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Pyramid Solitaire

Pyramid Solitaire. Katie, Kayla, Tayah. How to play. 20 cards: Aces, 5’s, 10’s, Q’s, K’s Complete both levels Level 1: lay down two cards, one MUST be a red card Level 2: lay down six cards one MUST be a red face card Win: if both rounds are beat Lose: if the proper card is not chosen.

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Pyramid Solitaire

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  1. Pyramid Solitaire Katie, Kayla, Tayah

  2. How to play • 20 cards: Aces, 5’s, 10’s, Q’s, K’s • Complete both levels • Level 1: lay down two cards, one MUST be a red card • Level 2: lay down six cards one MUST be a red face card • Win: if both rounds are beat • Lose: if the proper card is not chosen

  3. Round 1 Total ways= 20x19= 380 Probability of choosing two red cards: 10x9= 90 Probability of choosing a red and black card: 10x10= 100 Probability of choosing a black and red card: 10x10= 100 Probability of choosing two black cards: 10x9= 90 90+100+100=290 290/380= 0.76 ∴ The probability of winning round one: 76%

  4. Red Face cards(FC) In Round 1 • RR= 10x9=90: • 6x5 = 30 (no FC’s used) • 4x6 = 24 (1 FC used) • 6x4 = 24 (1 FC used) • 4x3 = 12 (2 FC’s used) 30+24+24+12= 90 • RB= 10x10= 100: • 6x10 = 60 (no FC’s used) • 4x10 = 40 (1 FC used) 60+40= 100 • BR=10x10= 100: • 10x6 = 60 (no FC’s used) • 10x4 = 40 (1 FC used) 60+40= 100 • 2 FC’s R1: 12/290 • 1 FC R1: 128/290 • 0 FC’s R1: 150/290

  5. Round 2 • Total ways: 18x17x16x15x14x13= 13,366,080 • 2 FC’s R1: 16x15x14x13x12x11= 5,765,760 • 1 FC R1: 15x14x13x12x11x10= 3,603,600 • 0 FC’s R1: 14x13x12x11x10x9= 2,162,160 • 2 FC’s R1: 5,765,760/ 13,366,080 • 1 FC R1: 3,603,600/ 13,366,080 • 0 FC’s R1: 2,162,160/ 13,366,080

  6. 5,765,760/ 13,366,080 =0.01784 • 3,603,600/ 13,366,080 =0.11899 • 2,162,160/ 13,366,080 • =0.0836 • 0.0178+0.11899+0.0836= 0.22043 (probability of losing R2) • 1- 0.22043= 0.77957 • (probability of winning R2) Round 1 FC Round 2 12/290 128/290 150/290 • 290/380

  7. *Must win round 1 and round 2 Round 1 Round 2 (Formula for (Formula for winning winning round round 2) 1) ∴ The probability of winning the entire game is 59% 290/380 x 0.77957 = 0.594935

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