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View Full Version : Calculating push EV (mistake in ZeeJustin's formula?)

Pete H
07-14-2005, 07:39 AM
I've been trying to calculate if my push was ok.

5 handed, blinds 50/100 (will rise before they hit me next time), I'm the small stack and SB with 425 before posting. Next smallest stack is at least 800. BB has the biggest stack, over 3000.

Folded to me and I push with K5s figuring he'll call with about 50% of hands.

Pokerstove tells me this (following range is 50.2%)

equity (%) win (%) tie (%)
Hand 1: 46.4163 % 44.02% 02.40% { K5s }
Hand 2: 53.5837 % 51.19% 02.40% { 22+, A2s+, K2s+, Q2s+, J4s+, T6s+, 96s+, 86s+, 76s, 65s, A2o+, K5o+, Q7o+, J7o+, T8o+, 98o }

So if I push and get called I have 46% equity of the pot. That's if I understand pokerstove's numbers properly.

My reasoning says this is how I should calculate my expected amount of chips after push:

0.5 x 525 [half of the time I win blinds without contest] + 0.5 x 0.46 x 850 [my equity of the pot when I'm called] = 460

If I fold, I have 375 chips -&gt; push EV = 460 - 375 = 85

I'm not 100% if this, so I tried to search some info.

Found ZeeJustin's push formula that gave different answer, and after I thought this a while I noticed that there seems to be a mistake in it.

Original post is here:

http://archiveserver.twoplustwo.com/showflat.php?Cat=&amp;Number=1160395&amp;page=&amp;view=&amp;sb=5&amp; o=&amp;vc=1

The formula:

[ QUOTE ]

X= your stack size (in terms of BB, assume the BB has an equal stack or has you covered. If you have the BB covered, X = the size of the BB's stack)
C = Percent of the time you are called
W = Percent of the time you win when you're called (use poker stove to figure this out)

(1-C)1.5 + WC(X+.5) - C(1-W)(X-.5)
translated this is:
1-C = % of the time you are steal the blinds
1.5 = the amount you win when you steal the blinds

WC = the percent of time you are called and win
X+.5 = the amount you win when you are called and win

C(1-W) = the percent of time you are called and lose
X-.5 = the amount you lose when you are called and lose

[/ QUOTE ]

This formula uses win/loss percentages, so we need to add the possibility of tie before it's accurate.

This would be the correct (I hope so) formula with tie.

(1-C)1.5 + WC(X+.5) + TC(0.75) - C(1-W-T)(X-.5)

T = percentage of ties when you are called

Also, I noticed Justin uses equity percentage instead of winning percentage in his example.

[ QUOTE ]

Example: You have 32o in the SB, and your opponent will call you with 22+, 54+, 86+, T7+, J6+ Q2+ (the loose range of hands in MJ's article).

According to poker stove, 32o wins 31% of the time against this range of hands, therefore W=.31

Shove EV w/ 32o and 10x BB = -1.572 x BB

[/ QUOTE ]

According to pokerstove 32o wins that range 30.06% and ties 2.18%

31.1504% is 32o's equity

I calculated Justin's example using my simple equity method:

Result: -1.54964 BB

And using updated formula with proper (if you can trust pokerstove) win/tie/lose percentages

Result: -1.54912 BB

I hope the minor differences in my results are just rounding errors as it's so much easier use the equity like I used it originally.

I know eastbay's SnGPT would calculate all this for me, but I want to be able to calculate these things myself before I even think of buying it.

So could someone check my calculations and tell me if I just made a fool of myself (wouldn't be the first or the last time).

brimstone1
07-14-2005, 07:52 AM
His calling range is basically: 22+,A2+,K2+,Q4o+,Q2s+,J8o+,J5s+,T9o,T7s+,98s

[ QUOTE ]

0.5 x 525 [half of the time I win blinds without contest] + 0.5 x 0.46 x 850 [my equity of the pot when I'm called] = 460

[/ QUOTE ]

Shouldn't this be:
0.5 x 525 (uncontested, you pick up 100t BB) + 0.5 x 0.467 x 920 = 477.32 ?

Isn't the pot 920 when you get called?

tigerite
07-14-2005, 07:56 AM
You'd get 375*2 + 50 + 100 = 750 + 150 or 900, I work it out as. Where's this extra 20 come from. /images/graemlins/confused.gif

Pete H
07-14-2005, 08:02 AM
[ QUOTE ]
His calling range is basically: 22+,A2+,K2+,Q4o+,Q2s+,J8o+,J5s+,T9o,T7s+,98s

[ QUOTE ]

0.5 x 525 [half of the time I win blinds without contest] + 0.5 x 0.46 x 850 [my equity of the pot when I'm called] = 460

[/ QUOTE ]

Shouldn't this be:
0.5 x 525 (uncontested, you pick up 100t BB) + 0.5 x 0.467 x 920 = 477.32 ?

Isn't the pot 920 when you get called?

[/ QUOTE ]

Nope (I think extra 20 came from 460x2). If I push and he calls the pot is 2 x 425 (my stack before posting the blind).

Remember that BB already has 100 in the pot, so my push is 325 for him to call.

tigerite's calculations missed that point also.

brimstone1
07-14-2005, 08:05 AM
Christ. I thought you had 460.. for no reason. Sorry about that.

tigerite
07-14-2005, 08:05 AM
Oops, yes, sorry. So 375 + 325 + 50 + 100 which is 850, as you said.

1C5
07-14-2005, 08:20 AM
just get eastbay's powertools.

Pete H
07-14-2005, 08:26 AM
[ QUOTE ]
just get eastbay's powertools.

[/ QUOTE ]

But I'm stupid enough (work as a software test engineer) to randomly check some of those results, so I want to know how to calculate these things.