Mental
Mental
Joined: Dec 10, 2018
  • Threads: 1
  • Posts: 25
October 14th, 2020 at 8:25:48 AM permalink
Quote: Tony8216

Hello,
Thank you for the posts. Are using the terms "sequential" and "reversible" as synonyms in your results?

It takes a lot of effort to be clear and comprehensive on terminology.
I did define Sequential Royal Flushes as SRF, and I use it to generically describe any sequential RF type. I also used RSRF to refer specifically to a two-way SRF. Since there are even wraparound sequential RFs, I would use the acronym WSRF if I ever cared to work on these.

I will try to tag each table in any future posts with one-way SRF or two-way SRF to be clearer. I will also include the game and pay table.
gordonm888
gordonm888
Joined: Feb 18, 2015
  • Threads: 38
  • Posts: 2607
October 14th, 2020 at 10:57:59 AM permalink
Quote: Mental

It takes a lot of effort to be clear and comprehensive on terminology.
I did define Sequential Royal Flushes as SRF, and I use it to generically describe any sequential RF type. I also used RSRF to refer specifically to a two-way SRF. Since there are even wraparound sequential RFs, I would use the acronym WSRF if I ever cared to work on these.

I will try to tag each table in any future posts with one-way SRF or two-way SRF to be clearer. I will also include the game and pay table.



I agree with Mental's use of terminology. From a math point of view, it does not matter whether a payout is for TJQKA or AKQJT RFs; it simply matters whether the payout is for one ordered sequence or for two ordered sequences.

Its interesting that in a game with a payout for both TJQKA and AKQJT RFs, when you have a hand such as:

2d-3c-Qs-6h-7c you will be drawing to the Queen with two ways to make a SRF.
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
Vegasrider
Vegasrider
Joined: Dec 23, 2017
  • Threads: 55
  • Posts: 556
October 14th, 2020 at 1:52:54 PM permalink
This was last night. I think this is the 3rd, maybe 4th time I have had this draw on the same machine over the course of a year.
http://imgur.com/gallery/8zPI3BY
Mental
Mental
Joined: Dec 10, 2018
  • Threads: 1
  • Posts: 25
Thanks for this post from:
unJon
October 15th, 2020 at 8:58:40 AM permalink
Quote: Vegasrider

This was last night. I think this is the 3rd, maybe 4th time I have had this draw on the same machine over the course of a year.


Your SRF would have paid 15,846 bets. Your EV was 339 bets. Here are the average EVs for each sequential hold. Even though the Q counts for two SRF draws on a two-way RSRF game, it still gives a worse EV than a jack or ace held in a sequential position.

1 1 3 4 5 9 80 160 160 400 50 50 800 15846 : Double Double Bonus
EVSeq Hold
0.323
0.440J
0.439Q
0.432K
0.464A
0.599JT
0.583QT
0.567KT
0.558AT
0.711QJ
0.696KJ
0.687AJ
0.696KQ
0.687AQ
0.687AK
8.381QJT
8.292KJT
8.201AJT
8.292KQT
8.201AQT
8.201AKT
8.388KQJ
8.297AQJ
8.297AKJ
8.297AKQ
339.606KQJT
338.419AQJT
338.419AKJT
338.419AKQT
338.482AKQJ

I noticed that the SRF progressive at Hard Rock was almost high enough to start holding a single ten in the right position. This would become the right play above 126,000 bets, and that progressive was already at 120,680 bets.
Mental
Mental
Joined: Dec 10, 2018
  • Threads: 1
  • Posts: 25
October 15th, 2020 at 1:42:14 PM permalink
I created a table of the average values of the sequential RF holds assuming two-way SRFs. The top column is the payoff for a SRF starting at 800 and going to 120,000 bets. Therefore, the second column is equivalent to normal 6/5 BP with a standard 800 payout on a RF. These numbers should be the same as the values you would get from any VP analyzer for 6/5 BP.

