Using One Strategy for Two Games

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:

  1. The unblended strategy is really close anyway.
  2. The unblended strategy is often the first one players learn, as it’s the one most teachers start with.
  3. 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.

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