New Table Game - Player Power Poker
I am the 2nd install. The first was in California. There is a list of other states including Nevada where they are getting the game approved.
Player Power Poker is similar to Three Card Poker but then ads a 4 card hand and then a 5 card hand. Here is the layout we use:
And the rack card... There is a mistake on the rack card though. On the five card hand it says that two pair or better wins. I reduced the house edge by adding a pair of aces as the minimum hand:
A couple of notes on the game...
1. There is no dealer qualifying.
2. The player never has to fold. A poor 3 card hand can and many times does turn into a winner on 4 card or 5 card hand.
3. 70% of the time (so says the inventor) players win at least one of the bets.
4. There is a definite strategy to this game that is not part of regular Three Card Poker. Deciding if you want to play risky for a possible 3-2 payoff or play safe if your power card helps the hand and play for 1-2 is a very tough decision sometimes (especially with no known optimal play at this time).
5. Players make out pretty well when they hit a pair of aces, two pair (only using one of course in the 3 card hand) and 3 of a kind, because they are guaranteed to win all three bets, with possibilities of improving on 5th and 6th street.
If the Wizard would like the math report on the game I can supply to save you some work if you want to do optimal strategy. If anyone has any questions about the game or thoughts, let me know.
ZCore13
Quote: BozWith your change on the Aces what is the calculate HE? Thanks!
3 Card - 2.14%
4 Card - 7.57%
5 Card - 10.34%
Three equal bets combined HE = 6.68%, which is almost exactly the same as our previous Three Card Poker with the 6 card bonus. If I was playing I would probably play something like $10 or $15 on the 3 card with $5 on the 4 and 5 card bets. $15/$5/$5 combined HE would then be 4.87%, compared to 5.46% for our Three Card Poker that it replaced.
EDIT: By the way, the game originally came to me with a 25.31% HE on the 5 card hand. I said no way in hell and adjusted the pay tables myself to get it down to 10.34% which is just about the same as the 6 card bonus bet in Three Card Poker and the pocket bonus bet in Heads up Holdem (similar to UTH)
ZCore13
http://playerpowerpoker.blogspot.com/2014/11/player-power-poker-now-for-class-ii.html
That version appears to suggest that the player's 3 cards are combined with a fourth card to make the best 3-card hand, and if the best hand happens to include the fourth card (which should happen 3/4 of the time) then a winning hand pays 1:2.
In your description above, though, it seems that the player makes a choice as to whether to play a strong 3-card hand without the 4th card (vs. the dealer's 4 cards) or whether to use the 4th card against the dealer's 4 cards for a lower payout on a win. Is that right?
Quote: MathExtremistThe rack card on the inventor's site has slightly different rules.
http://playerpowerpoker.blogspot.com/2014/11/player-power-poker-now-for-class-ii.html
That version appears to suggest that the player's 3 cards are combined with a fourth card to make the best 3-card hand, and if the best hand happens to include the fourth card (which should happen 3/4 of the time) then a winning hand pays 1:2.
In your description above, though, it seems that the player makes a choice as to whether to play a strong 3-card hand without the 4th card (vs. the dealer's 4 cards) or whether to use the 4th card against the dealer's 4 cards for a lower payout on a win. Is that right?
They are the same. Players make their best 3 card hand. If the player uses just the three cards and not the power card they win 3-2. If the player needs the power card and uses it (with 2 of the 3 other cards) to make a 3 card hand, they win 1-2. Same rules, just described a little differently (and better) by me. :)
If you notice their rack card also limits the ratio of the 3 card to the other bets to not allow a combined HE lower than recommended. I removed that rule and I'm fine with players that wager more getting a lower HE.
ZCore13
Quote: Zcore13They are the same. Players make their best 3 card hand. If the player uses just the three cards and not the power card they win 3-2. If the player needs the power card and uses it (with 2 of the 3 other cards) to make a 3 card hand, they win 1-2. Same rules, just described a little differently (and better) by me. :)
So there's no actual decision to be made? You made it sound like there was a strategy, like if I held AhAcKd and the fourth card was As, I could decide to stay on the pair of aces and go for a 3-2 win, or use the 3rd ace for trips and a nearly-guaranteed 1-2 win. The rack card you posted says "decide" on it, but the rack card at the other website doesn't. That gave the impression that you'd always make the best 3-card hand, which in the example here would be trip aces for a 1-2 win. Hence my confusion.
