more numbers - Phillips/Hansen/Tomko hand

[West]

I wanted to recalculate my numbers for Gus' call with TT of Paul's all in to reflect his actual raise (which apparently was 280,000, rather than 350,000), but I also wanted to include a larger range of hands that Paul could move in with. Because it appears that moving in with a larger range of hands may very well be +$EV for him.

50,000/100,000

15,000 ante

Phillips 2,800,000
Hansen 2,300,000
Tomko 800,000

Button - Hansen
SB - Phillips
BB - Tomko


If stacks are pre ante/blinds

5,900,000 total chips

according to % theory,

Tomko: 14%
Hansen: 39%
Phillips: 47%

chance of finishing 1st

Tomko chance of 2nd?

(.47 x (8/31)) + (.39 x (8/36)) = .121 + .087 = 21%

Hansen?

(.47 x (23/31)) + (.14 x (23/51)) = .349 + .063 = 41%

Phillips?

(.39 x (28/36)) + (.14 x 28/51)) = .303 + .077 = 38%

So:

Tomko: 14% 1st 21% 2nd 65% 3rd
Hansen: 39% 1st 41% 2nd 20% 3rd
Phillips: 47% 1st 38% 2nd 15% 3rd

Current Prize EV:

Tomko: .14 x 825 + .21 x 275 = $173,250
Hansen: .39 x 825 + .41 x 275 = $434,500
Phillips: .47 x 825 + .38 x 275 = $492,250

If:

Hansen (w/TT) raised to 280,000
Phillips, all in (w/AQ) (effectively 2,285,000 including the SB)
Tomko folds (left with 685,000), BB = 100,000
antes 45,000

2,005,000 to call for Hansen

pot is effectively: 45,000 + 100,000 + 280,000 + 2,285,000 = 2,710,000

Hansen getting over 1.35 to 1 on his call

If he folds:

Stacks will be:

Phillips: 2,800,000 + 30,000 + 100,000 + 280,000 = 3,210,000
Hansen: 2,005,000
Tomko: 685,000

Phillips: 54.4%
Hansen: 34%
Tomko: 11.6%

Chances of 2nd:

Tomko: (.544 x .255) + (.34 x .176) = .139 + .06 = 20%
Hansen: (.544 x .745) + (.116 x .384) = .405 + .045 = 45%
Phillips: (.34 x .824) + (.116 x .616) = .28 + .071 = 35%

Prize EV:

Tomko: .116 x 825 + .2 x 275 = $150,700
Hansen: .34 x 825 + .45 x 275 = $404,250
Phillips: .544 x 825 + .35 x 275 = $545,050


If he calls and wins:

Phillips: 500,000
Hansen: 2,300,000 + 2,300,000 + 115,000 = 4,715,000
Tomko: 685,000

Phillips: 8.5%
Hansen: 79.9%
Tomko: 11.6%

Prize EV would then be:

Tomko chance of 2nd =

(.799 x (685/1185)) + (.085 x (685/5400)) = .462 + .011 = 47.3%

Hansen?

(.116 x (4715/5215)) + (.085 x 4715/5400)) = .105 + .074 = 17.9%

Phillips?

(.799 x (500/1185)) + (.116 x 500/5215)) = .337 + .011 = 34.8%

So:

Tomko: 11.6% 1st 47.3% 2nd 41.1% 3rd
Hansen: 79.9% 1st 17.9% 2nd 2.2% 3rd
Phillips: 8.5% 1st 34.8% 2nd 56.7% 3rd

Prize EV if Gus calls and wins:

Tomko = .116 x 825 + .473 x 275 = $225,775
Hansen = .799 x 825 + .179 x 275 = $708,400
Phillips = .085 x 825 + .348 x 275 = $165,825

If he calls and loses, he finishes third = $0

So for Gus:

Folds to all in: $404,250
Calls and wins: $708,400
Calls and loses: $0

Z * 708,400 = 404,250
Z = 404,250 / 708,400
Z = 57.1%

If Gus wins ~57% of the time, it is a break even proposition.

What range of hands could Paul go all in on him with?

