EE8087 Presentation

8/12/2019 EE8087 Presentation

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IntroductionBy Kristianto
https://en.wikipedia.org/wiki/File:Nuvola_apps_atlantik.pnghttps://en.wikipedia.org/wiki/File:Nuvola_apps_atlantik.png


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Introduction

GAMBLING


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Introduction


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Introduction


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Introduction

LOSE

WIN


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How to PlayBy Stephen


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How to Play Texas Holdem

There will be four deals in this game:

1. The game start with two cards being dealtface-down to each player [pr flop]

2. Next, three cards is placed face-up [flop]3. Followed by a single card placed face-up

[turn]4. And another single card placed face-up

[riv r]On each deal, each player have option tocheck/call, raise the bet or fold


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How to Play Texas Holdem

So, there will be a total of seven cards foreach player

2 hand (hole) cards (face-down)

5 community cards (face-up)

Each player can choose any combination of5 from these seven cards to make the best

possible combinationThe player who have the highestcombination win the game


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EXAMPLEHe has threeoption:

High card of ace

Pair of Js Flush

The best option isFlush


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EXAMPLE His hand is flush

Mediums hand ispair of 9s

Stephens hand istwo pairs of As &Js

Jonathans hand istwo pairs of Js &9s

He has the highestcombination so he winthe game


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AnalysisBy Kenrick


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Before that,

Pre-requisite:CombinatoricsProbability theory


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Combinatorics

= , =

=

!

! !

Number of ways of choosing kelements from aset of nelements.

Example: From a set of bridge card, how many ways tochoose 4 cards?= (52, 4) = 270725

From a set of bridge card, how many ways tochoose 4 cards, where 2 of them are ace cards?= (4,2) (48,2) = 6768


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Probability theory

The numerical chance some event will occur

If trials of an experiment produce occurencesof an event , the probability of occurring() as follows:

= lim

Every events: = + ( )

Mutually exclusive events: = + ()

Independent events: = ()


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Probability theory (example)

What is the probability of getting a 3 on a fair dicetoss?

=

What is the probability of getting an ace from adeck of bridge cards?

=

=

,

,

What is the probability of getting 2 cards, whereone of them is ace, from a deck of bridge cards?

= , ,

, =

= 0.1448


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After flop, Community cards:

Your own hole cards:

Combinations for x & y: C(525, 2) = C(47,2) = 1081

X Y


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After turn, Community cards:

Your own hole cards:

Combinations for x: 52 6 = 46

X


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Full House Odds

PPPQQ or PPQQQ P,Q : value of card p: number of P-card q: number of Q-card

P P P Q Q

P P Q Q Q


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Full House Odds(after flop)

p \ q 0 1 2 3 40 0 0 0 0.555% 0.555%1 0 0 0.833% 12.211% 12.211%2 0 0.833% 8.141% 1 -3 0.555% 12.211% 1 - -4 0.555% 12.211% - - -

P P Q Q Q

P P P Q Q


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How to calculatethe table?

Take example of p = 1 and q = 3,

To make it PPQQQ or PPPQQ, we need: One P either at turn or at river Two P

Probability of getting PPQQQ or PPPQQ:

=3

47

43

46+

43

47

3

46+

3

47

2

46= 12.2109158%

or=

3,1 43, 1

(47,2) +

3,2

47,2 = 12.2109158%

P P Q Q Q

P P P Q Q


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Full House Odds(after turn)

p \ q 0 1 2 3 40 0 0 0 0 01 0 0 0 6.521% 6.521%2 0 0 8.696% 1 13 0 6.521% 1 1 -4 0 6.521% 1 - -

P P Q Q Q

P P P Q Q


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How to calculatethe table?