Quote: MathExtremistSo there's no actual decision to be made? You made it sound like there was a strategy, like if I held AhAcKd and the fourth card was As, I could decide to stay on the pair of aces and go for a 3-2 win, or use the 3rd ace for trips and a nearly-guaranteed 1-2 win. The rack card you posted says "decide" on it, but the rack card at the other website doesn't. That gave the impression that you'd always make the best 3-card hand, which in the example here would be trip aces for a 1-2 win. Hence my confusion.
There are definitely decisions to make. Let's say your Power Card is a 5h and your 3 other cards are Ad 10c 5s. Do you play the A/10/5 for a 3-2 payout if you beat the dealer or do you use the power card making your best 3 card hand 5/5/A (pair of fives). Obviously much more likely to win with a pair of 5's over A high, but only 1-2 payout for using the power card.
How about if you get a power card of Jd... Your 3 cards are 10c 10s, Qc. Are the 10's good enough to win and take the 3-2, or do you use the power card for the straight? A straight is obviously very strong and just like in Three Card poker beats a flush.
ZCore13
In other words, the player gets 3 cards to play against the dealer's best 3-of-4 for a 3-2 win, or they can choose to play best 3-of-4 against the dealer's best 3-of-4 for a 1-2 win. Right?
ZCore13
ZCore13
Maybe I missed it. Do you have to decide whether you're using the power card or not before the dealer reveals ?
If the power card improves your hand, but your base hand is still stronger than the dealer's, (assuming you don't have to decide - that the cards talk), what happens if your original hand beats the dealer? Do you get paid 3-2 because your base hand was "good enough" or is only your best hand considered, and thus pays 1-2?
I'd play. Hope it goes well for you. Really glad you made the HE reasonable with your adjustments.
How long will it take for you to see if this game will stay on your floor or not, 3 months or more?
Quote: beachbumbabsZCore,
Maybe I missed it. Do you have to decide whether you're using the power card or not before the dealer reveals ?
If the power card improves your hand, but your base hand is still stronger than the dealer's, (assuming you don't have to decide - that the cards talk), what happens if your original hand beats the dealer? Do you get paid 3-2 because your base hand was "good enough" or is only your best hand considered, and thus pays 1-2?
I'd play. Hope it goes well for you. Really glad you made the HE reasonable with your adjustments.
You decide after seeing your three down cards and thinking if you want to use the Power Card or not. Once you decide you either place your 3 cards in the 3-2 box, which means you are playing them alone or you place them in the 1-2 box, which means you are using the Power Card.
Now once the 3 card hand vs. the dealer is complete the dealer discards their hand and you use all 4 of your cards, whether you used the Power Card or not, for the 4 and 5 card hands.
ZCore13
Quote: UCivanWill U have it open everyday or only on the weekends? I am going to try it.
How long will it take for you to see if this game will stay on your floor or not, 3 months or more?
It is available to play anytime. If it is not open and someone asks we will open it.
I'll start looking at the numbers at about 90 days. I think because of the complexity and 3 stages of play, it might take a little time for players to decide if they really like it or not and how to play it.
ZCore13
Quote: HunterhillDo you have to play the 4 card and 5 card bets? What are the min and max bets allowed?
All 3 bets are required. Right now we are only requiring one bet to be $5. The others can be as low as $1. This may change after about 30 days of play. Not sure if I'll require at least 5 on each bet or a $10 minimum somewhere. With a 70% chance of winning something back, I don't think I can continue to allow a $7 total bet permanently. The hands per hour are very low and the table wouldn't have enough money wagered to be able to keep it.
ZCore13
ZCore13
Then if I get my ass kicked too much I'll make adjustments. :)
ZCore13
Quote: Zcore13At this point, yes you can. As a matter of fact, I might even raise the limit for you to $500 so you can do $490, $5 and $5.
