Pot odds answer

Right, you remember the scenario, you have 88 UTG and limped for 200, BB raised to 600 and you called but he turned his J3 over.

He is allowed to call but cannot bet.

The flop comes 246 so he has a gutshot and an over card, what is the best bet?

Here's my view on the matter and my calculations, I am happy for anyone to shoot me down if I have made a mistake in my calculations.

There are 45 cards left in the deck and 7 of them will improve his hand, 38 are safe.

So the chances of him going ahead on the turn are calculated as follows:

1-(38/45)=16%

So I currently have 1600 chips in the pot which will be mine if I go all in assuming he folds and my equity is 1600 chips.

If I bet nothing then I will win the 1600 chips 84% of the time giving me 1600*84%=1351 equity

Clearly I need to bet somewhere in between, so what is the break even number.

Taking the turn bet in isolation a little goal seek in excel tells me that if I bet 162 chips and he calls then I will have built the pot to 1924 which I will win 84% of the time. My equity is therefore

16% * -162 = -25

+

84% * 1924 = 1625

= 1600

and so my equity remains at 1600 meaning that my bet should be as much as possible over 162 chips that I think he will call.

Obviously there is a small factor relating to the turn bet as well and also the possibility that he could improve on the turn but I improve on the river but in essence I think this is somewhere near where I should have bet rather than the 500 I actually bet.

I was quite surprised when I worked out how small the bet should be and would love to hear if anyone thinks I have missed anything.

5-a-side in a minute so I'll have to go soon.