3 Card Poker or Blackjack?

General
1

I was in a discussion recently about whether you should cash your charms out on 3 card poker or blackjack.

I prefer blackjack with the basic strategy table I posted under the Topic “Why I like Blackjack” since it gives the player a 4% advantage in the long run.

Several people prefer 3 card poker because it’s simpler. Here is the basic strategy to maximize the expected value:

  1. Fold any starting hand lower than Q-6-4
  2. Never play pairs-plus

That’s it.

If you follow this strategy you will have an expected loss of 2.01%, not bad, but nowhere as good as an expected gain of 4% that blackjack gives.

Note: The pairs plus payoff table has a expected loss of 7.28%, one of the worst bets in CW!!

You might ask where does the Q-6-4 come from? It’s pure math.

If you fold Q 6 4, you have an expected loss of 1 bet.
If you play Q 6 4, you have an expected loss of 0.99 bets, so playing is better.

If you fold Q 6 3, you have an expected loss of 1 bet.
If you play Q 6 3 you have an expected loss of slightly more than 1.00 bets, so folding is better.

You might say what’s the big deal? I’m just playing off charms.

But over time (not counting charms)
I bet 100B in Blackjack, I’ve made 4B coins
I bet 100B in 3 card poker, I’ve lost 2B coins

The value of the charms are the same either way, and both games cash in the big charms fast.

But if I played 100B in Blackjack correctly using the basic strategy I have 6 Billion more coins, on average, than if I played 3 card poker.

3 Likes
2

Very good info Elanor, I’ll like to add a few more stats that I’ve been working on.

In 3-card poker, there are 22,100 possible hand combinations, covering all types such as straight flushes, three of a kind, straights, flushes, pairs, and high-card hands. Here’s the breakdown:

Hand Type Combinations:

  • Straight flush: 4 ×12 = 48
  • Three of a kind: 4 × 13 = 52
  • Straight: 12 × 43 − 48 = 720
  • Flush: (4 × 13 × 12 × 11) / 6 − 48 = 1,096
  • Pair: 13 × 6 × 48 = 3,744
  • High-card hands:
    • Ace-high: 64 × 60 = 3,840
      • (Examples: AKJ, AKT, AQJ, A24, etc.)
    • King-high: 54 × 60 = 3,240
      • (Examples: KQT, KQ9, K32, etc.)
    • Queen-high: 44 × 60 = 2,640
      • (Examples: QJ9, QJ2, Q32, etc.)

Dealer Qualification:

  • Total qualifying hands (Queen-high or better): 15,380
  • Total possible hands: 52 × 51 × 50 / 6 = 22,100
  • Dealer qualification probability: 15,380 / 22,100 ≈ 0.6959 or 69.59%

These calculations highlight the odds and hand distributions in the game, helping to understand both player and dealer scenarios.

To calculate the exact rank of Q-6-4 in 3 Card Poker, we need to consider the total possible hand combinations and the rules for ranking them. Here’s how it works:

  1. Total Hand Combinations in 3 Card Poker:

    • The deck has C(52,3)=22,100 unique hands.

Hand Rankings (Descending Order):

  • Straight Flush
  • Three of a Kind
  • Straight
  • Flush
  • Pair
  • High Card

High Card Hands:

  • There are no pairs, no flushes, and no straights in Q-6-4, so it’s a high card hand.
  • High card hands are ranked by the highest card, followed by the second-highest, then the third.

Calculation of Ranks for High Card Hands:

  • Hands are ordered from lowest to highest: 2-3-4 (lowest high card) to A-K-Q (highest high card).
  • Q-6-4 ranks higher than any hand where the highest card is Jack or lower, or where the highest card is Queen but the second card is 5 or lower.

For example:

  • All hands with a highest card of Jack or lower = C(48, 3) = 17,296 combinations.
  • Hands with a Queen as the highest card but a second card less than 6: C(11,2) = 55.
  • So, Q-6-4 ranks above at least 17,296 + 55 = 17,351 hands.

Approximate Rank:

The rank of Q-6-4 would be approximately 17,352 out of 22,100 possible combinations.

Game Strategy Implications

Knowing Q-6-4 is the dealer’s minimum qualifying hand helps guide player decisions. For example:

  • If your hand is weaker than Q-6-4, folding is generally the best option because the odds of the dealer qualifying and beating you are too high.
  • If your hand is stronger than Q-6-4, it’s usually worth raising, as you stand a good chance of beating the dealer.

Q-6-4 is the optimal qualifying hand because it balances the dealer’s qualifying probability, sustains the house edge, and simplifies gameplay strategy for both players and the casino.

2 Likes
3

TY Elanor and Night Guy for so kindly sharing your findings with us. While your math is not in dispute, I’ve always have doubts about whether the deck shuffling is done randomly but you both seem to have no problem with this. Therefore I will take the card games more seriously in the future.

1 Like
4

Ha ha. I have to trust the math geeks. :face_with_monocle:

1 Like
5

I have so much to learn!
I’d never played any poker before joining CW so I’m learning as I play.
I’ve only ever played Pontoon before and whilst it’s very nearly Blackjack it seems there might be some teeny-weeny subtle differences
All of this experience, knowledge and insights is very valuable
Every day is a school day!!