New style of Poker - Texas Jack Poker

Hello Everyone,
I have created a style of Poker that I call Texas Jack which combines the betting simplicity of Blackjack with the excitement of a Texas Hold 'em race. It is a single player banking style game in which a player places bets on which set of hole cards will win after a flop, turn, and river. I have created this video tutorial to easily demonstrate the gameplay. As you can see in the video, there is also a side bet option on the hand ranking of the winning hand. Written instructions can be found further down.

Texas Jack Tutorial Video

I have also developed an app game, so you can try out the game for free with Apple and Android devices. Click the link from your phone to be directed to the app store, or view my website: Texas Jack Website

Texas Jack App Game

I would love to hear some feedback of what you think of the game. Thanks!

Written Instructions for Texas Jack Poker:
Texas Jack Poker is a banking style poker game in which a player attempts to accurately bet on the set of hole cards that will end up making the best 5 card hand after a flop, turn, and river.

The game begins with the player placing an initial bet (or wager) in the amount that they choose.
The dealer will then deal 3 sets of hole cards upright, containing 2 cards each, for a total of 6 visible cards.
The player will then distribute their initial chip bet onto the hand that they determine will win the hand. A bet may be placed entirely on a single hand, or split between multiple hands. Splitting your bet will minimize your risk of losing chips, but also minimize your winnings.
After the initial bet has been distributed to the hand(s) chosen, you have the option to place a side bet on the winning hand ranking, or you can deal the flop, river, and turn cards to determine the winner. (See below for side bet rules).
Any bet placed on a winning hand will receive a 1/1 return plus the original bet. (For example, a bet of 5 chips placed on the winning hand would receive a 5 chip reward plus your original bet of 5 chips back.)
All hands that tie for a win are considered a winning hand and receive 1/1 return. If the best 5 cards are all on the flop, turn, and river, then all 3 hands tie, all 3 are considered winners, and all bets placed receive a 1/1 return.
Any bet that is placed on a hand that does not win, is lost to the dealer without a return.

Side bets rules:
An optional side bet can be placed after the 3 sets of hole cards are revealed and before the remaining 5 cards are dealt. A player may place a bet on which hand ranking the winning hand will have. (For example you could bet that the winning hand will be 2 Pair, or 3 of a Kind, or a Flush, etc..) If the winning hand wins with the ranking that was bet on, you will receive a return based on which hand was chosen.

Apparently I cannot post links until I have 20 posts. You can just Google "Texas Jack Poker" or search on Youtube to find the videos.

What's the house edge on the main bet and each of the side bets?

Interesting concept. I'll check it out.


ZCore13

I have not had professional analysis done, but my calculations determine the house edge to be approximately 1.1% when tie hands pay 1/1. If the house edge would end up being too low, you can easily make small adjustments to the percentages by making tie hands pay 1/2 or even a push. The side bets all have varying payouts and could again be adjusted to give an appropriate house edge. My current payouts per hand are:

SF Pays 100/1
4K Pays 20/1
FH Pays 3/1
FL Pays 2/1
ST Pays 2/1
3K Pays 2/1
2P Pays 1/1
1P Pays 1/1
HC Pays 3/1

Payouts for the side bet is tricky bc a player can wait for the best position to place a side betting after the cards are out. It makes the house edge quite high on the majority of hands, but smaller when the right sets of hands are dealt.

I think you'll find the side bets will be unworkable. Either they'll be beneath jurisdictional thresholds or beatable based on optimal strategy.

What steps did you use to calculate the 1.1% house edge on the main game?

Yes, I agree that the side bets are hard to implement. The house would have to plan for the worst which would make the payouts unreasonable to a player. My overall calculation of 1.1% was based off of recording the odds of 1000 hands and whether or not the best hand won or lost. I know it's not many hands and fairly inaccurate, but I also know that there are many adjustments possible to make for a correct house edge.

1000? Yeah, that's several orders of magnitude too small. You should hire a mathematician to make sure your game works before you talk to casino operators.

So if I understand correctly, under the camouflage of Texas hold'em, this game is really just 3 spots, each having a different probability of winning (that sums to 100%), that pays 1:1.

When none of the spots' probability is higher than 50%, then the house has the advantage. When 1 spot's probability is higher than 50%, then the player has the advantage for that game.

So when calculating the house edge, the question boils down to:
what is the frequency of Max (P1, P2, P3) > 50% ?

which, i don't know how to calculate.