Then if I get my ass kicked too much I'll make adjustments. :)
If you do get your ass kicked, it'll be because of variance, not theo. I don't know how much business you do but I presume you're bankrolled to handle $500 action. $500 action on a bet with three results (+500, -250, -750) shouldn't be too risky, and at 2.14% you're looking at nearly $11/hand in win. I could calculate the exact variance if I had the probability breakdown but that's uncertain because you'll have suboptimal play going on too. Not sure how that would factor in, whether players would stay too often or too little, but at least you'd increase the $11/hand to something greater.
You mentioned in the first post that there was no known optimal strategy at this time, but that can't be right if the house edge is correct -- the code would need to calculate the optimal play for every combination. Did you mean that the vendor didn't provide a concise, player-friendly optimal or near-optimal strategy (like "play Q/6/4 or better")?
Early on in the wild-west days of Internet gambling I worked with a lot of Caribbean operators who were under-funded but still allowed $1000 or $5000 slot machine bets. Then they wondered why they lost their $150,000 bank to one guy so they (a) didn't pay him and (b) required the software vendors to rig the games to go into "loss-mitigation" mode whenever they paid a jackpot. I had to do a lot of convincing to my clients that nobody would play those games after very long.
Quote: MathExtremistIf you do get your ass kicked, it'll be because of variance, not theo. I don't know how much business you do but I presume you're bankrolled to handle $500 action. $500 action on a bet with three results (+500, -250, -750) shouldn't be too risky, and at 2.14% you're looking at nearly $11/hand in win. I could calculate the exact variance if I had the probability breakdown but that's uncertain because you'll have suboptimal play going on too. Not sure how that would factor in, whether players would stay too often or too little, but at least you'd increase the $11/hand to something greater.
You mentioned in the first post that there was no known optimal strategy at this time, but that can't be right if the house edge is correct -- the code would need to calculate the optimal play for every combination. Did you mean that the vendor didn't provide a concise, player-friendly optimal or near-optimal strategy (like "play Q/6/4 or better")?
Early on in the wild-west days of Internet gambling I worked with a lot of Caribbean operators who were under-funded but still allowed $1000 or $5000 slot machine bets. Then they wondered why they lost their $150,000 bank to one guy so they (a) didn't pay him and (b) required the software vendors to rig the games to go into "loss-mitigation" mode whenever they paid a jackpot. I had to do a lot of convincing to my clients that nobody would play those games after very long.
Yes, of course you are correct that over the long haul I can't get my ass kicked with a 2.14% HE. I didn't fully describe what my thoughts were on that. The ass kicking could occur if the HE can swing the other way with the "known cards" strategy I mentioned and/or player collusion. There's always that risk on a single deck game and with such a low house edge (2.196%) with a $240/$5/$5 wager, I have to be very cognizant of the possibility.
GLI did the Math on the game and came up with the HE for the wagers but did not provide the optimal play (like Q/6/4 in Three Card). I don't know if they couldn't or just didn't. It is my belief from studying the game, rules, payouts, etc. that players should play with just the 3 cards and not the Power Card about 75% of the time. This being because even though sometimes the Power Card improves the hand, it doesn't improve it enough to make it worth taking 1-2 compared to 3-2 on a win. This is why I find the game so interesting at this point. The strategy seems very complex. Which may also end up causing the demise of the game as well. I'm not sure players can play it properly.
ZCore13
Quote: Zcore13Yes, of course you are correct that over the long haul I can't get my ass kicked with a 2.14% HE. I didn't fully describe what my thoughts were on that. The ass kicking could occur if the HE can swing the other way with the "known cards" strategy I mentioned and/or player collusion. There's always that risk on a single deck game and with such a low house edge (2.196%) with a $240/$5/$5 wager, I have to be very cognizant of the possibility.
GLI did the Math on the game and came up with the HE for the wagers but did not provide the optimal play (like Q/6/4 in Three Card). I don't know if they couldn't or just didn't. It is my belief from studying the game, rules, payouts, etc. that players should play with just the 3 cards and not the Power Card about 75% of the time. This being because even though sometimes the Power Card improves the hand, it doesn't improve it enough to make it worth taking 1-2 compared to 3-2 on a win. This is why I find the game so interesting at this point. The strategy seems very complex. Which may also end up causing the demise of the game as well. I'm not sure players can play it properly.