Take example of p = 1 and q = 3,

To make it PPQQQ, we need one more P at river;(PPPQQ is impossible case)

Probability of getting P at river:

=3

46= 6.521%

P P Q Q Q

P P P Q Q


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Three of a Kind Odds (after flop)

TTTxyT: value of triple card x and y: different valuefrom T

t: number of viewed T-cards

t Probability0 0

1 0.277%

2 8.325%

3 1

4 1

T T T x y


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Three of a Kind Odds (after turn)

TTTxy T: value of triple card x and y: different valuefrom T

t: number of viewed T-cards

t Probability0 0

1 0

2 4.347%

3 1

4 1

T T T x y


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Two Pairs Odds

PPDDx P and D: values of the paired cards x: different value from P and D p: number of viewed P-cards d: number of viewed D-cards

P P D D x


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Two Pairs Odds (after flop)

d \ p 0 1 2 3 40 0 0 0.555% 0.555% 0.555%1 0 0.832% 11.655% 11.933% 12.210%2 0.555% 11.655% 1 1 -3 0.555% 11.933% 1 - -4 0.555% 12.210% - - -

P P D D x


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Two Pairs Odds (after turn)

d \ p 0 1 2 3 40 0 0 0 0 01 0 0 6.521% 6.521% 6.521%2 0 6.521% 1 1 13 0 6.521% 1 1 -4 0 6.521% 1 - -

P P D D x


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One Pair Odds (after flop)

PPxyz P: values of the pairedcard

x, y, z: different valuefrom P

p: number of viewed P-cards

p Probability0 0.555%

1 12.210%

2 1

3 1

4 1

P P x y z


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One Pair Odds (after turn)

PPxyz P: values of the pairedcard

x, y, z: different valuefrom P


p Probability0 0

1 6.521%

2 1

3 1

4 1

P P x y z


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Four of a kind odds (after turn)

CCCCx C: value of the four of akind card

x: different value from C c: number of viewed C-cards

c Probability0 0

1 0

2 0

3 2.173%

4 1

C C C C x


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Flush Odds (after flop)

SSSSS S: card symbol (hearts,diamonds, spades, orclubs)

s: number of viewed S-cards

c Probability0 0

1 0

2 03 4.162%

4 34.967%

5 1

S S S S S


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Flush Odds (after turn)

SSSSS S: card symbol (hearts,diamonds, spades, orclubs)

s: number of viewed S-cards

c Probability0 0

1 0

2 03 0

4 19.565%

5 1

6 1

S S S S S


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Straight flush odds (after flop)

FLUSH F, L, U, S, and H:

unique cards

consecutive values

same symbol

m = number of viewedcards from F, L, U, S, H

cards

m Probability

0 0

1 0

2 0

3 0.092%

4 4.255%

5 1

F L U S H


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Straight flush odds (after turn)

FLUSH F, L, U, S, and H:

unique cards

consecutive values

same symbol

m = number of viewedcards from F, L, U, S, H

cards

m Probability

0 0

1 0

2 0

3 0

4 2.173%

5 1

F L U S H


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Straight Odds

PQRSTP, Q, R, S, and T: sequence of consecutive cards

as valuesThe value of probability depends on:


q: number of viewed Q-cards

r: number of viewed R-cards

s: number of viewed S-cards t: number of viewed T-cards

P Q R S T


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Straight Odds (after flop)

Let A as the event of achieving a straight at theriver. P(A) can take only four different possibleoutcome: If more than 2 parameters of p, q, r, s, and t are null, thenP(A) = 0

If exactly 2 parameters of p, q, r, s, and t are null, thenP(A) = 1.480%


If none of parameters of p, q, r, s, and t are null, then P(A)

= 1

P Q R S T


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Straight Odds (after turn)

Let A as the event of achieving a straight at theriver. P(A) can take only three different possibleoutcome: If more than 1 parameters of p, q, r, s, and t are null, thenP(A) = 0


If none of parameters of p, q, r, s, and t are null, then P(A)= 1

P Q R S T


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StrategyBy Hendry


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Advantage play

Developing a Game Strategy

Knowing the Probabilities

Reading Your Opponents


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ConclusionBy Hendry


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Conclusion

Gambling-based games involve risk, yetthere is scientific way on how to minimizethe potential lose.

Calculating risk deals with computing theoccurrence of win and lose; in this caseengaging concept of Combinatorics andProbability

Analysing Texas HoldemPoker, probabilityof optimum combination of own hole cardscould be calculated to lead in decisionmaking


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Conclusion

To finalize decision, do always plan andmake strategy

Mathematics concept does take important

role in daily life; helpful tools In this particular case, beauty of mathhelps in decision making process


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End of PresentationThank you

EE8087 Presentation

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