If it was: AA, KK, QQ, JJ, 99, 88, AK, AQ, AJ, AT (ignoring TT)

6,6,6,6,6,6,12,4,12,4,12,4,6,2 = 92 combos

against AA-JJ: ((24/92) x .19)
+
against 99-88: ((12/92 x .81)

against AKo-AJo: ((36/92) x .57)
+
against AKs-AJs: ((12/92) x .54)
+
against ATo: ((6/92) x .69)
+
against ATs: ((2/92) x .65)

= .05 + .106 + .223 + .07 + .045 + .014 = 50.8%

Gus' TT would win ~50.8% - if this is Paul's range, he should fold

What if Paul's range was: AA-33, AK-AT (ignoring TT)

66+12+4+12+4+12+4+6+2=122 combos

against AA-JJ: ((24/122) x .19)
+
against 99-33: ((42/122) x .81)
+
against AKo-AJo: ((36/122) x .57)
+
against AKs-AJs: ((12/122) x .54)
+
against ATo: ((6/122) x .69)
+
against ATs: ((2/122) x .65)

= .037 + .279 + .168 + .053 + .034 + .011 = 58.2%

Gus' TT wins 58.2% - CALL

Similar range:

AA-33, AK, AQ, AJ, AT, KQs, QJs, JTs (ignoring TT)

66+12+4+12+4+12+4+6+2+4+4+2=132 combos

against AA-JJ: ((24/132) x .19)
+
against 99-33: ((42/132) x .81)
+
against AKo-AJo: ((36/132) x .57)
+
against AKs-AJs: ((12/132) x .54)
+
against ATo: ((6/132) x .69)
+
against ATs: ((2/132) x .65)
+
against KQs, QJs: ((8/132) x .53)
+
against JTs: ((2/132) x .61)

= .035 + .258 + .155 + .049 + .031 + .01 + .032 + .009 = 57.9% CALL

Clearly the range of hands Gus thinks Paul will play this way is important to his decision of whether to call or not.

What about Tomko's decision when Paul moves in?

Based on Gus raising with any of 761/1225 starting hands, Paul holding AQ and moving in, and Gus calling with AA-TT, AK-AQ and assuming Tomko folds:

Prize EV When Paul moves in, all combined:

Tomko: .941 x 150,700 + .02 x 338,800 + .039 x 225,775 = $157,390
Hansen: .941 x 404,250 + .02 x 0 + .039 x 708,400 = $408,027
Phillips: .941 x 545,050 + .02 x 761,200 + .039 x 165,825 = $534,583

Based on Gus raising with any of 553/1225 starting hands, Paul holding AQ and moving in, and Gus calling with AA-TT, AK-AQ and assuming Tomko folds:

Prize EV When Paul moves in, all combined:

Tomko: .919 x 150,700 + .028 x 338,800 + .053 x 225,775 = $159,946
Hansen: .919 x 404,250 + .028 x 0 + .053 x 708,400 = $409,051
Phillips: .919 x 545,050 + .028 x 761,200 + .053 x 165,825 = $531,003

If Dewey calls all in against Paul, what % of the time must he win to break even in real $EV?

If we assume that Gus always folds,

If Tomko loses, $EV = 0

What if he wins?

Chips would be:

Hansen: 2,005,000
Phillips: 2,000,000
Tomko: 1,895,000

Chip % =

Hansen: 34%
Phillips: 33.9%
Tomko: 32.1%

Chances of 2nd?

Hansen = .339 x .514 + .321 x .501 = .174 + .161 = 33.5%
Phillips = .34 x .513 + .321 x .499 = .174 + .16 = 33.4%
Tomko = .34 x .487 + .339 x .486 = .166 + .165 = 33.1%

Prize EV=

Hansen = .34 x 825 + .335 x 275 = $372,625
Phillips = .339 x 825 + .334 x 275 = $371,525
Tomko = .321 x 825 + .331 x 275 = $355,850

Tomko $EV if he calls and Hansen folds =

His % chance of beating Phillips x $355,850

If we took the $159,946 $EV (see top) for Tomko when Paul moves in and he folds, then:

%W x 355,850 = 159,946

Breakeven hand winning % = 159,946 / 355,850 ~= 45%

What if Paul will move in with AA-33, AK-AT = 72+64=136 combos

What hands for Dewey stand to win 45%+ against this range?

55:

against AA-66 ((54/130) x .19)
+
against 44-33 ((12/130) x .81)
+
against AKo-ATo ((48/130) x .545)
+
against AKs-ATs ((16/130) x .51)

= .079 + .075 + .201 + .063 = 41.8% FOLD

66:

against AA-77 ((48/130) x .19)
+
against 55-33 ((18/130) x .81)
+
against AKo-ATo ((48/130) x .55)
+
against AKs-ATs ((16/130) x .515)

= .07 + .112 + .203 + .063 = 44.8% just about a call...