GLI doesn't do anything without being specifically directed to, so if the vendor asked only for an optimal house edge computation without also asking for a strategy write-up, they won't provide it. Intentionally designing a game with a particular player strategy is a very hard problem, much harder than just computing the edge under the optimal strategy, whatever it is, and hoping for the best.
For example, UTH is a killer because the mistakes players tend to make are very costly. The optimal strategy is hard or scary and the cost of making mistakes is very high. Some would argue too high, I recall hearing UTH is suffering from player burn-out. The edge on UTH for a player who plays perfectly except they only raise 3x instead of 4x (when appropriate) is -- get this -- 9.9%. That's brutal, but it neatly explains the high hold on the game. And I notice you didn't list UTH as one of your three carnival games -- if you had UTH but removed it, is that what happened on your floor?
By the way, that behavior stung Galaxy badly when they came out with a UTH competitor and moved some of the money from the 4x raise to some automatic (and mistake-free) pay. In practice, their game played much closer to optimal than UTH did and as a result held far less. Except they marketed it as a high-hold competitor to UTH, which it wasn't, at least not initially. I think Dan moved some things around after the initial rollout.
Can I assume your vendor didn't provide you with any information about how non-optimal players might play and what the edge would be under those alternate strategies? I'd hate to see you start with a game that the sell-sheet says is 2.14% but in reality it plays like 6.5% because you haven't been able to educate your players on even an approximate strategy.
Same story with a Power Card of 10d with Ac Ad 2d. Is the pair of Aces enough to win a majority of the time and take the 3-2 chance, or should the player play the flush using the Power Card and settle for a pretty sure 1-2.
It's all hurting my head... :)
ZCore13
Quote: Zcore13No optimal strategy exists that I know of. My Staff and I take the time to explain the game to players and inform them on the benefits of playing for the 3-2 when possible. Even with my experience and the thousands of hands I've watched by now I really can't even guess to an optimal strategy because of the fat that although using a Power Card of a 10d might improve a hand of Ks 9d 7c, to me it really doesn't improve it enough to settle for 1-2 in improving your hand. I have to ask players how risky they like to play and let them determine themselves.
Same story with a Power Card of 10d with Ac Ad 2d. Is the pair of Aces enough to win a majority of the time and take the 3-2 chance, or should the player play the flush using the Power Card and settle for a pretty sure 1-2.
It's all hurting my head... :)
Well, there *is* an optimal answer to both of those examples and the software used to compute the house edge should have taken that into account. If it didn't, it's not accurate. The strategic problem is that you and your players don't know what those optimal decisions are and they haven't been distilled into a concise strategy for player consumption. There aren't all that many combinations for a 3+1 vs. 4 card game, so putting together an optimal (or near-optimal) strategy wouldn't be that tough. It's just about a million starting-hand combinations before suit-folding so a concise strategy might only be a dozen lines or so. Maybe it'd look a bit like a BJ strategy chart, or maybe a hybrid like the UTH "Wizard Strategy" here:
https://wizardofodds.com/games/ultimate-texas-hold-em/
You should verify that GLI didn't just eyeball some strategy and simulate a few million hands to compute the edge based on that strategy, because if they did, someone else could compute the real optimal edge and that might be player-positive. Check the GLI report for their methodology, they're pretty good about describing what they've done in the lab even when it's not exactly what needed to be done. (Please PM me if you want to have a real discussion offline.)
"A computer program was developed to simulate 10,000,000 initial player hands. For each hand, all dealer outcomes were cycled to determine the optimal three-card poker strategy; that is, choosing to use only the three down cards or the three down cards and the up card to create the best three-card poker hand."
So it seems they did develop an optimal strategy. I guess the inventor did not pay for that extra information??
ZCore13
It also sounds like each hand was drawn randomly. If so, no defined strategy would be available.
10,000,000 is a big number, but for GLI purposes, seems small. Just how many possible player hands are there?
Edit: 1,082,900. Did I calculate that right? If so, why did GLI do 10,000,000?
ZCore13
Did the GLI report at least indicate how often the players used 3 vs 4 cards?
Quote: Zcore13The GLI wording also seems to indicate that the simulation would not choose a lesser hand over a better hand for the 3-2 option, which I do not believe would be optimal play. It says it chose the best of the 3 card or 4 card options. The pair of Aces over a flush or a straight over a flush going for 3-2 would seem to me to be a better play, but maybe I'm wrong.
