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Ratio method: I compare reward to risk (Rew:Risk) e.g. 3 To 1 (that might be 90 : 30, I refer to 30 as a constant later just for this example) My odds of hitting a hand is 33 %, hence 2 To 1

hand odds < pot odds ... call in abc poker

my question: how do i explain that if I have higher pot odds that i should call? These ratios work in this example like that on average from 3 games I win 1 of them, for those two losses I lose 1*some constant and for a win I win 3 times more than 1*constant, so on average from those 3 games my bankroll was boosted (bottom line) by 1*constant, is that correct?

In percentage method: I calc from those pot odds how much of the whole pot is mine... so from pot odds 3:1, mine is 1/4 = 25 %. Then I compare it with my pot equity (chances to win and also the amount of pot I win on average from this hand). If the percentage of my hand odds is higher, for example 33 %, then I on average win 33 % of the pot every time I play a hand like this and therefore I get back those 25 % of the pot invested by me counted from pot odds and plus being better than break-even by 8 %.

Is the whole thing I've tried to explain, correct?

Every book and every site covering poker "explain" this without actually explaining why this work (the comparison of hand and pot odds in either ratio or percentage method) and these are the only explanations I have been able to come up with.

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It does not matter if you use % or ratio as long as you are comparing apples to apples

If you use % for both pot and hand odds you are good

If you use odds for both pot and hand odds you are good and should come to the same conclusion

So a bet of 25% the pot odds is 5:1
odds = (100 + %) / %

On a 9 out flush draw your odds are about 4:1 and your % is about 20%
odd = (100 - %) / %

To me odds is more intuitive, easier to memorize, and easier to calculate
Remember you (MY) is always on the bottom
Pot odds = pot / MY bet
Hand odds = outs not me / MY outs
If pot odds is better than hand odds then call
On the flop the bet is 1/3 the pot
Pot odds = (4/3) / (1/3) = 4:1
Just add one to the bottom - every time - e.g. 3+1
On the flop 5 unknown cards are out
On a flush you have 9 outs
Hand odds = (52 - 5 - 9) / 9 = 38 / 9 = 4.22 : 1
Pot odds is less than (immediate) hands odds so do NOT mathematically call
A quick way is to multiply the 9 (your outs) buy the pot odds
4 X 9 = 36 36 < 38 so do NOT mathematically call

On the flop 1/3 pot bet barely prices you out
1/2+ pot bet is the norm to chase out a draw since 1/3 is close

If they bet 1/4 the pot then 5:1
Hand odds are the same
5:1 > 4.22 : 1 so YES call the bet
5 X 9 = 45 45 > 38 so YES call the bet

% confuses me and I am a mathematician
1/3 pot bet is (1/3) / (1 + 1/3 + 1/3) = 20%
Their bet and your call is in the pot
19% < 20% so a close NO call
% is not used much in practice for a good reason

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  • This doesn't answer my question, though.. I know how to count both things and how to compare them to each other. I asked if I'm correct about why it actually works, it should be clear from my post, because ratio method is not usually that intuitive for Europeans as percentages, for example.
    – rensdavid
    Apr 18, 2016 at 15:59
  • @rensdavid Really, you need an explanation why pot odds better than hand odds is good? Math is different for Europeans? Don't expect me to answer any more of you questions.
    – paparazzo
    Apr 18, 2016 at 16:22

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