Calculating EV of a simple card game

Jaquemir

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Aug 1, 2019
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I want to know my current EV in a side game to a poker game.

Rules are as follows:

3 cards come on the flop, 1 card on the turn and 1 card on the river (like in Texas Holdem). So 5 cards are turned over of a deck of 52 cards.

My card is 9c (clubs) (and hence both black 9's trigger a payout)
My friends card is 7h (hearts) (both red 7's trigger a payout)

Payouts are (from my perspective - the same for him with his 7h):

hit 1 red nine (and NO black) = 0
hit 1 black nine = $100
hit 2 nines (at least one black) = 200
hit 3 nines (at least one black) = 400
hit 4 nines (at least one black) = 800

Multipliers for when the black nine(s) come:

flop x1
turn x2
river x4

So if say,
Flop K 9h Q
Turn 2
River 9c

my payout is calculated: 2 nines (one is black so there is a payout) = 200
The black one comes on the river so multiplier is 4
I get 200 x 4 = 800

My maximum payout is hence, two red nines on the flop, black nine turn and black nine river: 800 (4 nines) x 2 (turn multiplier) x 4 (river multiplier) = 6400

This is ofc an even game for me and my friend. (We do it "forever" and never stop).

Here is the special thing:

When I hit EXACTLY the 9c my next payout is on a 2x future multiplier. If I hit 9c again I go up to a 3x future multiplier, and if I hit 9c again I go to 4x multiplier and so on...

My future multiplier goes down ONE step whenever my friend gets a payout. (He goes up when he hits 7h same way I do on 9c).

Hands where none of us gets a payout doesn't affect the future multipliers.

CURRENT SITUATION:
I am on a 6x multiplier
he is on a 2x multiplier

So say next hand he hits 7h --> he then gets a payout as calculated above x 2 (his multiplier). He also goes up to a 3x future multiplier AND I go down to a 5x multiplier.

WHAT IS MY CURRENT EV OF THE FACT I AM ON 6X FUTURE MULTIPLIER AND HE IS ONLY ON 2X FUTURE MULTIPLIER??

I hope I explained the game okay, otherwise I will try in more detail....

Hope someone can help me calculate this :)
 
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