77:

against AA-88 ((42/130) x .19)
+
against 66-33 ((24/130) x .81)
+
against AKo-ATo ((48/130) x .55)
+
against AKs-ATs ((16/130) x .52)

= .061 + .15 + .203 + .123 = 53.7% CALL

AQo:

3+6+3+54+12+9+12+12=111 combos against

against AA ((3/111) x .08)
+
against KK ((6/111) x .28)
+
against QQ ((3/111) x .3)
+
against JJ-TT (12/111) x .425)
+
against 99-33 (42/111) x .45)
+
against AKo (9/111) x .26)
+
against AKs (3/111) x .24)
+
against AQ (9/111) x .49)
+
against AJo-ATo (18/111) x .73)
+
against AJs-ATs (6/111) x .69)

= .002 + .015 + .008 + .046 + .17 + .021 + .006 + .04 + .118 + .037 = 46.3% CALL

AJo:

3+6+6+3+48+12+12+9+12=111 combos against

against AA ((3/111) x .08)
+
against KK-QQ ((12/111) x .28)
+
against JJ (3/111) x .3)
+
against TT (6/111) x .42)
+
against 99-33 (42/111) x .45)
+
against AK-AQ (24/111) x .26)
+
against AJ (9/111) x .49)
+
against ATo (9/111) x .72)
+
against ATs (3/111) .68)

= .002 + .03 + .008 + .023 + .17 + .056 + .04 + .058 + .018 = .405 FOLD

What if Paul added KQs, QJs, JTs to the range of hands he'd move in with?

AJo:

111+4+3+3=121

against AA ((3/121) x .08)
+
against KK-QQ ((12/121) x .28)
+
against JJ (3/121) x .3)
+
against TT (6/121) x .42)
+
against 99-33 (42/121) x .45)
+
against AK-AQ (24/121) x .26)
+
against AJ (9/121) x .49)
+
against ATo (9/121) x .72)
+
against ATs (3/121) x .68)
+
against KQs (4/121) x .56)
+
against QJs-JTs (6/121) x .675)

= .002 + .028 + .007 + .021 + .156 + .052 + .036 + .054 + .017 + .019 + .033 = 42.5% FOLD

66:

against AA-77 ((48/142) x .19)
+
against 55-33 ((18/142) x .81)
+
against AKo-ATo ((48/142) x .55)
+
against AKs-ATs ((16/142) x .515)
+
against KQs-JTs ((12/142) x .49)

= .064 + .103 + .186 + .058 + .041 = 45.2% CALL

In reality he does have to worry about Gus calling as well
so for now let's say Dewey goes with AA-77, AK-AQ, when Paul moves in with AA-33, AK-AT

(Note that this doesn't really change if Paul also moves in with KQs, QJs, JTs)

How is Paul's $EV affected (assuming Gus always folds when Dewey calls)?

If Dewey is calling with a tighter range of hands than Paul is moving in with, than we know he will be better than 50% overall to win on average when he calls. It seems like it will take quite a while for me to try to calculate his range of hands vs. Paul's range of hands, so I'm not going to try right now. But what if I assume Dewey will win say, 57% of the time:

If Dewey is calling with: AA-77, AK-AQ = 48+32=80 combos

80/1326 possible hands = 6%

~ half the time, Paul will have an ace when he moves in, removing 11 combos for Dewey,

leaving 69/1225 = 5.6%

So ballpark, Dewey is calling 5.8% of time

So 94.2% of time, Paul's $EV will be what it is when Tomko folds

5.8% of time:

When Tomko calls and wins, $EV is (from above):

Prize EV=

Hansen = .34 x 825 + .335 x 275 = $372,625
Phillips = .339 x 825 + .334 x 275 = $371,525
Tomko = .321 x 825 + .331 x 275 = $355,850

When Tomko calls and Phillips wins:

Chips =

Hansen: 2,005,000 (34%)
Phillips: 3,895,000 (66%)

Prize EV=

Hansen: .34 x 825 + .66 x 275 = $462,000
Phillips: .66 x 825 + .34 x 275 = $638,000

If Paul wins his confrontation with Dewey 43% of the time:

.43 x 638,000 + .57 x 371525 = $486109

.942 x 531000 + .058 x 486109 = $528,396

Comments? Errors?

[Daliman]

See, this is your problem, West. You pay no attetion to detail....

[ClaytonN]

holy

[SCfuji]

now if we could all do this in the blink of an eye (within the action-clock limit) we would all be pros winning millions of dollars on the WPT!

great post. im still reviewing but it looks pretty clean.

[Moovyz]

God, you have WAY too much free time! I got windows need cleaning, since you can spare the time. Hell, I'll even let you sleep with my wife. Cuz we all know you definately need to get laid!

BTW, line 174 has an error in it. It's off by .00000001%

[Moovyz]

You MUST be David's son.

[Moovyz]

While your at it... could you build me a time machine? I wanna go back and fold those pocket Aces that got cracked.