The mathematical analysis in this blog was done by Rick Percy. I do not have the tools to do that analysis myself. Thank you, Rick!
My personal goal is to learn the best strategy for every game I play. Not everybody shares that goal. Some people want to minimize their work, or don’t have the time, or have trouble keeping the differences between strategies straight.
Let’s say one such person was going to learn one strategy for both 9/6 Jacks or Better and 8/5 Bonus Poker. The games are similar, but not identical.
Percy used the strategies created by the wizardofodds.com video poker strategy calculator. He looked at the basic strategy and the advanced strategy. These strategies are very close to the Dancer/Daily strategies for the same game — but whether you include a particular play in the basic strategy or the advanced strategy is somewhat arbitrary.
| Playing 9/6 JoB | Playing 8/5 BP | |||
|---|---|---|---|---|
| Return | Loss | Return | Loss | |
| Using 9/6 JoB basic strategy | 99.543% | 0.001% | 99.161% | 0.005% |
| Using 9/6 JoB advanced strategy | 99.544% | 0.000% | 99.158% | 0.007% |
| Using 8/5 BP basic strategy | 99.524% | 0.020% | 99.159% | 0.007% |
| Using 8/5 BP advanced strategy | 99.537% | 0.007% | 99.166% | 0.000% |
The columns show the result of using various strategies on the two games. The column called “Loss” indicates how much you lose using that particular strategy on that particular game. Obviously, that number is zero if you’re using the advanced strategy designed for that game. That’s what an advanced strategy is all about.
The rows show the basic and advanced strategies for each of the two games.
There are a number of interesting takeaways from this analysis.
a. For playing 9/6 JoB, using basic strategy 9/6 JoB only costs you 0.001% (compared to learning each of the penalty card situations in the advanced strategy), which is one penny for every $1,000 coin-in (or $1 for every $100,000 coin-in).
b. For playing 9/6 JoB, using 8/5 BP basic strategy gives up 0.020%. That’s $20 for every $100,000 coin-in. Using the 8/5 BP advanced strategy only gives up about 1/3 of that amount.
c. For playing 8/5 BP, using 9/6 JoB basic strategy gives up LESS than using 9/6 JoB advanced strategy! Further, and this is probably the most shocking part of this analysis, using 9/6 JoB basic strategy while playing 8/5 BP is BETTER than using 8/5 BP basic strategy for the same game!
d. If you’re going to learn one strategy and for both of these games, and you play the games approximately equally, learn the 9/6 JoB basic strategy, not the 9/6 JoB advanced strategy! Added to this is the observation that 9/6 JoB has a much simpler strategy than 8/5 BP.
I’ve been asked many times how much of a difference does it make to learn an advanced strategy compared to the basic strategy. The answer is that it depends on the game. Another answer is “not much,” but that, of course depends on the value you place on gleaning every nano-penny of value out of playing this game.
I found the conclusions today interesting. Thank you, Rick Percy.
It is possible to create a mixed strategy exactly halfway between the two games. To do this, you add the payouts together. That is, for full houses, you add 8 (the value for 8/5 BP) to 9 (the value for 9/6 JoB) and you get 11. For four aces, you add 80 to 25 and get 105. You then use Video Poker for Winners or the Wizard of Odds strategy calculator and create a blended strategy.
I didn’t do that here because:
- The unblended strategy is really close anyway.
- The unblended strategy is often the first one players learn, as it’s the one most teachers start with.
- This procedure works if you play the two games equally. If you play JoB twice as much as you play BP, a 50-50 blended strategy is no longer optimal.
The old school approach was to get the cycle times (or frequency) for each winning hand (RF, STFL, etc) in game 1 and superimpose them in game 2, respectively.
Then you would multiply the pay table in game 2 using game 1’s cycle times, respectively. This will give you the “slippage” or loss from using one strategy on two or more different VP games.
We know this to be true because the strategy generates the EV and variance (and the EV is based on the pay table and respectively cycle times). The thought experiment would be: Suppose you hidden the pay table from the player and the player then used the strategy from game 1.
For the longest time, VP APs were using VPSM to create customized strategies and then using the old school method to see loss in EV, etc. over multiple games.
Lastly, what Rick Percy did is commonly known as attribution analysis in the institutional investment community.
BD wrote: “I do not have the tools to do that [mathematical] analysis myself.“
To be clear, the math needed for the analysis is grade school math: multiplication, subtraction, and addition (once you know the cycle times or frequencies of each hand, respectively). So you need VP software that can analyze strategy which was available since Frugal VP and later Wolf VP. This type of math analysis should best be performed on a spreadsheet available on a smartphone.
Since the pay tables are known ahead of time (game #1 or JoB vs game #2 or BP), the only thing that was missing was the cycle times for a specific VP strategy (which were 4 distinct VP strategies in BD’s article). Recall strategy drives cycle times!
So I will now explain attribution analysis, which is the mathematical process of pulling apart the delta’s (or changes). Attribution analysis is based on (a) ceteris paribus and (b) the whole is the sum of it’s parts when comparing one fund’s performance (e.g. game #2) against a benchmark (e.g. game #1), respectively.