Optimal play should really mean "what's the play that maximizes the player's EV" rather than "what's the play that makes the strongest hand." For a given hand, if using the power card wins 81% of the time at 1:2 and standing wins only 49% of the time at 3:2, you still stand even though the power card clearly gives you the best hand. (This assumes no pushing, but I assume pushing actually happens in the game.)
If GLI's analysis simply took the best 3 card hand (whether it did or didn't use the power card) it would be very, very wrong. One one hand, there would be no need to cycle over anything to determine that strategy, you'd just look at the cards. On the other hand, determining the frequency of winning vs. losing would still require the looping so I hope that's not what they did.
ZCore13
Quote: Zcore13
GLI did the Math on the game and came up with the HE for the wagers but did not provide the optimal play (like Q/6/4 in Three Card). I don't know if they couldn't or just didn't.
ZCore13
Regarding the Optimal Strategy, here are some possibilities::
(1) Like Zcore said, GLI could be incapable of deriving the Optimal Strategy;
(2) Game Inventor did not (want to) pay for it (for certain business reasons)
(3) 10,000,000 hands are not be enough; the math we have on 4 Card Split uses 797,329,220,688,000 hands to derive the optimal Strategy
(4) There is an Optimal Strategy, however it is impossible to document (i.e. to put on papers.)
Our experience shows that when players do not play optimally, the hold of the game would become unnecessarily high and the game would lose popularity. Here is the catch. In playing popular games like UTH, players will learn to improve play strategy gradually, meanwhile casinos are happy to see high hold; for new games, casinos do not offer the same opportunities: if the hold is high and the drop is down, the new game is out.
Quote: Zcore13No optimal strategy exists that I know of. My Staff and I take the time to explain the game to players and inform them on the benefits of playing for the 3-2 when possible. Even with my experience and the thousands of hands I've watched by now I really can't even guess to an optimal strategy because of the fat that although using a Power Card of a 10d might improve a hand of Ks 9d 7c, to me it really doesn't improve it enough to settle for 1-2 in improving your hand. I have to ask players how risky they like to play and let them determine themselves.
Same story with a Power Card of 10d with Ac Ad 2d. Is the pair of Aces enough to win a majority of the time and take the 3-2 chance, or should the player play the flush using the Power Card and settle for a pretty sure 1-2.
It's all hurting my head... :)
ZCore13
My laptop sucks or I would do analysis, so you'll have to settle for a hand analyzer. No guaranties I don't have a typo or braino some where.
Quote: etablegamesRegarding the Optimal Strategy, here are some possibilities::
(1) Like Zcore said, GLI could be incapable of deriving the Optimal Strategy;
(2) Game Inventor did not (want to) pay for it (for certain business reasons)
(3) 10,000,000 hands are not be enough; the math we have on 4 Card Split uses 797,329,220,688,000 hands to derive the optimal Strategy
(4) There is an Optimal Strategy, however it is impossible to document (i.e. to put on papers.)
Our experience shows that when players do not play optimally, the hold of the game would become unnecessarily high and the game would lose popularity. Here is the catch. In playing popular games like UTH, players will learn to improve play strategy gradually, meanwhile casinos are happy to see high hold; for new games, casinos do not offer the same opportunities: if the hold is high and the drop is down, the new game is out.
I think you could be correct on any of the 4 possibilities you list. I'm leaning toward not being able to come up with an optimal strategy for the reasons I've described previously. One could definitely come up with a strategy of keeping the better of the two hands, but I do not believe that is optimal.
In regards to players not playing optimally, not playing optimally is part of the reason some games stay on the floor. I would not have 3-2 Blackjack at roughly a .7 house advantage if everyone played optimally. Games like Blackjack, Three Card Poker and UTH are consistently and continuously played sub-optimally, which is why a game that plays so slow can have a 2-3% house edge. A game like High Card Flush is a little different. It's almost impossible to not play optimally. I would expect to hold less in High Card Flush compared to a game that players can make mistakes, even if the other game has the same or lower house edge.
