3 Card Brag - Ante Return Table

Are the combinations/probabilities in the Ante Return Table for 3 Card Poker on the Wizard of Odds site calculated or compiled from a simulation?

Is it possible to calculate those probabilities?

Quote: Trevor

Is it possible to calculate those probabilities?

It is possible. I've done it myself and the Wizard's table is also an exact calculation.

I bet that was difficult.

Quote: Trevor

I bet that was difficult.

This is what I do for a living. It was more fun than difficult.

So how would you go about that? Do you have to calculate the chance of the dealer beating, equaling or losing against all possible hands?

or are there shortcuts you can use?

Quote: Trevor

So how would you go about that? Do you have to calculate the chance of the dealer beating, equaling or losing against all possible hands?

Yes, you must calculate the number of times you beat (which includes the dealer not qualifying), tie, or lose to the dealer.

The brute force method would involve dealing C(52,3) player hands, then dealing C(49,3) dealer hands, then comparing the hands, which is roughly 4 billion hands. This is not a big deal when it comes to computing these days. But, there are shortcuts you can take. I just took a look at my code and it is under 250 lines and takes about 240 milliseconds to run, and I am not concerned about speed, nor would I know where to start optimizing my code.

Some of the things that I did to speed things up:
1. I came up with a method to assign a unique number to each hand which represents the hand's score. A higher score is a better hand.
2. Using the same method as video poker, which you can find on Wizard of Odds under VP programming tips, I made arrays that represent all the hands that 0, 1, or 2 cards can "draw" to. Using these arrays, you can calculate all possible dealer hands given a player hand, and it will be far faster than looping through all C(49,3) dealer hands. Learn this page and take it to heart; it is gold. VP programming tips. In that sheet, the Wizard says to initialize some arrays with the second dimension of 16. In Three card poker, the dimension I used is 780, which covers every unique score from bullet #1.

Brill. Thanks for the advice CrystalMath. So you would need to write a program to iterate through the hands. I was wondering whether it was possible to calculate in a spreadsheet?

Hi,

I've written a program to analyse a 3 Card Brag game played on-line in the UK. Same as 3 Card Poker except a Prial beats a straight flush. The Ante bonus table is:

Prial 5 - 1
Running Flush 4 - 1
Run 1 - 1

and my results are:

Win Val Hits % Chance Total Value
7 667840 0.0016 0.0115
6 903940 0.0022 0.0133
5 266196 0.0007 0.0033
4 144 0.0000 0.0000
3 8976732 0.0220 0.0661
2 91100416 0.2237 0.4475
1 80955780 0.1988 0.1988
0 249216 0.0006 0.0000
-1 132923304 0.3265 -0.3265
-2 91126832 0.2238 -0.4476
407170400 -0.0335

RTP: 96.645%

Does anyone concur? Crystal Math?

Cheers,

Trev

Sorry about the formatting. It looked alright before i sent it.

Quote: Trevor

Hi,

I've written a program to analyse a 3 Card Brag game played on-line in the UK. Same as 3 Card Poker except a Prial beats a straight flush. The Ante bonus table is:

Prial 5 - 1
Running Flush 4 - 1
Run 1 - 1

and my results are:

Win Val Hits % Chance Total Value
7 667840 0.0016 0.0115
6 903940 0.0022 0.0133
5 266196 0.0007 0.0033
4 144 0.0000 0.0000
3 8976732 0.0220 0.0661
2 91100416 0.2237 0.4475
1 80955780 0.1988 0.1988
0 249216 0.0006 0.0000
-1 132923304 0.3265 -0.3265
-2 91126832 0.2238 -0.4476
407170400 -0.0335

RTP: 96.645%

Does anyone concur? Crystal Math?

Cheers,

Trev

Good job! I calculate the same return (96.6451186%).

Quote: CrystalMath

Good job! I calculate the same return (96.6451186%).

Thanks CrystalMath.