Note to reader: The original version of this contained an arithmetic mistake. It was pointed out to me by a man who posts under the name “New2vp”. The error, which affected one of the tables in the chart, are in the section relating to quad 5s-Ks. The corrected version follows. Thank you New2vp.
I received an email: Sam’s Town in Las Vegas has three different banks of 8/5 Bonus. Two of those banks have progressives on the royal flush only. The third has that progressive, plus three additional ones for the quads: aces, 2s-4s, and 5s-Ks. Since the game starts out at 99.17%, sometimes these games must be pretty good. How do I figure out how to calculate the return of these games quickly if I don’t bring computer software into the casino?
I’ve received similar emails about Double Double Bonus Poker. Eventually I’ll have strategy cards published so that you can just look up these things, but today I want to describe the process of “How do you figure it out?” using Bonus Poker.
To do this you need access to computer software. I’m using WinPoker today.
The base game with a 4,000-coin royal flush returns 99.1660%. I now set the royal flush to 8,000 coins and discover the game returns 101.4376%. Subtracting the first from the second, I get 101.4376% – 99.1660% = 2.2716%.
From here I make the assumption that the change in return happens evenly. That is, for each 100 coins of progressive, the royal changes 2.2716% / 40 = 0.05544%, which I’ll round to 0.055%.
That is, at 4,100 coins, the game is worth 99.166% plus 0.055% = 99.221%. It doesn’t take much effort to create the following chart:
| Royal | Game |
| Value | Return |
| 4,000 | 99.166% |
| 4,100 | 99.221% |
| 4,200 | 99.276% |
| 4,300 | 99.331% |
| 4,400 | 99.386% |
| 4,500 | 99.441% |
| 4,600 | 99.496% |
| 4,700 | 99.551% |
| 4,800 | 99.606% |
| 4,900 | 99.661% |
| 5,000 | 99.716% |
The value of the royal progressive is seldom exactly at one of these numbers, but you can extrapolate. That is, a royal amount of 4,234 coins is worth 99.276% + 0.34 * 0.055% = 99.294%.
Next we look at four aces. As the progressive of four aces rises, the change in value for that progressive is largely independent of the value of the royal. So, we can just add these increments together.
With the royal at 4,000 coins and four aces at 400 coins, the game returns the same 99.166% we used before. We’ll now set the value of four aces to 500 coins and we get 99.558%. So for the 100-coin increment of aces, we get 99.558% – 99.166% = 0.392%. This means for every 10 coins of increment, the progressive rises by 0.039%. For practical purposes, I use 0.04%. It’s close enough and is much easier to work with. But using the correct amount, we get:
| Add to | |
| Aces | Game |
| Value | Return |
| 400 | 0.000% |
| 410 | 0.039% |
| 420 | 0.078% |
| 430 | 0.117% |
| 440 | 0.156% |
| 450 | 0.195% |
| 460 | 0.234% |
| 470 | 0.273% |
| 480 | 0.312% |
| 490 | 0.351% |
| 500 | 0.390% |
Obviously if there is only a progressive on the royal, we don’t make any adjustment for the aces.
For four 2s-4s, the process is similar. The return on the game with the royal and aces at reset, but four 2s-4s at 300 (instead of 200) is 100.2205%. So for every 10-coin increment of the value of these quads we get 0.10 * (100.2205% – 99.1660%) = 0.1055%. Creating a similar chart as before we get:
| Add to | |
| 2s-4s | Game |
| Value | Return |
| 200 | 0.000% |
| 210 | 0.106% |
| 220 | 0.211% |
| 230 | 0.317% |
| 240 | 0.422% |
| 250 | 0.528% |
| 260 | 0.633% |
| 270 | 0.739% |
| 280 | 0.844% |
| 290 | 0.950% |
| 300 | 1.055% |
Finally, for the value of four 5s-Ks, we start at 125 coins and now check 225 coins, where the return is 102.4459%. Because this progressive hits so frequently, I’m going to display the chart in increments of five coins rather than 10. That is, for every five coins in increment we add (102.446% – 99.166%) / 20 = 0.164%. Creating the same sort of chart as before, we get:
| Add to | |
| 5s-Ks | Game |
| Value | Return |
| 125 | 0.000% |
| 130 | 0.164% |
| 135 | 0.328% |
| 140 | 0.492% |
| 145 | 0.656% |
| 150 | 0.820% |
| 155 | 0.984% |
| 160 | 1.148% |
| 165 | 1.312% |
| 170 | 1.476% |
| 175 | 1.640% |
When you come across the progressives, you simply add up the value of each of the progressives. I would also add in the amount of the slot club, which is normally 0.05%, unless you’re playing on a “Young at Heart” day (for seniors at least 50 who are Sapphire level or higher) the return is 0.5%.