For example, the table indicates that the value of a xxQJT hold averages to 1.463. (For 6/5 BP, the EV of TJQxx ranges from around 1.4191 to 1.4903, depending on penalty cards.)

Also, AxxxT is not a hold if the SRF pays 800, but AxxxT in the sequential positions is better than holding just an ace when the SRF pays 5000. ('-nan' means 'not a number'. Since there are zero cases, the average is undefined)

You could use this table to find the strategy break points for the two-way SRF progressive at different levels by interpolating the table. There are very few strategy break points for 4-card SRF holds, so I omitted these. Also, these are average EV values that don't consider penalty cards.

1 2 3 4 5 6 40 80 25 50 800 ???: Bonus Poker
Seq Hold800500010000150002000030000400006000080000100000120000
0.3560.3560.3560.3560.3560.3570.3570.3580.3590.3590.360
J0.4740.4750.4760.4770.4780.4800.4830.4860.4900.4930.496
Q0.4700.4720.4740.4760.4790.4830.4860.4930.5000.5080.516
K0.4650.4660.4670.4690.4700.4720.4740.4790.4840.4870.491
A0.4780.4790.4800.4810.4820.4830.4840.4860.4890.4940.498
JT0.4880.5260.5770.6270.6790.7810.8781.0831.2881.4941.689
QT0.4740.5120.5610.6120.6630.7660.8631.0681.2731.4791.674
KT0.4640.4970.5450.5960.6470.7500.8481.0531.2581.4641.658
AT-nan0.4850.5330.5830.6350.7370.8361.0401.2461.4511.657
QJ0.5960.6380.6890.7400.7920.8940.9971.2011.4061.5911.797
KJ0.5800.6220.6730.7240.7760.8790.9821.1861.3911.5761.782
AJ0.5670.6100.6610.7120.7640.8670.9701.1741.3791.5741.769
KQ0.5800.6220.6730.7240.7760.8790.9821.1861.3911.5761.782
AQ0.5670.6100.6610.7120.7640.8670.9701.1741.3791.5741.769
AK0.5670.6100.6610.7120.7640.8670.9701.1741.3791.5741.769
QJT1.4633.3945.7008.01210.32514.95019.57628.82638.07747.32856.578
KJT1.3703.3005.6117.92310.23614.86119.48728.73737.98847.23956.489
AJT1.2753.2085.5207.83210.14514.77019.39528.64637.89747.14856.398
KQT1.3703.3005.6117.92310.23614.86119.48728.73737.98847.23956.489
AQT1.2753.2085.5207.83210.14514.77019.39528.64637.89747.14856.398
AKT1.2753.2085.5207.83210.14514.77019.39528.64637.89747.14856.398
KQJ1.4703.3975.7078.02010.33314.95819.58328.83438.08547.33556.586
AQJ1.3763.3055.6167.92910.24114.86719.49228.74337.99447.24456.495
AKJ1.3763.3055.6167.92910.24114.86719.49228.74337.99447.24456.495
AKQ1.3763.3055.6167.92910.24114.86719.49228.74337.99447.24456.495
gordonm888
gordonm888
Joined: Feb 18, 2015
  • Threads: 38
  • Posts: 2607
October 15th, 2020 at 5:01:15 PM permalink
One difficulty with a lot of these types of analysis is what to assume about the discarded cards.

Obviously, holding a Qs in a sequential position is affected if one of the cards you discard is a 10s.

But the return on a Qs is also affected if you discard a 10d or an 8 spades - or both. Or discarding 2 suited cards, decreasing the chances of a flush even further.

For the numbers being provided what are you assuming about the discards?

Edit: I just noticed the comment about "average EV with no penalty cards." I guess that's a reasonable way to simplify the analysis, but the fact that you have also discarded 2-4 cards that are known not to be Royal cards may not be trivial. And for a decision like whether to draw to Ks or KsTs with Ts-2h-4c-Ks-7d, you need to take into account that no royal is possible if drawing to the King.
Last edited by: gordonm888 on Oct 15, 2020
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
Mental
Mental
Joined: Dec 10, 2018
  • Threads: 1
  • Posts: 25
October 15th, 2020 at 6:00:28 PM permalink
Quote: gordonm888

One difficulty with a lot of these types of analysis is what to assume about the discarded cards.

