Net Loss Probability Grid and Random Walk Model
2014-04-21 14:56
This applet demonstrates probability and random walks on a grid. Right moves mean wins, up moves mean losses; remaining losses are net losses. It models a drunkard's walk with a one-sided cliff or a two-player game with a net loss elimination threshold, visualizing state transitions and probability distributions in 2D stochastic processes.
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<objColor r="255" g="0" b="0" alpha="0.1"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Sum">
<input a0="nDeadP"/>
<output a0="pDead"/>
</command>
<element type="numeric" label="pDead">
<value val="0.3876953125"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<command name="Sum">
<input a0="nAliveP"/>
<output a0="pAlive"/>
</command>
<element type="numeric" label="pAlive">
<value val="0.6123046875"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="text3" exp=""存活機率：" + pAlive + """ />
<element type="text" label="text3">
<show object="true" label="false" ev="3"/>
<objColor r="0" g="51" b="204" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<font serif="false" sizeM="1.4" size="5" style="0"/>
<absoluteScreenLocation x="625" y="35"/>
</element>
<expression label="text4" exp=""敗亡機率：" + pDead + """ />
<element type="text" label="text4">
<show object="true" label="false" ev="3"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<font serif="false" sizeM="1.4" size="5" style="0"/>
<absoluteScreenLocation x="625" y="85"/>
</element>
<element type="point" label="OffsetDeadF">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-1.036963314750198" y="0.6805291357296513" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Text["C^{" + (nLose + (2 * k)) + "}_{" + (k) + "}-2C^{" + (nLose + (2 * k) - 1) + "}_{" + (k - 1) + "}", Element[endsDead, k + 1] + OffsetDeadF, true, true]" a1="k" a2="0" a3="x1"/>
<output a0="txtWaysDeadFormula"/>
</command>
<element type="list" label="txtWaysDeadFormula">
<show object="true" label="false"/>
<condition showObject="Picker ≟ ChoiceFormula"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<element type="point" label="OffsetDeadP">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-0.8579556701322948" y="0.22306515503945626" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Text[Element[nDeadP, k], Element[endsDead, k] + OffsetDeadP]" a1="k" a2="1" a3="x1 + 1"/>
<output a0="txtDeadP"/>
</command>
<element type="list" label="txtDeadP">
<show object="true" label="false"/>
<condition showObject="Picker ≟ ChoiceP"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
<font serif="false" sizeM="1.4" size="5" style="2"/>
</element>
<command name="Sequence">
<input a0="Text["(C^{" + nTurns + "}_{" + (k) + "}-C^{" + nTurns + "}_{" + (nTurns - nLose - k) + "})p^{" + (k) + "}q^{" + (nTurns - k) + "}", Element[endsAlive, k - x1] + OffsetAliveF, true, true]" a1="k" a2="x1 + 1" a3="nTurns"/>
<output a0="txtAlivePFormula"/>
</command>
<element type="list" label="txtAlivePFormula">
<show object="true" label="false"/>
<condition showObject="Picker ≟ ChoicePFormula"/>
<objColor r="0" g="51" b="204" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<element type="point" label="OffsetDeadPF">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-1.3706783973302494" y="0.6606393974387756" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="text5" exp=""( q=1-p )""/>
<element type="text" label="text5">
<show object="true" label="false" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="1"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.0" size="0" style="0"/>
<absoluteScreenLocation x="499" y="71"/>
</element>
<command name="Sequence">
<input a0="Text["(C^{" + (nLose + (2 * k)) + "}_{" + (k) + "}-2C^{" + (nLose + (2 * k) - 1) + "}_{" + (k - 1) + "})p^{" + (k) + "}q^{" + (nLose + k) + "}", Element[endsDead, k + 1] + OffsetDeadPF, true, true]" a1="k" a2="0" a3="x1"/>
<output a0="txtDeadPFormula"/>
</command>
<element type="list" label="txtDeadPFormula">
<show object="true" label="false"/>
<condition showObject="Picker ≟ ChoicePFormula"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="1"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<element type="point" label="ChoiceNone">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="2"/>
<labelOffset x="-9" y="-11"/>
<labelMode val="3"/>
<fixed val="true"/>
<ggbscript val="SetValue[Picker, ChoiceNone]"/>
<coords x="7.02" y="3.02" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="2"/>
<caption val="無"/>
</element>
</construction>
</geogebra>