Frequency for AKo shove pre-flop?

[TonyTwoCheeks]

I played a home game last night. It can be an action-heavy game at times. $1-$1 with a winnable $5 straddle for the button. If the straddle is not in play then usually the button plays it anyway. I did well enough and made $150 for the night but the night could have way better with one hand.

SB stack: $195
HJ (Hero) stack: $400
BTN stack: $50

*** PRE-FLOP ***
BTN: straddles $5
Small Blind: calls
UTG+1: calls
HJ (Hero): raises to $30 with ​

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BTN: calls $30
Small Blind: raises to $75
HJ (Hero): calls
I believed he had a good hand (JJ+) and was very suspicious of the call-raise. Villian gets sneaky with his plays which actually hurts him in long run (fancy play syndrome).
I changed my decision six times in the span of 1 minute. Call, fold, shove, call, shove....I finally chose to call.
BTN: calls
Main Pot: $156
Side Pot: $50

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Equilab Analysis
SB: 45% TT+,AQs+,KQs,AKo
HJ: 33% AKo
BTN: 22% 99-88,ATs-A5s,KJs-KTs,QTs+,JTs,T9s,98s,AJo-ATo,KTo+,QJo

This is where BTN (80+ year-old OMC) throws over his hand ​

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*** FLOP *** ​

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SB: shoves for $120
HJ: folds
Seeing one of my outs dead really upset me and I folded.

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Equilab Analysis after A6o card removal
SB: 60% TT+,AQs+,KQs,AKo
HJ: 28% AKo

SB shows ​

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*** RUNOUT *** ​

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King hits the river and it burns. I can't help but think about the pre-flop shove.
So the question is...
With what frequency should this be a pre-flop shove versus flat?

The second time I considered shove I could see the debate playing out in my head...
Logic: "I really think we're supposed to shove here."
Prudence: "Hold on cowboy. Why don't we see a flop first?" ​

 

[sedlacekj]

Yeah it sucks when you river the nuts after folding for sure. However, the call preflop is best with your relative stacks the way they are. He was never folding QQ no matter what you did. From an equity standpoint, the $120 shove with you only having 28:% chance to win, put you in a non-profitable situation. Calling the shove at $120 means you are calling $120 into a pot of $396 for 30% pot odds. Since 30 is bigger thatn 28 per cent to win, you fold. You will get an A or K on the turn or river about 20% of the time 2 outs for A and 3 for K = 5 outs per card left to play, so 5 outs X 2% X 2 cards = 20% The odds are too great to risk $120 for the chance you will get an A or K. If you chose to call the shove for this amount over several games you will generally lose money. Folding is the best answer. Call the preflop, fold if the price is too high later. sometimes like this one, you will see you folded a winning hand, but the percentage of time that will happen is too low to call that price. If the shove had been $100 instead and you only needed to call $100, then your pot odds would have been 28% matching the equity 28%, in that case you call the shove.