Suppose I have a bed that is 4’ by 6’ or a volume of 24 sq feet. Now, I enlarge that bed to 5’ by 7’ or a volume of 35 sq feet. The delta is a gain of 11’ sq feet (35 less 24). Using attribution analysis:
a) increase in width of 4’ to 5’ ceteris paribus or holding the length constant is a gain of 6 sq ft. [If 4 * 6 = 24 & 5 * 6 = 30, then the delta must be 6].
b) increase in length of 6’ to 7’ ceteris paribus is a gain of 4 sq ft. [If 4 * 6 = 24 & 4 * 7 = 28, then the delta must be 4].
c) the gain of 1 sq ft is the gain not explained by (a) or (b), e.g. this is the interactive effect of both “marginal” increases in width and length, respectively, that was not previously explained.
So based on attribution analysis, the 11 sq ft gain (summary statistic) in volume is due to individual gains of 6’ & 4’ & 1’, respectively.
Percy’s analysis is simply using a spreadsheet by looking at the respective delta’s of each specific hand cycle time. BD gave us the summary statistics. What VP APs were doing when altering strategy was looking at the specific hand delta’s as well as the Variance (which BD omitted in his article).
You are seeing this type of attribution analysis on Bonus Slots (especially online version with 96%+ RTPs) because you want robust Beta Estimators to identify when the gaming company nerfed the game.
In summary, the math is simple but the guts of calculating the delta’s requires knowing the algorithm of attribution analysis and requires the brute force of a spreadsheet. Once you get the cycle times, it’s just a mechanical process unless you want to tweak the strategy (as opposed to BD’s weight pay table method).
Sounds like fun but full pay deuces and jokers are back
James, can you officially confirm that full pay deuces wild is back in place? Can you name the casinos where it can be played? Is it Station’s casinos? Thanks for your info and best regards from Switzerland.
Michael Shackleford did sort of the same thing a few years ago. Here is the discussion about it from his WoV.
https://wizardofvegas.com/forum/gambling/video-poker/25990-cost-of-using-the-wrong-strategy-in-video-poker/
1. People were doing attribution analysis over 20+ year ago in VP; AP’s are now using this type of analysis in bonus slot machines and making huge $$$$!!
2. Attribution analysis helps you understand the strategy impacts at the most basic level as opposed to the summary statistics level. Notice in Shack’s table’s, he doesn’t look at the “Variance” impact. Most AP’s I worked with focus on the Variance side because it was a time-specific but high EV promotion, e.g. at what point do you stop trading lower variance for lower EV?
To summarize:
1) Dancer stated or implied this type of analysis was difficult, e.g. required complicated math. This is simply not true as it only requires basic math skills.
2) Dancer stated or implied this type of analysis required special “tools”. Again this is not true. Take computer perfect play: the WinPoker app will give you the cycle times or hand frequencies for Max EV strategies numerous “popular” VP games. Therefore, anyone with a VP analyzer can compare the impact of strategies when using computer perfect plays, respectively (assuming the analyzer can handle the pay table).
In attribution analysis, you will encounter two situations:
A) both game pays the same for the winning hand, e.g. both 9/6 JoB & 8/5 BP pay 4 for 1 for a Straight. Therefore, the strategy impact is due to different cycle times.
B) both games pay differently for the winning hand, e.g. for a Flush, 9/6 JoB pays 6 for 1 whereas 8/5 BP pays 5 for 1, respectively.
In (B), you have
– cycle time for 9/6
– cycle time for 8/5
– 9/6 pays 6 for 1 for a Flush
– 8/5 pays 5 for 1 for a Flush
– numerous interactive effect, e.g. ceteris paribus like holding 9/6 cycle time constant and look at impact at lower 5 for 1 win amount.
– each “effect” can be discerned
The analysis gets very granular but that is why some people are AP’s.
For Mr. Dancer,
Since your expertise is unmatched on video poker… I am asking your take on the statement below. I am a game designer/creative director, focused on slots, with many years in the gaming industry.
Was playing with a complete newbie (recent grad – economics/data science, no exposure to gaming industry) and a former physicist (not a new player, but only a few years in the past in the gaming industry) and they both claimed the following was true:
“…if one played 1,000,000. through the same 97% paytable, one would be GUARENTEED 97% of the total bets….”
My take is “…a 97% paytable COULD pay 97% of the total bets, if one played using absolute and unwavering perfect strategy for that paytable AND one had a bit of luck…Nothing is ‘guaranteed’…”
Admittedly, I was offended neither of them gave the two words, ‘strategy’ and ‘luck’ any weight, and they both used the word, ‘guaranteed’.
So, I spent the weekend on Bonus Poker, focusing on defined best strategy for consistent pays in the lower end of the paytable, to sustain my play; and I got them. I also got a nice Straight Flush, 4 Four of a Kinds, and plenty of two pair pays, playing on several different machines, at 3 properties at Tahoe. And some of the paytable were 7/5…but few machines were open.
I left with more money than I bet. It was work, trying to play ‘perfect’ strategy for that paytable. I felt and stated my success was due to focus on strategy AND luck….which both of them poo-pooed. And, both of them left very, very down. In every session.
So – my question is…is their statement (“…if one played 1,000,000. through the same 97% paytable, one would be GUARENTEED 97% of the total bets….”) true at all? If it is not, how should I respond?
Anything would be better than my ‘whatever’!
analisa burden
analisa burden:
The statistical term you are looking for is Confidence Intervals.
For example, the gaming industry give a return calculation in slots based on 10,000,000 “pulls” (now spins) at the 90% Confidence Interval.
Both a “data science” graduate and a “physicist” ought to know Confidence Intervals.