Video Poker Return To Player(RTP) Calcualtor with Simulator

Introduction

This program calculates or simulates some kinds of video poker games to get Return To Player(RTP) value. RTP means average expected pay when you spend unit wager 1. In other word, if you pay 100 and get 95 on average, we can call its rtp is 0.95. I heard 1 - RTP is called house edge maybe?

This program is implemented based on https://wizardofodds.com/games/video-poker/methodology/ article. However, I skipped Using this same logic the number of different kinds of starting hands can be cut from 2,598,960 to 134,459. part of the article, because it assumes no suit discriminated hands like Spade Royal Straight Flush exist. This calculator is not fast enough, but unfortunately it became far slower unfortunately.

Both rtp calculation and simulation are processed under assumption that player always replaces cards in optimal way. (except Ultimate X Poker)

Supported Hands

Hands supported in those game rules:

Jacks or Better
Double Bonus
Deuces Wild Bonus

to see all individual hand lists, see allPayTitleToJudgeFuncMap variable in src/video-poker/supported-pay.ts file.

Supported Game Types and Features

Plain Video Poker with 52 cards
- RTP Calculator
- Simulator
Ultimate X Video Poker
- Simulator
Chated Poker (when you know next 5 cards)
- Simulator

How to use

Prerequisite

To install dependencies, first execute npm install command.

Next step might be optional, you can just use ./node_modules/ts-node/dist/bin.js instead of ts-node.

Then, install ts-node and typescript globally, using commands below

npm install -g typescript@3.1.6 ts-node@7.0.1

Usage

3 sample usage files exist: calculate_rtp.ts, ultimate_x_poker_simulation.ts and cheated_poker_simulation.ts

Basic Video Poker RTP Calculation

modify pay table inside calculate_rtp.ts file, then execute ts-node calculate_rtp.ts

default pay table looks like this:

ROYAL_STRAIGHT_FLUSH: 250,
STRAIGHT_FLUSH: 50,
FOUR_OF_A_KIND: 25,
FULL_HOUSE: 9,
FLUSH: 6,
STRAIGHT: 4,
THREE_OF_A_KIND: 3,
TWO_PAIR: 2,
JACKS_OR_BETTER: 1,

for example, you can modify example above like this:

STRAIGHT_FLUSH: 100,
FOUR_OF_A_KIND: 25,
FULL_HOUSE: 9,
FLUSH: 6,
STRAIGHT: 4,
THREE_OF_A_KIND: 3,
TWO_PAIR: 2,

In this case, royal straight flush flush is treated as straight flush and jacks or better will not be payed, but staright flush now pay 100x of wager.

if you run the program without modifications, the result will be like:

Raw result data:
{
    "hand_count": 2598960,
    "expected_value_sum": 2556686.796702761,
    "statistics": {
        "case_count": 2598960,
        "result": {
            "ROYAL_STRAIGHT_FLUSH": 50.48376865053717,
            "STRAIGHT_FLUSH": 275.25591095863285,
            "FOUR_OF_A_KIND": 6141.983483285694,
            "FULL_HOUSE": 29894.93966931592,
            "FLUSH": 31153.18406377575,
            "STRAIGHT": 28637.368102899087,
            "THREE_OF_A_KIND": 193276.5846772999,
            "TWO_PAIR": 335232.64616746036,
            "JACKS_OR_BETTER": 555935.391729087
        }
    }
}
-----------------------------
[ROYAL_STRAIGHT_FLUSH]
    Frequency: 1 for 51481.10114343347
    Probability: 0.000019424603937935624
    Pay: 250
    RTP: 0.004856150984483907
[STRAIGHT_FLUSH]
    Frequency: 1 for 9441.977071259289
    Probability: 0.00010591002206984058
    Pay: 50
    RTP: 0.0052955011034920285
[FOUR_OF_A_KIND]
    Frequency: 1 for 423.14669309557786
    Probability: 0.002363246638380619
    Pay: 25
    RTP: 0.059081165959515486
[FULL_HOUSE]
    Frequency: 1 for 86.93645241463942
    Probability: 0.011502654780880014
    Pay: 9
    RTP: 0.10352389302792013
[FLUSH]
    Frequency: 1 for 83.42518038218812
    Probability: 0.011986788586117427
    Pay: 6
    RTP: 0.07192073151670456
[STRAIGHT]
    Frequency: 1 for 90.75414998548334
    Probability: 0.011018779859212565
    Pay: 4
    RTP: 0.04407511943685026
[THREE_OF_A_KIND]
    Frequency: 1 for 13.446843570519926
    Probability: 0.07436689471069192
    Pay: 3
    RTP: 0.22310068413207576
[TWO_PAIR]
    Frequency: 1 for 7.7527055604892645
    Probability: 0.12898722803254392
    Pay: 2
    RTP: 0.25797445606508784
[JACKS_OR_BETTER]
    Frequency: 1 for 4.674931725279508
    Probability: 0.21390686725809055
    Pay: 1
    RTP: 0.21390686725809055
total RTP: 0.9837345694827012

Ultimate X Poker Simulation

modify pay table, multiplier table and iteration count inside ultimate_x_poker_simulation.ts file, then execute ultimate_x_poker_simulation.ts

pay table modification is described above, then skip decribtion for that.

Ultimate X Video Poker has special feature. When you win with some hand, your next game pay will be multiplied by some exent as written in multiplier table.

multiplier table has the same shape as pay table (which is required).

default multiplier table looks like this:
```
ROYAL_STRAIGHT_FLUSH: 7,
STRAIGHT_FLUSH: 7,
FOUR_OF_A_KIND: 3,
FULL_HOUSE: 12,
FLUSH: 11,
STRAIGHT: 7,
THREE_OF_A_KIND: 4,
TWO_PAIR: 3,
JACKS_OR_BETTER: 2,
```
With this multiplier table, if you win with flush, then next game pay will be multilied by 11.

also, as this sample usage is for simulation, you can set game iteration count. modify const trialCount = 10000000; part which located in bottom of the code. dfeault iteration count is 10M.
Cheated Poker Simulation

Cheated poker is the same with basic poker game, except that player knows what next 5 cards are. To simulate games for such cheated player, execute ts-node cheated_poker_simulation.ts.

setting parts are the same as describe in other sample usage file descriptions, thus skip description for this one.

You can arbitrarily modify those sample files or create new ones. However be careful when you modify pay tables very strangely (especially when you handle deuces wild hands, those hands are implemented in ugly way). Many unexpected results can occur. I recommend you to understand how pay-calculator works.

TODO

reconstruct file structures (merge, split, hierarchy)
remove undefined behavior dependent logic on pay table setting: // WARNING: property should be ordered by priority (higher first)

thaolt / video-poker-calculator