How much difference does it make?

[PairTheBoard]

In our home game, after dealing cards to the players, we burn all but the last 5 cards in the deck which are then used for the flop, turn and river. In this way we eliminate suckouts altogether.

PairTheBoard

[Kerth]

I'm sorry that this ended up being long and boring, but hopefully this'll be of some help.

This is an example where the play is heads-up, no cards are burned before this situation and now we're finding out whether or not player A should want to burn a card before dealing the river.

Player A: A[img]/images/graemlins/heart.gif[/img]K[img]/images/graemlins/heart.gif[/img]
Player B: 8[img]/images/graemlins/spade.gif[/img]8[img]/images/graemlins/diamond.gif[/img]

Board: 8[img]/images/graemlins/heart.gif[/img]8[img]/images/graemlins/club.gif[/img]Q[img]/images/graemlins/heart.gif[/img]J[img]/images/graemlins/heart.gif[/img]

8 cards are used, 44 are left in the deck. Player A has just one out, the ten of hearts, so the probability that he will win is 1/44. Now let's see how that probability changes if we decide to burn one card before dealing the river.

The probability that the burn card is the Th is 1/44. After burning the T[img]/images/graemlins/heart.gif[/img], there are 43 cards left in the deck, none of which help the Player A to win, so the probability that he will win is 0/43 = 0. One time in 44 burning causes the Player A's situation to be hopeless.

The probability that the burn card is NOT the T[img]/images/graemlins/heart.gif[/img] is 43/44. After burning the non-T[img]/images/graemlins/heart.gif[/img] card, there are 43 cards left in the deck, 1 of which turns the Player A into a winner, so then the probability that he will win is 1/43. 43 times out of 44 burning causes Player A to win a little bit more often than if there was no burning. Often enough to overcome the rare catastrophe of burning the T[img]/images/graemlins/heart.gif[/img]? Let's find out:

If you're familiar with EV calculations, the following should be self-explanatory. In case you're not: Calculating the expected value happens by multiplying the different possible values with their probabilites and then adding those together. Here we calculate the expected probability of Player A winning when a card is burned before dealing the river:

1/44 x 0 + 43/44 x 1/43 = 0 + 43/1892 = 1/44

Indeed, the rare catastrophe of burning the winning card is offset exactly by the small help Player A gets most of the time from burning, so it doesn't matter whether you burn a card or not. The probability of Player A winning stays the same: 1/44

It doesn't matter if you burn half the deck. It doesn't even matter if everything but the bottom card is burned. It changes nothing.

You get one random card. That's what happens whether you burn or not. Why would the Th reside more or less likely on the top of the deck? You could fan out the deck and pick the river yourself, it would still make no difference. You would
get one random card. You could shuffle the remaining deck before dealing the river and the situation would remain the same. I suspect that the confusion of burning's effect is caused by the perceived loss of possibilities that the burning supposedly causes. But that's just silly. If you deal the top card, then all the cards below that are "burned", they're not used, it's as if they weren't in the deck at all. The point is that you will get exactly ONE random card anyway, it doesn't matter if it's the first, second, third, or thirty first card, because the deck is randomized. Cards have no will, they don't care where they end up and have no means to alter their position. If you have one out before the river, the card you're hoping to get won't suddenly decide to move to the top of the deck to be burned away and piss you off. I keep repeating myself, but here it is once again: YOU GET ONE RANDOM CARD. You could feed half of the deck to your dog and it wouldn't change the probabilities as long as no one knows what those cards
were.

Burning is done to prevent cheating and has nothing to do with sucking out.

I chose this situation because of its simplicity. The points I make are true for different situations too (2 cards to come, preflop, more outs, whatever), and you could do the redundant math yourself if you wish to be sure. Hopefully you don't need to though, as you should be able to understand why it's redundant in the first place.

Everything I've said of course assumes a well-randomized deck. If the dealer wanted to deal in an unconventional way (e.g. from the bottom), it's probably still best to be suspicious in case you're being cheated. [img]/images/graemlins/smile.gif[/img]

[OrangeKing]

To put it another way:

There is no difference between a card being burned, being in a hand that was folded, being at the bottom of the deck or anything else - they're all unknown cards to you, and you still have to calculate your odds as though the entire deck is in play. It doesn't matter if some cards are sitting on the table; you're still just as likely to get any card you haven't seen yet out of the entirety of the unknown deck.

[m1illion]

Thanks to you and lastcardcharlie(I found your answer in the other thread [img]/images/graemlins/laugh.gif[/img])
This was what I was looking for.
Pairtheboard - typical response from you

[Winenose]

Thank you

[SamIAm]

[ QUOTE ]
Pairtheboard - typical response from you

[/ QUOTE ]
I agree; I chuckled. PtB, keep up the good work.
-Sam

[Shroomy]

[ QUOTE ]
In our home game, after dealing cards to the players, we burn all but the last 5 cards in the deck which are then used for the flop, turn and river. In this way we eliminate suckouts altogether.

PairTheBoard

[/ QUOTE ]

Thats a hell of an idea. [img]/images/graemlins/laugh.gif[/img]

[TopArsenal]

I looked at long explanations. I hope this is the shortest.

You have 1/48 chance that 1 of your outs is gone. But in other hands equally 1 card is gone and it will be the one your opponent/s need, he'll lose 1/48 chance.

[TopArsenal]

Yeah, actually it does eliminate suckouts, but only 1-outer. It would be helpfull on internet in future for decreasing pro's variance [img]/images/graemlins/grin.gif[/img]

[AmonRaa]

[ QUOTE ]
In our home game, after dealing cards to the players, we burn all but the last 5 cards in the deck which are then used for the flop, turn and river. In this way we eliminate suckouts altogether.

PairTheBoard

[/ QUOTE ]

Yeah, but you cant run it twice now, can you? [img]/images/graemlins/tongue.gif[/img]