ZCore13
Well said. Just to show, the mere H.E. is not the whole story.Quote: Zcore13
In regards to players not playing optimally, not playing optimally is part of the reason some games stay on the floor. I would not have 3-2 Blackjack at roughly a .7 house advantage if everyone played optimally. Games like Blackjack, Three Card Poker and UTH are consistently and continuously played sub-optimally, which is why a game that plays so slow can have a 2-3% house edge. A game like High Card Flush is a little different. It's almost impossible to not play optimally. I would expect to hold less in High Card Flush compared to a game that players can make mistakes, even if the other game has the same or lower house edge.
ZCore13
Quote: mipletMy laptop sucks or I would do analysis, so you'll have to settle for a hand analyzer. No guaranties I don't have a typo or braino some where.
There are only a million options. Just iterate. You know you want to. :)
Quote: MathExtremistQuote: mipletMy laptop sucks or I would do analysis, so you'll have to settle for a hand analyzer. No guaranties I don't have a typo or braino some where.
There are only a million options. Just iterate. You know you want to. :)
LOL. It would take my server 58 hours to do. And that would not give a strategy. Maybe later.
Quote: MathExtremistOptimal play should really mean "what's the play that maximizes the player's EV" rather than "what's the play that makes the strongest hand." For a given hand, if using the power card wins 81% of the time at 1:2 and standing wins only 49% of the time at 3:2, you still stand even though the power card clearly gives you the best hand. (This assumes no pushing, but I assume pushing actually happens in the game.)
If GLI's analysis simply took the best 3 card hand (whether it did or didn't use the power card) it would be very, very wrong. One one hand, there would be no need to cycle over anything to determine that strategy, you'd just look at the cards. On the other hand, determining the frequency of winning vs. losing would still require the looping so I hope that's not what they did.
IMO, Zcore, it would be worth putting the info that the dealer uses 4 cards back on the rack card, though I'm sure it's apparent on the first hand. (Comparing your card to the inventor's.) Just FWIW; it was a point of confusion for me until ME mentioned it.
I was trying to see what the median 3 card value of a 4 card hand is, but I'm not finding it trying to look it up. I guess it's an exercise for the student, but maybe it's not far off, assuming the median is similar to 3CP, near Q-6-4 (and thus, the strategy). For example, to get a flush:
11154 (13combin3)x(39combin1) hands with exactly 3 out of 4 of a suit, + 715 (13combin4) 4 out of 4, x 4 suits, = 47,476 ways for the dealer to make a flush out of 1,082,900, or 4.3842%.
In 3CP, it's 1096 ways out of 22,100 for 4.9412%.
Why would it be more likely to get a flush 3 cards out of 3 than 3 cards out of 4? That doesn't make sense. If I'm doing this wrong, please correct me. But if I'm doing it right, maybe a player should stand on, say, K high or so, unless the power card is a king or ace.
OTOH, it HAS to be more likely to get a pair in 4 cards than in 3, so maybe the stand point is around a pair of 6's in hand.
Quote: beachbumbabs
11154 (13combin3)x(39combin1) hands with exactly 3 out of 4 of a suit, + 715 (13combin4) 4 out of 4, x 4 suits, = 47,476 ways for the dealer to make a flush out of 1,082,900, or 4.3842%.
In 3CP, it's 1096 ways out of 22,100 for 4.9412%.
Why would it be more likely to get a flush 3 cards out of 3 than 4 cards out of 3? That doesn't make sense. If I'm doing this wrong, please correct me.
If you're only looking at 4 cards overall, without regard to which is the power card, then the denominator isn't 1,082,900 but 52c4 or 270,725.
Quote: MathExtremistIf you're only looking at 4 cards overall, without regard to which is the power card, then the denominator isn't 1,082,900 but 52c4 or 270,725.
Ah, that helps, thanks. So that makes it 17.5366% of 4 card hands will make a 3 card flush, vs. 4.9412% of 3 card hands. That makes a lot more sense.
Still, though, when you have a flush in hand, even if there's a higher flush card than at least one of yours on the power spot, it would only make sense to play the hand for 3:2 and not use the highest possible flush. The dealer would need 2 of 9 remaining suiteds (or a better flush in a different suit without the power card) to beat you with a flush. So that would be a case where marginal improvement would not necessarily be best EV with a 3x difference in return.
