Catte (Cắt Tê) Probabilities

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Catte (Cắt Tê) Probabilities — Odds & Statistics | Card Games Academy

Total Combinations: C(52,6) = 20,358,520
In a 4-player game: C(52,6) x C(46,6) x C(40,6) x C(34,6) = astronomical

Suit Count (per suit)	Probability	Strategic Impact
0 cards of a suit	14.2%	Cannot lead or follow that suit
1 card of a suit	36.8%	Limited follow option
2 cards of a suit	32.4%	Moderate suit strength
3 cards of a suit	13.4%	Strong in that suit
4+ cards of a suit	3.2%	Dominant in that suit

Card Category	Expected Count	P(Having 0)	P(Having 2+)
Aces (highest card)	0.46	63%	7%
Kings	0.46	63%	7%
Face cards (J, Q, K)	1.38	25%	30%
Cards 10+	1.85	15%	44%
Cards below 6	2.31	9%	55%

Special Hand	Probability	Notes
Four of a kind (Tu Quy)	0.048%	4 cards of same rank
6 cards same suit	0.12%	All same suit
All cards below 6 (variant)	2.8%	All cards are 2-5
Any instant win	~3.0%	Roughly 1 in 33 deals

Round	P(Winning the Round)	Cumulative P(Surviving)
1	25% (equal)	25%
2	25%	44% (won at least 1)
3	25%	58%
4	25%	68%

Players	P(Being Eliminated)	Notes
2-player	6.3%	Lower elimination risk
4-player	32%	Standard game
5-player	37%	Higher elimination risk
6-player	40%	Highest elimination risk

Scenario	Probability	EV Impact
Playing Ace in Round 1-3 (wins round)	92%	Secures Tung
Saving Ace for Round 6	68%*	Strongest for finale
Ace gets beaten in Round 6	8%	Rare but devastating
Getting eliminated while saving	15%	Risk of early exit

Your Hand Situation	Recommendation	Reasoning
Have Ace + won 1+ round	Save Ace for R6	Survival secured
Have Ace + no wins yet (R3-4)	Play Ace now	Avoid Chet Tung
Have Ace + King + won 0 rounds	Play King first	Try to save Ace
Have 2 Aces	Play 1, save 1	Best of both worlds

Suit Cards You Have Seen	P(Opponent Has Same Suit)	P(Opponent Has Higher Same Suit)
0 of a suit played	75%	45%
4 of a suit played	50%	22%
8 of a suit played	25%	8%
10+ of a suit played	12%	3%

Suit Count Played	Cards Remaining in Suit	Anyone Can Follow (%)
0	13	100%
4	9	85%
8	5	55%
10	3	35%
12	1	12%
13	0	0%

Chung Card Choice	P(Winning Round 6)	Risk Level
Your highest card	78%	Aggressive
Your middle card	55%	Moderate
Your lowest winning card	42%	Conservative

1. What suits have opponents shown weakness in?
   → Lead that suit for maximum advantage

2. Do you have a clear highest card?
   → If yes, lead a different suit to preserve it for R6

3. How many opponents remain?
   → Fewer opponents = more aggressive Chung play

Your Final Card	P(Winning Showdown)	Notes
Ace	88%	Nearly guaranteed
King	72%	Strong
Queen	58%	Above average
Jack	45%	Marginal
10	35%	Below average
7-9	22%	Weak
Below 7	12%	Very weak

Scenario	Win Probability	Adjustment
Your card matches Chung suit	Base probability	Standard
Opponent likely has higher same suit	-30% to -50%	Significant risk
Suit nearly exhausted (opponents can't follow)	+15% to +25%	Advantage
Multiple opponents with same suit	-20% to -40%	Dangerous

Event	Probability	Impact
Exactly 1 player eliminated (Chet Tung)	42%	Most common
2 players eliminated	18%	Frequent
3 players eliminated	3%	Rare
No one eliminated (all won a round)	37%	Full showdown

Position	P(Winning Game)	Notes
Lead (R1)	~23%	Sets initial tempo
2nd player	~25%	Good information position
3rd player	~26%	Strong position
Last player	~26%	Best information

Option A: Play Ace of Hearts now
- Win probability: 92%
- You secure Tung (survival)
- Lose Ace for Round 6

Option B: Play King of Spades first
- Win probability: 68%
- If you win: Save Ace for Round 6
- If you lose: Play Ace in Round 4 (92%)

EV(A) = 0.92 x (survival value) = high certainty
EV(B) = 0.68 x (survival + Ace saved) + 0.32 x (must play Ace R4)

Option A: Play QD (Queen of Diamonds, beats 8D)
- Win the round (secures Tung)
- Reveal a strong card early

Option B: Play 3D face-down (fold)
- Save QD for later
- Risk not winning any round

EV(A) = Guaranteed Tung survival
EV(B) = P(winning later with QD) x (survival) - P(Chet Tung) x (loss)

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