Three Card Sabotage
I meant to label the strategy decisions this way:
For basic strategy, I am currently getting:
Raise 2: AQ2 or higher
Raise 1: K97 Or Higher
Fold: K-9-6 or lower
I still have a bug relating to when the sabotage cards are paired and match a dealer card. When I fix it, my recommended strategy may change a skootch.
Again ignoring the Player's cards, which would have a slightly impact on the boundary as it would reduce the chances of the Dealer getting A-high, I get the boundary is AQ5. Chances of AQ6+ = 49.82% AQ4- = 49.93%.
Added: I'm guessing when the Player's cards are considered it will be similar to other poker games. In those cases when you have a card, that reduces the chances of the Dealer getting one, while if you don't then the chances for the Dealer is better. Thus I can imagine the same logic might apply here; so you raise any AQx (as you have one of the Queens) and only call with AJx (as the Dealer has more chance to beat you with an AQ).
Quote: charliepatrickI agree that it would be in the area of AQx.
Again ignoring the Player's cards, which would have a slightly impact on the boundary as it would reduce the chances of the Dealer getting A-high, I get the boundary is AQ5. Chances of AQ6+ = 49.82% AQ4- = 49.93%.
Added: I'm guessing when the Player's cards are considered it will be similar to other poker games. In those cases when you have a card, that reduces the chances of the Dealer getting one, while if you don't then the chances for the Dealer is better. Thus I can imagine the same logic might apply here; so you raise any AQx (as you have one of the Queens) and only call with AJx (as the Dealer has more chance to beat you with an AQ).
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I have a composition dependent spreadsheet. The removal of the Ace in AQx will increase the EV of AQ2 by more than 4 percentage points (i.e., the win percentage of AQ2 goes up by about 0.7%). Because you are reducing the probability of dealer's AKx and AQx hands that you will lose to.
Quote: charliepatrickI agree that it would be in the area of AQx.
Again ignoring the Player's cards, which would have a slightly impact on the boundary as it would reduce the chances of the Dealer getting A-high, I get the boundary is AQ5. Chances of AQ6+ = 49.82% AQ4- = 49.93%.
Added: I'm guessing when the Player's cards are considered it will be similar to other poker games. In those cases when you have a card, that reduces the chances of the Dealer getting one, while if you don't then the chances for the Dealer is better. Thus I can imagine the same logic might apply here; so you raise any AQx (as you have one of the Queens) and only call with AJx (as the Dealer has more chance to beat you with an AQ).
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I have a composition dependent spreadsheet. The removal of the Ace in AQx will increase the EV of AQ2 by more than 4 percentage points (i.e., the win percentage of AQ2 goes up by about 0.7%). Because you are reducing the probability of dealer's AKx and AQx hands that you will lose to.
Three Card Sabotage Basic Strategy
Raise-2 on AJT or Higher.
Raise-1 on K94 to AJ9
Fold on K93 or lower.
Quote: gordonm888Found the glitch in my spreadsheet, and it should be accurate now.
Three Card Sabotage Basic Strategy
Raise-2 on AJT or Higher.
Raise-1 on K94 to AJ9
Fold on K93 or lower.
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That’s awesome that you’ve worked out the strategy! Any chance that the house edge is an “easy calculation” from here? Just curious…
Quote: camapl
That’s awesome that you’ve worked out the strategy! Any chance that the house edge is an “easy calculation” from here? Just curious…
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First we don't yet know what the bonus payouts are for the high hands.
Second, there are two ways to calculate the house edge, both of which will be much easier now that we have defined the strategy rules:
- a loop code that runs through every combination of player, dealer and sabotage cards. (This is a 9 card game, which is not too bad although the UTH game that Teliot was evaluating in another thread was also 9 cards and that looping code run was stated to take about 4 days.)
- a simulation, just run 100M or 1B hands and accumulate statistics.
There are multiple members who could do either or both but they need to have an interest. The sabotage cards are a novel innovation (which I kinda like) but it does make algorithms for automated hand evaluation a bit more difficult because the dealer's hand can range from 0 to 4 cards.
We'll see if anyone steps up.
The Player's hands could be simplified to types of hands (e.g. AsKsJs, AsKsJh, AsKhJs, AsKhJh, AsKhJd, with appropriate factors, to cover all the AKJ possibilities).
But then I'd go onto looping all 52/51/50/49 remaining cards, ignoring any scenarios with ones already held by the player... (while this is longer than working out the types of hands the dealer can make, it's less error prone). I think at the knockout stage one may be able to work out the chances of matching cards rather than looping, but again it might be easier just to loop.
(If I wasn't busy working on a Blackjack project I might have looked into this in more detail!)
Quote: charliepatrick^ I agree it's a lot of work although in this case, unlike UTH, there's only one decision point for the Player.
The Player's hands could be simplified to types of hands (e.g. AsKsJs, AsKsJh, AsKhJs, AsKhJh, AsKhJd, with appropriate factors, to cover all the AKJ possibilities).
But then I'd go onto looping all 52/51/50/49 remaining cards, ignoring any scenarios with ones already held by the player... (while this is longer than working out the types of hands the dealer can make, it's less error prone). I think at the knockout stage one may be able to work out the chances of matching cards rather than looping, but again it might be easier just to loop.
(If I wasn't busy working on a Blackjack project I might have looked into this in more detail!)
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Charlie, I agree with everything you say. As you state, there are indeed ways, such as suit folding, to somewhat simplify the House Edge calculation (almost all of which I did indeed incorporate into my composition-dependent spreadsheet to evaluate KISSC hand decisions.) Having said all that, it is still a considerable undertaking. Other than Wizard and JB, I can think of 8 forum members* off the top of my head who I personally know are adept and efficient at doing loop codes or simulations for (non-BJ) table games. However, some (but not all) of those people may be accustomed to charging fees and/or have various terms and conditions for performing analyses.
My point, though, is that game strategy optimization and House Edge calculations for non-BJ games involve a considerable amount of work requiring considerable niche expertise, and that not everyone gives it away for free -i.e., just for the joy of doing calculations and for the joy of being helpful.
* BTW, there may be dozens of forum members whom I am not aware of who routinely do these type of looping code or monte carlo simulation calculations for non-BJ table games. Because, obviously, some WOV forum members choose not to advertise their capabilities for various reasons! And because I certainly don't know everyone and everything.
