River exposed early...

[Lottery Larry]

you're wrong

[zoneblitz]

OK, now I'm really curious as to the correct answer. This should be simple math right?

I think Larry had it right. If I replay the hand...as far as I knew after the turn there were a possible 4 jacks out of 47 unseen cards.

So, I have a 4/47=8.51% chance of hitting a Jack on the river. No one disputes this.

If there is a burn and turn of the river before action is complete...we agree (I think) the correct action is to mix the river card back into the stub, shuffle and deal 1 card, leaving the burn card alone.

So now, my chances of hitting a Jack are 4/46=8.7%. Negligible yes, but still a better chance to hit.

I think the subtlety I originally missed (but Larry pointed this out with his example) is that dealing the river is a singular event, you don't stop after the burn card re-calculate odds and then deal the river. So, if the burn card is not in the mix, the chances go slightly up.

This is how I understand it....please correct me if wrong (now this is bugging me).

Thanks again to all....

[PantsOnFire]

[ QUOTE ]
The dealer burns, deals a 3d, puts the 3d back in the stub, shuffles and deals the top card. The only change in this whole situation comparing it to before the dealer dealt the river prematurely is that now you KNOW there is a 3d in the stub left. However the impact that has on your chance to catch a Jack is negligible.

[/ QUOTE ]
This is correct, however in OP, the 3d is not put back in the stub so the chances of a J increases.

If you have X out and Y cards and you reduce Y, the chances of X increases. You simply misread the original post. And that's why I said reshuffling in the 3d is more fair.

[Arito]

[ QUOTE ]
It just comes down to the fact that you've removed the burn card for the (original) river, so your chance of getting ANY card (the same Jack or 3, or any of the remaining cards) is greater because there is one less card to "dilute" your chances for the river card.

[/ QUOTE ]

This is what Larry says in pretty much all his posts in this thread. It is wrong, because you don't know what the burn is. Your chance of hitting a jack are not greater simply because the burn is now out.

If you would take the 3d back, shuffle and burn EVERY card in the deck except for one (the last card) and use that as a river, your chance of catching that Jack would still not be influenced.

The only change is that you know know the 3d is in the stub, so you have one unseen card less and thus a slightly higher chance to hit a Jack, but this has nothing to do with the burn. Zoneblitz's math is correct, but the reason you have one less unseen card is the 3d, not the burn.

[Lottery Larry]

[ QUOTE ]
This is what Larry says in pretty much all his posts in this thread. It is wrong, because you don't know what the burn is. Your chance of hitting a jack are not greater simply because the burn is now out.

[/ QUOTE ]

actually, in this case, we DO know the burn card isn't the 3 nor the Jack. Therefore, special information.

You wouldn't normally adjust the odds, but since we "know" that the stub has certain cards and is smaller...

[Arito]

You only know the Jack is in because we are discussing it after the fact. I was assuming you want to know the influence it has on your pre-river chance of catching a J on the river. Which makes sense. So the only information you have is that one of the cards in the stub is the 3d. The smaller size of the stub has 0 influence, because you don't know what the burn was.

[Lottery Larry]

[ QUOTE ]
[ QUOTE ]
It just comes down to the fact that you've removed the burn card for the (original) river, so your chance of getting ANY card (the same Jack or 3, or any of the remaining cards) is greater because there is one less card to "dilute" your chances for the river card.

[/ QUOTE ]

This is what Larry says in pretty much all his posts in this thread. It is wrong, because you don't know what the burn is.

[/ QUOTE ]

btw- relooking at this part of my statement, independent of the discussion, it is incorrect as written... since I didn't add the "in this special case" part

[Lottery Larry]

[ QUOTE ]
I was assuming you want to know the influence it has on your pre-river chance of catching a J on the river. Which makes sense.

[/ QUOTE ]

Not in this situation, it didn't.



[ QUOTE ]
So the only information you have is that one of the cards in the stub is the 3d. The smaller size of the stub has 0 influence, because you don't know what the burn was.

[/ QUOTE ]

The size of the field also doesn't matter, since the odds are always 4 unseen jacks out of (normally) 46 unseen cards to catch on the river, no matter if we have 2 players or 21 players.

Even in the OP case, if only the 3 had been exposed and shuffled back in, it would still have been 4/46 or a 8.9% for a Jack to be dealt on the river.

KNOWING the Jack is in the stub.... may be beyond my math skills to figure out how that changes the odds of getting a Jack.

With 6 players dealt in, possibly (3/46 + 1/33) = 9.55% to catch a Jack on the river, I think.

Work for you?