Yes, I certainly would not proceed without getting professional analysis done on the odds. I have a couple feelers out, and have already heard confirmation from one that my calculations seem accurate on the surface. Again, there are numerous ways to adjust odds both towards the player and the dealer. We'll see how it all boils down.

Quote: andysif

So if I understand correctly, under the camouflage of Texas hold'em, this game is really just 3 spots, each having a different probability of winning (that sums to 100%), that pays 1:1.

When none of the spots' probability is higher than 50%, then the house has the advantage. When 1 spot's probability is higher than 50%, then the player has the advantage for that game.

So when calculating the house edge, the question boils down to:
what is the frequency of Max (P1, P2, P3) > 50% ?

which, i don't know how to calculate.

According to WoO, it's only 3.77%:

https://wizardofodds.com/games/texas-hold-em/3-player-game/

The rules of the OP's game change things somewhat by paying all players a full win on what, in Hold'em, would be a split pot.

I used http://www.propokertools.com/pql for a higher sample of 322753. The highest ranking hand won or tied 157124 (48.68%) for a house edge of 2.635%. You'll still want a higher sample and one that selects the best hand of the 3 instead of just the highest ranking one.

Quote: miplet

I used http://www.propokertools.com/pql for a higher sample of 322753. The highest ranking hand won or tied 157124 (48.68%) for a house edge of 2.635%. You'll still want a higher sample and one that selects the best hand of the 3 instead of just the highest ranking one.

select count(winsHi(p1)or tiesHi(p1)) 
from game="holdem", p1="**", p2="**",p3="**"
where handRankingFor(p1,'3h')<handRankingFor(p2,'3h')
and handRankingFor(p1,'3h')<handRankingFor(p3,'3h')

Well done! A small amendment gets you there, I think:

This ran for about 10 seconds and returned 790 trials, of which 381 (48.23%) were winners. That's an edge of 3.54%, but I think the sample is too small. I'd do a desktop run overnight and see what it converged to. Either way, somewhere in the 2.5%-3.5% range is decent for a fast-ish game like this.

Edit: definitely do a longer run; I re-ran it with strictly greater-than in the equity calculation and it came out to 51%, that is, a player advantage. So I'd need to think about which is the right operator to use, but either way the sample size needs to be larger.

I have the paid desktop version of PPT, I can run that PQL for a long time once I get home.

Quote: BTLWI

I have the paid desktop version of PPT, I can run that PQL for a long time once I get home.

I just did a 5-minute skim of the docs, I'm not sure if I set up the right query because I've never used this tool before. Please double check the query semantics vs. the rules described by the OP. I don't know whether it should be

equity(p1,preflop)>=equity(p2,preflop)
or
equity(p1,preflop)>equity(p2,preflop)

select count(winsHi(p1)or tiesHi(p1))
from game="holdem", p1="**", p2="**",p3="**"
where equity(p1,preflop)>=equity(p2,preflop)
and equity(p1,preflop)>=equity(p3,preflop)

600,000 trials
49.3535% (296121) Count 1

select count(winsHi(p1)or tiesHi(p1))
from game="holdem", p1="**", p2="**",p3="**"
where equity(p1,preflop)>equity(p2,preflop)
and equity(p1,preflop)>equity(p3,preflop)

600,000 trials
49.3640% (296184) Count 1

Excellent, thanks. So it looks like there isn't a meaningful semantic difference after all and that the optimal house edge is about 1.3%. How long did those 600k trials take on your machine (and what's in it)?

Quote: MathExtremist

I just did a 5-minute skim of the docs, I'm not sure if I set up the right query because I've never used this tool before. Please double check the query semantics vs. the rules described by the OP. I don't know whether it should be

equity(p1,preflop)>=equity(p2,preflop)
or
equity(p1,preflop)>equity(p2,preflop)

The more I think about it, the more I think it should be >=. Otherwise the results would exclude cases where the top hand has exactly the same equity as one or more of the other hands, such as
AhKd / AdKc / AcKh (all are exactly 1/3) or
AcAs / AdAh / 2c2d (about 40/40/20).

They're rare but, for the sake of completeness, important to consider.

I did a 20,000,000 overnight trial and it also came out to 49.35%.

~8 Hours on a 6-core Intel i7 3970X w 32GB DDR3.

Nice. Does the poker tool actually make use of the multiple cores? I've got an i7 4700MQ (quad core, two threads/core) w/ 16GB and I've parallelized some of my own poker code. I don't get a full 8x speedup but it's still about 5-6x. Of course, I can't do much else while it's running and it makes a nice room heater...