It’s conceivable that there is a game somewhere where there is also a progressive on the straight flush. You figure it out the same way as described above.
I do not carry around the above charts with me. I do have a note on my iPhone that says for Bonus Poker, add 0.055% for 100 coins of royal, 0.04% for 10 coins of aces, 0.10% for every 10 coins of 2s-4s, and 0.16% for every five coins of 5s-Ks. When I come across such a game, I figure it out at the time.
I have similar notes for several other games. They are not difficult to create once you know how. Knowing the return on the game doesn’t tell me when to make adjustments. That is, from Q♠ J♥ T♥ 5♣ 2♦, how high does the royal have to be to change the correct play from QJ to JT? That is an extremely important question, but one we’re going to have to leave for another day.
the problem is that progressives are very seldom just 1 single machine. Did you also calculate that risk? If there are somewhat like 5 or 6 other players chasing that game it must have an impact on your overall result, even if it’s just a matter of variance. How often will you be the one to get the progressive and not somebody sitting next to you? I find myself more in the comfort zone when playing late at nights, or perhaps even early in the morning while nobody else is chasing the Royal besides me….
And of course, the tax thing has not been discussed yet……it has a huge impact on those progressives, in particular by figuring out the true mathematical numbers….
From Switzerland
Boris
The 8/5 BP with the RF/SF/5-K 4oak progressives are pretty popular upstairs at The D.
The 8/5 BP with the RF/SF/5-K 4oak progressives are pretty popular upstairs at The D.
Same game is found at Golden Gate.
Bob…
I very much appreciate the breakdown and the math on this game. Sometimes I have a hard time thinking in quantitative terms. These type of columns really help me personally.
QUESTION:
If you’re playing the D and GGate games (which I do on occasion), and you break it down to each progressive, can penalty cards be taken into account with these calculations? or are they mostly negligible? I’m thinking, in one example, if you have 8-9-10 suited. The 10 is going to affect the Royal, but the play is the SF draw. Would it be better just to run the analysis with all progressives so they would be taken into consideration?
I do appreciate how you broke it down for whichever game you’re playing, so that you can just add each number
for the specific game. I’m just wondering if my thought processes are working correctly.
I try to think in advantage terms, but it’s obvious I’m only a recreational player.
ND
I don’t really see why other players would affect your game, EV is EV regardless of how many others are playing. Even if you are the only player there is no guarantee that your terminal will hit the royal.
Penalty cards would certainly make some difference but to create a strategy that considers all possibilities would be way to big to fit on a strategy card. In your example, the 8,9,10 would always be the play, the royal would have to be astronomical to just hold the 10. In most circumstance there is no need to consider all options, in the case of AA*** all other progressives would be irrelevant, like wise for 22***, 88*** etc. There would be more considerations for hands like kJQK* where the play would be determined by which progressive gives the most ev
When playing at the upstairs D make sure you are playing at the Vue bar and not the new Canadian bar. Big difference in pay schedules.
the odds of hitting a progressive are the same no matter how many people are playing.
I was playing the 8/5 BP $0.25 progressive machines at Orleans when I was in town in October, the royal was over $2,000. I used the Wizard of Odds website on my phone to calculate the return to be over 100% so I started playing. I was dealt a pair of jacks and two more cards to the royal, I didn’t pause to think it through, and I held the 2 jacks which according to Win Poker is the correct play. The next two cards that came up filled the royal, but I had only the 2 jacks. It was then I realized that with the royal being so high I should have held three the royal and I confirmed that later on the software. I should have slow down and thought it through. Maybe I’ll do better next time.
PK
The mathematical point of view may be correct. Still I would prefer to play alone against the progressive instead of playing along with 50 other players. The Southpoint bank in the middle, although just a 9-5 ddb or 9-15 Deuces game may be ok at time. However, if there are 50 or 60 other players in the game I just don’t like it. I avoid the big progressive banks and if I play it I prefer being on my own . That is , mostly in the graveyard hours…..
From Switzerland
Boris
A miscalculation I made in the original article was pointed out to me and is now fixed.
I wonder how often that Sam’s Town progressive is a really attractive play; Boyd meters (at least downtown) have a tendency to be SLOW…
Sam’s Town has a few very good banks. The problem there is see is actually that for some reason Sam’s Town turned in to Sam’s Ghost Town. Last 2 visits I was there and it was deserted. The buffet was closed, Roxy’s dance hall was dark, the poker room was dark. They cancelled the cashout option when leaving town and not using the points anymore. Dining options are extremely limited. At nights a lot of non gambling patrons are loitering which made me feel extremely uncomfortable. So there is less gaming activity at Sam’s Town. The 2 super old jackpots (Super Joker Jackpot) near the East Entrance and by the movie theaters hardly move their meters. In 1 year they went up probably 200 dollars or so……
From Switzerland
Boris