extra action poker

[EDC1977]

Given the 12 extra hands and the 15 extra coins for this game, how does one go about figuring out a marginal ER for this game? I'm no mathematician but I can utilize a calculator like Shadow and New2vp utilize their skills.  )  Thanks for any help

[New2vp]

It's not extremely difficult to calculate the marginal EV of the Extra Action bonus hands.  Given the structure of the game, this marginal EV is completely based on luck.  Nothing the player can do can enhance or decrease that EV.  It is totally based on the number of dealt aces (or deuces on the wild games) and the Extra Action pay schedule.  I don't know if the pay schedules can be different in the casinos but when I examined the games here in March, there appeared to be a single schedule for all non-wild games and another for the Deuce games.The probability distribution for the number of dealt aces (or deuces) is always:




Aces
Combos
Percent


0
1712304
65.8842%


1
778320
29.9474%


2
103776
3.9930%


3
4512
0.1736%


4
48
0.0018%







Total
2598960


That is just how the cards fall and is no different than the deals from any other game with the same 52-card deck.So, 34% of the time, we will be accumulating coins on the bonus hands.  It is progressively more difficult to determine the final hand distribution as you go from 4 dealt aces (or deuces) to 1 dealt ace (or deuce).  However, this distribution, once calculated, is the same for each and every game.  For any given pay schedule, you can figure the average payoff.When 4 aces are dealt, all bonus hands will be quads; when 3 aces are dealt, you get about 4% quads, 6% full houses, and 90% trips; when 2 aces are dealt, you get <1% quads, 1% full houses, 11% trips, 16% 2 pairs, 72% pair of aces.  Any final hand on the pay schedule is possible when one ace is dealt, including 69% of the time getting no paying hand.The marginal bonus-hand EV is > 99% for the non-wild games (and all the base game EVs that can be selected are < 99%), meaning it is a good bet when playing the pay schedules on the Web site to select as many bonus hands as possible if you want to maximize EV.  Since the marginal bonus-hand EV is also < 100%, this means that the expected loss in coins per hand will be greater with more bonus hands.  So you have the normal decision when faced with negative machines:  You have to decide whether you want a higher EV or a lower per-hand coin loss.My first look at the deuce game showed the bonus hand EV to be LOWER than the base game EVs (between 96 and 97% vs. 98.8% and 98.9%), so it did not look like a good deal to add the bonus hands to the deuce games.  However, the base game EV on the deuce games WAS higher than all the non-wild base game EVs that you could select when playing Extra Action except for DDB.My combinatorics were completed by plugging numbers into an Excel spreadsheet without the aid of a vp program, so I could be off, but I did take some precautions to check my work. 

[EDC1977]

  I appreciate the help. Mike Shackelford and Dancer hadn't done any research on it. I was just wondering if anyone here did. Nothing from Anthony Curtis either. Thank you New!!

[New2vp]

You're welcome.  I didn't say it earlier, but you do have one other choice.  When the bonus EV is greater than the base game EV, you should choose to play fewer hands if you can play the same number of bonus hands...if the pay schedules are equal.  (And of course, vice versa, if the order of the EVs is reversed.)On site, 3 of the 4 games that are offered in both 3-play and 5-play have different pay schedules with the 3-play being better than the 5-play.  I presume that they just wanted to give us a choice of pay schedules to practice on here.

[EDC1977]

Not only knowing EV/ER but checking paytables. Vigilance vs. just putting money in the bill acceptor. Often, the PE game isn't always available but 99% plus club benefits will make it PE. Thanks!!!