Calculating pot odds

SSH introduces the concept of raising on the come when you have a strong draw and correct pot odds. The reason is that although you will lose more when you miss, you will gain a lot more when you hit, and the magnitude of your profit when you hit will more than offset the losses you accumulated from your misses.

Let's game this out and see if it's really true.

You limp in MP with {9s 8s}. LP raises, you and 3 others call.

Pot contains 10 SB.

Flop is {7h Tc Ad}. You have an OESD. With 8 outs, your odds of catching on the turn are 5:1.

EP bets. You raise, getting 11:2 pot odds, which is better than 5:1. LP calls, EP calls.

Pot now contains 16 SB (8 BB).

Turn is {2s}. No help. You still have 8 outs. Your odds of catching on the river are 5:1.

EP bets. You raise, getting 9:2 pot odds, but at least 10:2 (5:1) if EP or LP calls. LP folds, EP calls.

Pot now contains 12 BB.

River is {3d}. You missed your draw.

EP bets. You fold.

You are now down 4 BB.

This happens five times in a row.

You are now down 20 BB.

On the sixth time, you hit your draw on the river and raise headsup against EP, who calls.

You scoop 16 BB.

But 6 BB came from your stack, so your profit on the hand is +10 BB.

You are now down 10 BB.

What the hell happened here? All of your decisions were based on correct "breakeven" pot odds, yet you came out a net loser!

With 5:1 odds, you expected to miss your draw 5 times for every 1 hit. But by playing with correct pot odds, you also expected to recoup your 5 losses when you did make that 1 hit. Why didn't it happen?

I believe it is because you are counting your own dead money whenever you count the pot to make a pot odds calculation.

To recoup your prior losses, you needed to make +20 BB in profit. The bets that you contributed to the pot are technically not "yours" any more -- they are dead money -- but because they came from your stack, they
do not constitute potential profit if you win the hand. You have to subtract your own bets from the pot to make a true pot odds calculation.

So, on the turn, when there are 8 BB in the pot, 2 BB came from your stack, therefore the part representing your potential profit is only 6 BB. When EP bets into you, you are only getting 7:1 if you call and only 8:2 if you raise. You do not have the correct odds to raise the turn.

Let's game it out then:

The hand proceeds as above, but you just call the turn instead of raising. LP still folds, so you are heads up vs EP on the river with 10 BB in the pot. Each time you miss the river, you fold and lose a total of 3 BB. This happens 5 times in a row, putting you down 15 BB.

On the sixth time, you hit your draw, raise the river, and scoop 14 BB. But you invested 5 BB in the hand so your profit is only +9 BB.

You are still down 6 BB. Less than before, but still losing!

What is going on here??

ChezJ

5 - 1 says that you win 1 time out of 5... not 1 time out of 6.

4BB + 4BB + 4BB + 4BB = 16BB

And you win 16BB

It's right =)


============

Oops I thought that the 16BB was counting the 4BB loss.

At the end we are ending up with more than 1/5 of the pot from your stack...

I dont have time ot check now, but something is wrong ( or I could just me missing something. ) =)

no, 5:1 means 5 losses and 1 win out of 6.
that's why your 1 win needs to equal 5 losses.

for example, with OESD, you have 8 outs from the remaining 47 cards.
8/47 is roughly 1/6. 1/6 = 1 win in 6. this implies 5 losses in 6.
hence 5:1 against.

ChezJ

There are 8 cards that make your straight and 39 that don't.
Your odds of making the straight are 39:8 or 4.875 : 1, or about 1 time out of 6 with one card to come.
You have 2 cards to come. So the probability of making the straight by the river is
1-(39/47*38/46) = 0.3145

or 2.18 : 1 against.
So you will make your straight almost 1 in every 3 times.

we'll assume you raise every time there are 4 people in the pot and call when there are 3 or less (This, I believe is optimal when comparing to pot odds)

So in the above example you lose 3BB 2.18 times and win 10BB once for a total profit of 6.54 BBs.

There are a lot more things to consider though, most imporatantly Whether your raise will knock out potential callers. This is a play you only make in late position with multiple callers in the pot.
You also need to take into account whether you are drawing to the nuts. if there is also a pair and a flush draw on the flop, It might be right to fold. Or you could be drawing to the small end of the straight and be beat by a larger straight.

thanks for clearing that up. i was not taking into consideration the fact that you hit your draw on the turn 1 out of 6 times. i was looking only at the river, and that was the flaw in my logic.

ChezJ

upon further reflection, i was also not accounting for the times when you hit the flop with your 98s. every decision on every street is separate and cannot be lumped together with all the other decisions previously made. that was the fundamental flaw in my thinking.

ChezJ