3 Card Poker or Blackjack?

General
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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.

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Why I like Blackjack
Why I love 3-Card Poker...
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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
    • King-high: 54 × 60 = 3,240
    • Queen-high: 44 × 60 = 2,640
    • (J-high or lower): 6,720

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 count from the worst hand up.

  1. “Made” Hands (Pair or better): There are 5,660 hands that are a Pair or better.
  2. “High Card” Hands: This leaves 16,440 “High Card” hands.
  3. J-High or Lower Hands: The absolute worst 6,720 high-card hands are all Jack-high or lower (e.g., J-10-9 down to the worst hand, 5-3-2).
  4. Worse Queen-High Hands: Next, we count the Queen-high hands that are worse than Q-6-4. A hand is ranked by its highest card, then its second-highest, then its third.
  • Q-3-2: (60 combinations)
  • Q-4-2, Q-4-3: (120 combinations)
  • Q-5-2, Q-5-3, Q-5-4: (180 combinations)
  • Q-6-2, Q-6-3: (120 combinations)
  1. Total Hands Worse than Q-6-4: 6,720 (J-low) + 60 + 120 + 180 + 120 = 7,200 hands.

Actual Rank:

The rank of Q-6-4 is 7,201st (out of 22,100), as it ranks just above the 7,200 hands that are worse than it.

Game Strategy Implications

The hand Q-6-4 is critical for player strategy, not dealer qualifying.

  • The dealer’s minimum qualifying hand is Q-3-2 (any Queen-high).
  • Q-6-4 is the player’s optimal cutoff hand.

This means:

  • If your hand is weaker than Q-6-4 (like Q-6-3 or any J-high), folding is the best option.
  • If your hand is Q-6-4 or stronger, it is strategically correct to make the Play bet.
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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.

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

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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!!

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Interesting, thank you!

I still feel I win more at 3-card, because the dealer with 16 draws a 5 way too often (or so it seems).

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The dealer sure does draw a lot of 21’s in blackjack. I think more than statistics would say is possible. But you can win a lot fast also which is what lures me back. Then bums me out!! LOL

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Thanks for the information about these two games @Elanor. Is there a minimum number of games you need to play in BJ to achieve the expected gain of 4%, or is there too much variance to give a number? Also, do the games have to be played in one session or can they be over multiple sessions? I have no idea, so just curious.

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The more you play, the lower the standard deviation. You can see the 5 sigma table I created on my post Why I like blackjack. So the longer the play, you will be closer to +4%

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@nguyet I completely agree! I trust the math geeks too! :star_struck:

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@Night_Guy and @Elanor I was told a long time ago that you should always bet the Pair Plus at 25% of your primary bet, because that’s the percentage of hands that will be a Pair Plus combination. I don’t keep track of my losses and wins by game, so I don’t know whether I’m losing or winning over time by betting this way.@Night_Guy, thank you for working out the amount of those combinations as shown above, but I don’t know how to calculate the percentage of hands they’ll occur. @Elanor, you say you never bet the Pair Plus, so I’m thinking that the 25% number is incorrect or maybe correct but to translate it to betting that percentage amount isn’t a valid strategy. Would one of you please let me know what the correct percentage is?

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Hey @Luck_Is_ALady,

Whoever told you that was actually spot on about the percentages!

If you add up all the winning Pair Plus combos (5,660) and divide them by the total possible 3-card hands (22,100), you get about 25.6%. So yes, you really do hit a Pair Plus around 25% of the time!

But here’s the catch - betting 25% of your main bet just because you win a quarter of the time doesn’t actually work out in your favor. It’s a common trap, but bet sizes shouldn’t be based on how often a hand hits. It all comes down to the House Edge.

Using the regular CW payouts:

  • 40:1 Straight Flush
  • 30:1 Three of a Kind
  • 6:1 Straight
  • 3:1 Flush
  • 1:1 Pair

Since you lose the other 74.4% of the time, those payouts have to make up for the losses. If you crunch the numbers, this specific pay table gives the house an edge of about 7.28%. Basically, for every 100 coins you bet on Pair Plus over the long haul, you are mathematically expected to lose 7.28 coins.

Because the odds are against you, betting 25% isn’t a winning strategy - it just makes your bankroll drain a little slower than if you matched your main bet. The absolute best move mathematically is to skip it entirely (which is probably why @Elanor ignores it!).

But hey, it’s a fun side bet! If you enjoy the thrill of chasing those huge payouts, there’s nothing wrong with playing it. Just view that 7.28% edge as the cost of entertainment rather than a secret system to beat the game.

If you want to see exactly how that 7.28% is calculated, below is the math made simple:

Imagine you sit down and play all 22,100 possible hands in the game, betting 1 coin on the Pair Plus every single time.

  • The Cost: You make 22,100 bets, spending a total of 22,100 coins.
  • The Losses: You will lose on 16,440 of those hands, handing the dealer 16,440 coins.
  • The Wins: You will win on the remaining 5,660 hands. When you add up all the payouts from those straight flushes, pairs, etc., your total profit is 14,832 coins.
  • The Bottom Line: You made 14,832 coins in profit, but lost 16,440 coins. Overall, you are down exactly 1,608 coins.

To find the house edge, just divide your total loss by the total amount of coins you put on the table:

1,608 ÷ 22,100 = 0.07276.

Move the decimal over, and you get a 7.28% loss. That is the house edge.

Hope this helps make sense of it all!

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It was our dear departed friend and self proclaimed 3 Card expert, Bond Girl 007, RIP. Ty @Night_Guy for doing the calculation on this. I think I’ll stick with the 2.5M Pair Plus bet and keep track for awhile to see how I’m doing with it. I feel like I’m winning with it often enough that the loss amount is negligible, since it’s not my main game these days. I’ll let you know if I’m beating the odds.

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