MathCurious
• Posts: 8
Joined: Nov 27, 2020
December 7th, 2020 at 5:04:29 PM permalink
Suppose I have 21 balls, 4 are black, 4 are yellow ,4 are red ,4 are orange and 5 are blue. How many ways can I get a pair? 2 balls of the same color?
unJon
• Posts: 4658
Joined: Jul 1, 2018
December 7th, 2020 at 5:55:34 PM permalink
Quote: MathCurious

Suppose I have 21 balls, 4 are black, 4 are yellow ,4 are red ,4 are orange and 5 are blue. How many ways can I get a pair? 2 balls of the same color?

16/21 of the time you draw not blue with the first ball and need the same color 3/20. 5/21 of the time you draw blue and need another blue 4/20.

16/21*3/20 + 5/21*4/20 = 68/420 = 16.19%
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Wizard
• Posts: 26626
Joined: Oct 14, 2009
December 7th, 2020 at 6:27:38 PM permalink
Quote: MathCurious

Suppose I have 21 balls, 4 are black, 4 are yellow ,4 are red ,4 are orange and 5 are blue. How many ways can I get a pair? 2 balls of the same color?

4*combin(4,2)+combin(5,2) = 4*6 + 10 = 34
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Tolik
• Posts: 3
Joined: Jan 24, 2021
January 24th, 2021 at 4:05:24 PM permalink
At first: sorry for my english. I use a translator. Iwant to know the breakeven point in 3 card poker progressive jackpot. Ante bonus: 1-4-5. Pair plus:1-4-6-30-40. And minimum bet for ante and pair plus 10\$ + 2\$ for progressive jackpot. Progressive payouts : mini royal AKQ all spades 100%, any royal AKQ(clubs,hearts,diamonds) 25%
Wizard
• Posts: 26626
Joined: Oct 14, 2009
January 25th, 2021 at 1:17:30 PM permalink
Forgive me if I just analyze the Pairplus by itself and not fuss with the base game. In that case, the answer to your question is 384x the bet amount.

Hand Pays Combinations Combinations Return
Mini royal in spades 384 1 0.000045 0.017376
Mini royal 96 3 0.000136 0.013032
Straight flush 40 44 0.001991 0.079638
Three of a kind 30 52 0.002353 0.070588
Straight 6 720 0.032579 0.195475
Flush 4 1096 0.049593 0.198371
Pair 1 3744 0.169412 0.169412
Other -1 16440 0.743891 -0.743891
Total 22100 1.000000 0.000000

For every extra 100 bets in the meter, the return goes up by 0.79%.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Tolik