Runlikegod777
Runlikegod777
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Joined: Oct 15, 2017
August 29th, 2025 at 5:55:53 PM permalink
casino is starting this bonus which if you play a hand its free.

4 of kind (3's, 4s.8s, 9s) first 4 cards $1000

4 of kind (3's, 4s.8s, 9s) first 4 cards $10000 suited

6 of kind any card $10000
6 of kind any card suited $100000

what are the odds of these, and what value does it add? (looking for overall e.v. per hand)

It is better if you are a solo player as you get all of it, if you are playing with 4 other players (it would be divided). But assuming I am only player does this add maybe like
25-30 cents value per hand? (the corporation is paying $1 to the house for it each hand to fund)
ThatDonGuy
ThatDonGuy
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Joined: Jun 22, 2011
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Runlikegod777
August 29th, 2025 at 7:22:43 PM permalink
Assuming an 8-deck shoe, I get:

There are 1,229,930,520 possible sets of 4 cards
Of these, 280 consists of four 3s, 4s, 8s, or 9s that are suited, and 143,560 consist of four that are not suited
The probability of winning either of the two amounts is 1 / 8567, and the probability of winning the 10,000 is 1 / 4,392,609.
The value is 11.9 cents per hand.

The 6 of a kind one is a little harder to do, as you have to take into account the fact that both the player and the banker have to take a third card.
However, even if they did not - i.e. they would always show the top 6 cards of the shoe - the value would be only 0.7 cents per hand.
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