Quote: beachbumbabsIMO, Zcore, it would be worth putting the info that the dealer uses 4 cards back on the rack card, though I'm sure it's apparent on the first hand. (Comparing your card to the inventor's.) Just FWIW; it was a point of confusion for me until ME mentioned it.
I was trying to see what the median 3 card value of a 4 card hand is, but I'm not finding it trying to look it up. I guess it's an exercise for the student, but maybe it's not far off, assuming the median is similar to 3CP, near Q-6-4 (and thus, the strategy). For example, to get a flush:
11154 (13combin3)x(39combin1) hands with exactly 3 out of 4 of a suit, + 715 (13combin4) 4 out of 4, x 4 suits, = 47,476 ways for the dealer to make a flush out of 1,082,900, or 4.3842%.
In 3CP, it's 1096 ways out of 22,100 for 4.9412%.
Why would it be more likely to get a flush 3 cards out of 3 than 3 cards out of 4? That doesn't make sense. If I'm doing this wrong, please correct me. But if I'm doing it right, maybe a player should stand on, say, K high or so, unless the power card is a king or ace.
OTOH, it HAS to be more likely to get a pair in 4 cards than in 3, so maybe the stand point is around a pair of 6's in hand.
I understand what you are saying in regards to the rack card, but the rack card is just a synopsis. It's pretty obvious to see from the first minute you are watching the game that all players and the dealer get 4 cards from the shuffler. The rack card also doesn't say anything about the extra 4 card pack dealt for 5th and 6th street. The rules of play detail every minute part of the game. The rack card is just a quick read to give someone an idea of the game flow.
ZCore13
Quote: beachbumbabsAh, that helps, thanks. So that makes it 17.5366% of 4 card hands will make a 3 card flush, vs. 4.9412% of 3 card hands. That makes a lot more sense.
Still, though, when you have a flush in hand, even if there's a higher flush card than at least one of yours on the power spot, it would only make sense to play the hand for 3:2 and not use the highest possible flush. The dealer would need 2 of 9 remaining suiteds (or a better flush in a different suit without the power card) to beat you with a flush. So that would be a case where marginal improvement would not necessarily be best EV with a 3x difference in return.
Exactly, and thus the reason for my intrigue on this game from the beginning. But I'm sure you are more likely to win with a A high flush than a 5 high. So how do you play it. I've seen plenty of risky plays like that fail as well as win. And when the player takes that chance on such a hand they tend to smack themselves in the face if they would have won using the Power Card.
ZCore13
Quote: Zcore13I understand what you are saying in regards to the rack card, but the rack card is just a synopsis. It's pretty obvious to see from the first minute you are watching the game that all players and the dealer get 4 cards from the shuffler. The rack card also doesn't say anything about the extra 4 card pack dealt for 5th and 6th street. The rules of play detail every minute part of the game. The rack card is just a quick read to give someone an idea of the game flow.
ZCore13
So the Power card is not a community card. Somehow I thought it was, but each player and the dealer gets their own power card. Thanks for clarifying that. I was calculating based on you and the dealer sharing the power card (in my EV example), and so that's incorrect. Do you get to see the dealer's power card before you bet?
Quote: beachbumbabsSo the Power card is not a community card. Somehow I thought it was, but each player and the dealer gets their own power card. Thanks for clarifying that. I was calculating based on you and the dealer sharing the power card (in my EV example), and so that's incorrect. Do you get to see the dealer's power card before you bet?
Yes, each player has their own Power Card face up in front of them along with their three cards face down. This is why I believe the HE can be even lower than the 2.14%. A player can see not only their 3 cards, but everyone elses Power Card and maybe even the 3 cards of the player(s) next to them.
Nobody gets to see the dealers 4 cards. They are all face down and not exposed until all players choose how to play. Same as Three Card Poker.
ZCore13
Pair of 10's or Better: Never use Power card.
Pair of 9's: Only use Power card to make the 789 straight flush
Pair of 8's: Only use Power card to make trip 8's or straight flush
Pair of 7's: Only use Power card to make trip 7's or straight flush or 567 straight if you have only 2 suits.
