New Game from G2E - Triple Shot Rummy

I'm finally getting time to go through some of the more interesting table games I saw at G2E. I enjoyed this one a lot, but I don't know if it will catch on, as several other players at the table with me seemed confused by it.
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Triple Shot Rummy

This game has a similar betting structure to 3 Card Poker, with an Ante/Play for the main and both Pair Plus and 6 Card Bonus side bets. Both side bets are identical to TCP.

The object of the game is to get a lower point total than the dealer. Cards are assigned points as follows:
K/Q/J - 10 points
A - 1 point
2-10 - face value

Matching ranks (Pairs and 3-of-a-kind) have a zero point value. Suited 2 card runs (Partial straight flushes) have a zero point value.

Example hands:
Ad 2d 5h = 5 points. Suited A2 is zero
6c 7d 8h = 21 points
Kh Kd Js = 10 points. Pair of Kings is zero
5s 5h 6h = 0 points. Pair plus a suited 2 card run are all zero
As Ks 2s = 0 points. Two suited 2 card runs, wrapped around (I asked about this hand specifically)

As with TCP, you put up an Ante bet, receive 3 cards, then decide if you wish to play them. If you do, you match the Ante with a Play bet. Dealer qualifies with 20 points or less, otherwise the Play pushes and the player is paid on the Ante. If the dealer qualifies, you get additional odds on point totals of 5 or less, as explained below:

Player's total Payout
6-19 1:1
1-5 2:1
0 4:1
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Differences versus TCP

- Additional odds are only paid if dealer qualifies, as they are attached to the Play bet. TCP pays good hands on the Ante, regardless of whether the dealer qualifies or wins.
- Comparing the Play odds directly with the Ante Bonus in TCP, there will be more top paying hands in this game, due to the additional 0 point hands mentioned above. For each hand with a pair, there are 4 possible singletons that will create a suited run, making the hand worth 0 points. This is offset by both the lower payout and the dealer qualify condition.
- If you play Pair Plus in conjunction with the Ante, there will be a handful of straights and flushes that are not playable on the Ante/Play. A good example would be 6h 8h Jh. Obviously it's a paying flush, but 24 points is too many to reasonably play. Another would be 9h Ts Jh, at 29 points
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Strategy and Simulation

The intuitive strategy for me seemed to be to play any hand the dealer would play, which is <= 20 points. The additional Play odds should offset the occasional player fold.

In preparation for the simulation, I manually reviewed ~100 generated individual hands, plus 10-15 specified edge cases (including the AK2 flush I mentioned above) in order to ensure the points were calculated correctly. After that, I manually reviewed ~100 generated Player/Dealer showdowns to ensure the game rules were followed (Play/Fold, Dealer qualify, additional Play odds if applicable, correct winner chosen).
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Simulation

Each cycle was one billion trials. I ran three full cycles, one each with a player fold threshold of 19, 20, and 21 points.

Results are as follows:

q=19
House Edge: -0.010028954 (1.03%)
Average bet: 1.621541622

q=20
House Edge: -0.005745537 (0.57%)
Average bet: 1.675847069

q=21
House Edge: -0.008109341 (0.81%)
Average bet: 1.738456016

Observations

Clearly, the house edge is extremely low. This would raise a bigger red flag if it weren't at G2E. The side bet was the all-but-extinct 1-4-6-30-40 paytable, so I suspect they were generous with the odds. If this games makes it to a casino, I'm sure they will depress the odds on the Play bet, or change the point totals. Taking the 0 point hands to 3:1 or possibly changing the 2:1 payouts to point totals of 1-4 would probably make the game more casino ready.

I welcome feedback

Who was showing this game? What company?

Quote: mrsuit31

Who was showing this game? What company?

It was SciGames. Most of the games that I found interesting were theirs. There were one or two independents that caught my eye, but not many.

I really like the idea of this game. The reason I think it may or may not catch on is the players will have to look for more non-obvious stuff. Players will think "face cards are bad!" but then hopefully they'll remember pairs are zero and 2 card SF's are zero! So even if they have KKQ so long as KQ are suited that's a phenomenal hand!

I like this game a lot because it involves a tiny bit more consideration. Do you know of a demo you can play online by chance?

Bovada has this rummy game, called Vegas Rummy.

Quote: Romes

I really like the idea of this game. The reason I think it may or may not catch on is the players will have to look for more non-obvious stuff. Players will think "face cards are bad!" but then hopefully they'll remember pairs are zero and 2 card SF's are zero! So even if they have KKQ so long as KQ are suited that's a phenomenal hand!

I like this game a lot because it involves a tiny bit more consideration. Do you know of a demo you can play online by chance?

I haven't found one aside from the one mentioned above. I had planned on building one, but I haven't had much time to do it, unfortunately. It's still in the works.

Quote: Paigowdan

Bovada has this rummy game, called Vegas Rummy.

Just tested this version, and it doesn't treat a pair with a suited run as a 0 point hand. Looking through the rules, it also says AK suited is not a suited run. I'm wondering if the dealer explained the game wrong, as that would account for the extremely low house edge. I'll edit my program and retest

Doing a quick test with the rules changed, it seems much more in line with a casino game (House Edge 3.8-4.0%). I'll run a full cycle and post the results

Quote: Ncell

Quote: Paigowdan

Bovada has this rummy game, called Vegas Rummy.

