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Poker Cards Probability Calculations

Introduction

iTech Labs have conducted analysis of Poker cards for a number of major Poker operators. We calculate Odds for various hands, Outs and Card distribution for the cards captured from the Poker system. The results of these calculations are compared against theoretical probabilities. The calculations are done for very large number of hands, usually half a million or more. This has proven to be very useful in enhancing the confidence of both players and poker operators in the randomness and fairness of actual cards dealt.

Theoretical calculations

Odds on various hands

Hands Number of possibilities Probability
Royal Flush 4324 0.00003
Straight Flush 37260 0.00028
4 of a kind 224848 0.00168
Full House 3473184 0.02596
Flush 4047644 0.03025
Straight 6180020 0.04619
3 of a kind 6461620 0.04830
2 pairs 31433400 0.23496
1 pair 58627800 0.43823
High card 23294460 0.17412
  1.34E+08 1

Outs:

Outs Holding Aim Turn River Turn or River
1 3 of a Kind 4 of a kind 2.13% 2.17% 4.26%
1 Inner Flush Straight Flush 2.13% 2.17% 4.26%
2 Pair 3 of a kind 4.26% 4.35% 8.42%
2 Open flush Straight Flush 4.26% 4.35% 8.42%
4 2 pairs Full House 8.51% 8.70% 16.47%
4 Inside straight Straight 8.51% 8.70% 16.47%
8 Open straight Straight 17.02% 17.39% 31.45%
9 4 Flush Flush 19.15% 19.57% 34.97%

Calculations on Poker cards

Odds on various hands:

We calculate the occurrence of various hands in the cards obtained from the Poker system. The results are then compared against the theoretical calculations. Detailed explanations and comments on the results are provided.

Outs:

We calculate the conversion rates from holdings to various hands in the cards obtained from the Poker system. The results are then compared against theoretical calculations. Detailed explanations and comments on the results are provided.

Card distributions:

We calculate the distribution of cards provided. The distribution is calculated for each type of card and each position the cards are dealt. We verify whether the observed values are within 95% confidence limits.

What are the deliverables after completion of Poker cards calculations?

On completion of Poker cards calculations, our deliverables will be the following:

  • A report outlining the evaluation conducted and the results of that evaluation. The hot-linked original report will be maintained on the iTech Labs web site so authenticity can be verified.

Online Gaming Systems tested and certified most recently

  • Poker Systems (ring games, single and multi-table tournaments, jackpots games)
  • Casino Systems (slot games, card games, table games, dice games, jackpots and tournaments)
  • Bingo Systems (single player, multiplayer)
  • Backgammon Systems