Pair of 2's to 6's: Use Power card to make Straight or better
Flush exemptions:
Pair of 4's: Ace High flush
Pair of 3's: 2,J kicker: Q or higher flush
4-T,Q kicker : A or K high flush
K,A kicker: All Flushes
Pair of 2's: 3-T kicker: J or higher flush
J-A Kicker: All flushes
Edit to add no pair strategy:
Any that make a flush or better
AK: None
AQ: A pair, Q pair with 6 or less kicker (7 kicker ok if it is suited to A or all suits present)
AJ to A7:Pair from top two ranks
A6 to A4: A pair
KQ: Any Pair but 2
KJ to K3 Any Pair or A kicker with KT5 or worse
Q: Any pair , A kicker, K Kicker with QT7 or worse
-----Below this line there are lots of exceptions that I didn't feel like writing out.
J-9: Any pair, Any Kicker that beats your highest card.
8-7: Any improvement using a 6 or higher
6: Any improvement
Quote: mipletHere is my strategy when dealt a pair or better as your non power card hand. Kicker refers to the unpaired card in your non power card hand.
Pair of 10's or Better: Never use Power card.
Pair of 9's: Only use Power card to make the 789 straight flush
Pair of 8's: Only use Power card to make trip 8's or straight flush
Pair of 7's: Only use Power card to make trip 7's or straight flush or 567 straight if you have only 2 suits.
Pair of 2's to 6's: Use Power card to make Straight or better
Flush exemptions:
Pair of 4's: Ace High flush
Pair of 3's: 2,J kicker: Q or higher flush
4-T,Q kicker : A or K high flush
K,A kicker: All Flushes
Pair of 2's: 3-T kicker: J or higher flush
J-A Kicker: All flushes
Edit to add no pair strategy:
Any that make a flush or better
AK: None
AQ: Q pair with 6 or less kicker (7 kicker ok if it is suited to A or all suits present)
AJ to A7:Pair from top two ranks
A6 to A4: A pair
KQ: Any Pair but 2
KJ to K3 Any Pair or A kicker with KT5 or worse
Q: Any pair , A kicker, K Kicker with QT7 or worse
-----Below this line there are lots of exceptions that I didn't feel like writing out.
J-9: Any pair, Any Kicker that beats your highest card.
8-7: Any improvement using a 6 or higher
6: Any improvement
Pretty complex. I'm not sure many people could remember it.
On your new non pair strategy, does it mean for example if you have A6-A4 you only use the Power Card if it pairs you up? So you wouldn't use the Power Card if you had A 6 3 if it was a King?
ZCore13
Quote: Zcore13
Pretty complex. I'm not sure many people could remember it.
On your new non pair strategy, does it mean for example if you have A6-A4 you only use the Power Card if it pairs you up? So you wouldn't use the Power Card if you had A 6 3 if it was a King?
ZCore13
Only if it pairs your ace. Pairing your 6 is not enough. "A pair" means pairing the ace not any pair.
Edit to add: my AQ line was missing A pair.
ZCore13
Quote: Zcore13Unless I'm reading it wrong, it says that you would use the Power Card with something like 9c 9d 10c if the power card creates a straight flush. Why would you use the power card in that case yet not if the Power card was a 9h giving you a 3 of a kind. There is no bonus or extra payment for a straight flush. You'd be taking a chance on 3-2 payment with a three of a kind but going to a 1-2 payment for the straight flush.
ZCore13
First I assumed standard 3 card poker ranking of Straight flush >Trips >Straight > Flush > Pair > High card.
A pair of 9's is a good hand with an EV of around .5 depending on kicker and Power card. A 9 or higher Power card, or a ten or higher kicker always makes the EV higher then .5, so you would never use the power card. The only improvement for a pair of 9's is the 789 straight flush. ( A 89T straight flush means you have a ten so the dealer has one less card to make a higher pair and the EV of not using the power card is greater than .5)
Don't forget you can use my hand analyzer for the EV of any hand.
Quote: beachbumbabsWhy would it be more likely to get a flush 3 cards out of 3 than 3 cards out of 4? That doesn't make sense.
This is just a guess, but the fourth card probably makes it easy for a Flush to become a Straight or a Straight Flush. For example, suited K75 with a 6.