Obviously, holding a Qs in a sequential position is affected if one of the cards you discard is a 10s.

But the return on a Qs is also affected if you discard a 10d or an 8 spades - or both. Or discarding 2 suited cards, decreasing the chances of a flush even further.

For the numbers being provided what are you assuming about the discards?



I am averaging over only those hands where the hold listed in the left column is the best hold for the given deal. This eliminates holding Qs and discarding Ts. Under no circumstance would the single Qs be the best hold if another spade royal card is present in the dealt hand. be the best hold. I realize it would be very deceptive to average the EV over all holding of a bare Qs without regard to the discards, since the worst penalties (RF penalties) would lower the average EV.

For purposes of this table, I am averaging over all penalty situations that are not bad enough to prevent the sequential RF hold from being the best hold. Near the strategy break points, when the SRF hold is very close to another hold, this means my average will be slightly higher than the generic average. When I am not near strategy break points, every penalty situation is included in the average, except that RF penalty cards are never included in the EV averages.

For example, the EV average for the AxxxT hold doesn't average over very many single flush penalty situations of hands that also contain a king, and includes no double flush penalty situation. The EV average for xxQJT includes every penalty situation under the sun, except for RF penalty cards.
gordonm888
gordonm888
Joined: Feb 18, 2015
  • Threads: 38
  • Posts: 2607
October 15th, 2020 at 6:09:01 PM permalink
Quote: Mental

I am averaging over only those hands where the hold listed in the left column is the best hold for the given deal. This eliminates holding Qs and discarding Ts. Under no circumstance would the single Qs be the best hold if another spade royal card is present in the dealt hand. be the best hold. I realize it would be very deceptive to average the EV over all holding of a bare Qs without regard to the discards, since the worst penalties (RF penalties) would lower the average EV.

For purposes of this table, I am averaging over all penalty situations that are not bad enough to prevent the sequential RF hold from being the best hold. Near the strategy break points, when the SRF hold is very close to another hold, this means my average will be slightly higher than the generic average. When I am not near strategy break points, every penalty situation is included in the average, except that RF penalty cards are never included in the EV averages.

For example, the EV average for the AxxxT hold doesn't average over very many single flush penalty situations of hands that also contain a king, and includes no double flush penalty situation. The EV average for xxQJT includes every penalty situation under the sun, except for RF penalty cards.



Excellent methodology. You've put a lot of thought into that -as well as a lot of work. I'm impressed.
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
Mental
Mental
Joined: Dec 10, 2018
  • Threads: 1
  • Posts: 25
October 15th, 2020 at 6:15:55 PM permalink
Also, my own VP strategy generator breaks hands down by flush penalties, straight penalties, and high-card penalties. It just isn't possible to present all this information in a simple table. Also, a 6/5 bonus progressive is almost always very negative EV and unplayable or very positive where penalties are fairly unimportant compared to the huge variance of the game.
Mental
Mental
Joined: Dec 10, 2018
  • Threads: 1
  • Posts: 25
October 15th, 2020 at 6:24:23 PM permalink
Quote: gordonm888

Edit: I just noticed the comment about "average EV with no penalty cards." I guess that's a reasonable way to simplify the analysis, but the fact that you have also discarded 2-4 cards that are known not to be Royal cards may not be trivial. And for a decision like whether to draw to Ks or KsTs with Ts-2h-4c-Ks-7d, you need to take into account that no royal is possible if drawing to the King.



I absolutely agree. Of course, once you discard the Ts, any ordinary EV calculator will give you the correct EV and the best hold with respect to other possible holds.

The question only comes up if the K and T are in sequential order. I can't imagine that you would ever hold a bare K. The conflict would be with KJ-offsuit, etc.

  • Jump to: