four deuces or better, which pays 200 for 1, in two Deuces Wild games. It also shows the same thing for achieving a five of a kind or better, which also pays 200, in full pay Joker Wild (kings or better).
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% |
Following is the average bankroll needed to hit a win of 200 or more by 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 shows the probability of a win of 25 or more for various bankroll sizes. I chose 25 because it the usual minimum pay for a four of a kind in games without wild cards. It is also a common win for a wild royal in deuces wild games.
For example, suppose a 9-6 Jacks or Better player puts a $100 bill into a 25¢ machine. What is the probability he will see a win of 25 bet units or more before going bust? $100 will buy 100/1.25 = 80 full bets on that machine. The table shows the probability of seeing a four of a kind win or more before the $100 is gone 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% |
Following is the average bankroll needed to hit a win of 25 or more by 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
A random simulation was used for this page. As usual, optimal player strategy is assumed.
External Links
Discussion of this topic can be found under the topic Bankroll Requirement to Hit a Royal at my forum at Wizard of Vegas.