Just tested this version, and it doesn't treat a pair with a suited run as a 0 point hand. Looking through the rules, it also says AK suited is not a suited run. I'm wondering if the dealer explained the game wrong, as that would account for the extremely low house edge. I'll edit my program and retest

Yeah, I've played it a lot there, but blanked on who it was had it, reading your description. Thanks, PGD!

Bovada's version has been available for at least a couple of years. Unless it's the same inventor/distributor, I'm thinking there may (may - speculating, nothing firmer) be IP issues, it's that similar.

I would also guess that the rule changes you cite are what gives the game a viable HE. I'll be very interested to see what your analysis shows. Thanks a lot for the detailed info and taking the time to analyze it!

Quote: Ncell

Quote: Paigowdan

Bovada has this rummy game, called Vegas Rummy.

Just tested this version, and it doesn't treat a pair with a suited run as a 0 point hand. Looking through the rules, it also says AK suited is not a suited run. I'm wondering if the dealer explained the game wrong, as that would account for the extremely low house edge. I'll edit my program and retest

These rules are correct. If you have a pair and a suited run, you will take the lower score. For instance 2H, 2C, 3C = 2. Also, Ace is always low, so it doesn't make a run with QKA or KA.

Quote: CrystalMath

Ace is always low, so it doesn't make a run with QKA or KA.

Explained that way, it makes perfect sense. I don't fault the dealer, because they're only given a day or two's worth of training on the games. It seems like that is something that should have been properly explained though

This shouldn't be that hard to analyze; there are only 1755 "unique" 3-card hands.

The "total" column indicates how many actual hands there are per "unique" hand, except in the bottom row.
For example, for "three different, two suited", there are (13 x 12 x 11) / 6 combinations of values of the three cards, but for each one, each of the three can be the offsuit card, so that's 286 x 3 = 858 unique hands; of these, there are 4 possible suits for the "suit pair" and 3 for the "unsuited card", or 4 x 3 = 12 per unique hand.

Hand	Unique	Total
Three of a kind	13	4
Pair, and third card matching either suit	156	12
Pair, and third card not matching either suit	156	12
Three different, all three suited	286	4
Three different, two suited	858	12
Three different, unsuited	286	24
Total	1755	22100

Quote: beachbumbabs

I would also guess that the rule changes you cite are what gives the game a viable HE. I'll be very interested to see what your analysis shows. Thanks a lot for the detailed info and taking the time to analyze it!

Always happy to contribute if I can. The rule changes did indeed make it viable:

House Edge: -0.038027254 (3.8%)
Average bet: 1.671859222
Element of Risk: -0.02274548807674669 (2.27%)

This puts it more on par with TCP and other carnival games.

Quote: Ncell

Always happy to contribute if I can. The rule changes did indeed make it viable:

House Edge: -0.038027254 (3.8%)
Average bet: 1.671859222
Element of Risk: -0.02274548807674669 (2.27%)

This puts it more on par with TCP and other carnival games.

I'm getting slightly different results:

Hand	Pays	Ways	Probability	Return
0 Points	5	1188508	0.002918945	0.014594725
1-5 Points	3	24848032	0.061026126	0.183078377
6+ Points	2	59826252	0.146931732	0.293863464
No Qualify	1	91156848	0.223878867	0.223878867
Tie	0	11487776	0.028213682	0
Fold	-1	132800192	0.326153846	-0.326153846
Lose	-2	85862792	0.210876802	-0.421753605
Total		407170400	1	-0.032492018

Quote: miplet

I'm getting slightly different results:

Hand	Pays	Ways	Probability	Return
0 Points	5	1188508	0.002918945	0.014594725
1-5 Points	3	24848032	0.061026126	0.183078377
6+ Points	2	59826252	0.146931732	0.293863464
No Qualify	1	91156848	0.223878867	0.223878867
Tie	0	11487776	0.028213682	0
Fold	-1	132800192	0.326153846	-0.326153846
Lose	-2	85862792	0.210876802	-0.421753605
Total		407170400	1	-0.032492018

It looks like you're enumerating the combinations. Mine was random simulation over a billion trials. I'm sure that accounts for the difference

Quote: Ncell

It looks like you're enumerating the combinations. Mine was random simulation over a billion trials. I'm sure that accounts for the difference

Ok. I was worried I had a typo somewhere. And your basic strategy is correct. There are no composition exemptions. Fold with 21 or more points and raise with 20 or less.

Quote: miplet

And your basic strategy is correct. There are no composition exemptions. Fold with 21 or more points and raise with 20 or less.

I tested with an exception for the case of a 3 card 21 with three ranks <=9 points (Leaving more 10 value cards that would increase the chance of a dealer no-qualify) to see if there was an impact, but there overall effect was negative. It may be worth exploring simple collision using a high low system, as enough dead small cards may push the chance of a no-qualify to where any hand is worth playing, similar to hold carding TCP. The question would be whether the increase in a pairs/runs from more 10 value cards would offset it. I'll see about an EV calculator with dead card input.