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Poker is a family of games that exhibit imperfect information, where players do not have full knowledge of past events. Whereas many perfect-information games have been solved (e.g., Connect Four and checkers), no nontrivial imperfect-information game played competitively by humans has previously been solved.
The relative odds according to calculations are: Losing cards= Outs/Winning cards= 38:10, which is 3:8:1. Another shortcut for calculating poker odds is, that there are 10 outs when the flop is dealt, which means you have a 104= 40% chance of winning probability to get a winning card on Turn or River.

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I was co-chilling with my poker-playing cousin and the rest of his family shortly after

Christmas when an opportunity to 💴 play some cards with his neighbors came up. Never one

to pass up such an opportunity, I made the short 💴 trip to the neighbors and once

introductions were complete, we were gambling it up.

And I mean gambling... we first

played 💴 7-Card No-Peek Baseball. In this house, five-of-a-kind beats straight flushes,

and I skillfully flipped over quad queens with my first 💴 5 cards, only to be outdone by

quad kings. Of course, I had 2 cards to go and one was 💴 a wild. Thank you for the

5-of-a-kind hours rule! :) After a couple cracks at follow the queen (the variant 💴 where

the queens are always wild, of course) we settled in for a long game of Acey

Deucey.

The Game

If you 💴 don't know the rules, here it is. Everybody antes into the pot.

Each player takes a turn, starting with the 💴 left of the dealer until there is no money

left in the pot. A turn consists of two cards being 💴 dealt face up and the player

betting an amount of money whether or not the third card will fall in 💴 between the first

two (thus, the name "In-Between"). A player may bet anything from zero to the pot. If

the 💴 third card is in between, the player wins from the pot the amount that was bet. If

the card is 💴 outside the first two cards, the player has to add the bet into the pot. If

the third card matches 💴 one of the first two, the player must pay twice the bet into the

pot.

The best possible two-card combination is 💴 an ace and a two: you only lose if an

ace or a two comes up. Thus the other name 💴 "Acey Deucey".

Some variants include:

You

can only bet up to half the pot until everybody has a turn (so the game 💴 can't be over

right away)

As the first two cards are dealt out, if the first card is an ace, the

💴 player can call it to be high or low. The second ace is always high

If the first two

cards dealt 💴 out are the same, you can get two new cards or you can bet if the third

card is higher 💴 or lower instead of in between

You can bet an amount and call "inside"

or "outside". This creates more action (people 💴 will make bets when a six and and an

eight come out instead of just passing

You must bet some minimum, 💴 regardless of the two

cards

What Happened

So all seven of us antedR$1 and I was first. I saw the and and

💴 thought "jackpot". I bet the pot, and my cousin promptly dealt the off the deck. Nice!

I'm in forR$14 more. 💴 It goes around a few times and the host graciously only bets about

half the pot both times he's dealt 💴 so the game can keep going. I get dealt another

great pair: and bet the pot again only to see 💴 a . Wow. I run out of money and go meet

my friends for dinner.

The good news is I'll be 💴 invited to future games after

droppingR$30. To them, I was a gambling fool who didn't care about losingR$30. To me, 💴 I

maximized my value by betting the pot whenever it was the right move. Which got me

thinking...

The Solution

Disclaimers: This 💴 solution assumes:

Your bankroll is large

enough that you can handle some crazy swings!

You aren't counting cards in order to

calculate 💴 your exact outs (it's as if the deck is reshuffled each time)

The rules are

as above with no variants (most 💴 importantly, you have to pay double your pot when the

third card matches and you can pass or bet zero)

The 💴 Ace will always be high

Bet the

Pot when there are 8 ranks in between your cards: or better, or better, 💴 or better, or

better.

Pass or Bet Zero all other times

With only 7 ranks in between, the bet is

completely even 💴 money. You have 28 outs to win your bet, there are 16 cards that cause

you to lose your bet, 💴 and 6 cards cause you to lose twice your bet.

With 6 or less

ranks in between, it's a losing bet.

Considerations

You 💴 probably aren't playing this

game solely to make a profit. Sometimes it's fun to betR$1 that you can hit that

💴 one-outer. Or at least the minimum bet just to juice the pot a bit and seem

friendly.

If your bankroll is 💴 not big enough to handle losingR$40 at a time, you may

want to only bet the pot when you have 💴 6 or 10 ways to lose instead of 18 ways as the

solution suggests.

Also

If you like to be nasty, you 💴 can also call this game "Between

the Sheets". LOL.

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