Is this a good prop bet ?
 

Last night I was at my local casino and this guy says that he will bet even money all night that each flop will contain either a jack, seven or duece.

My reasoning was that he had (12/52) so 1 out of every 4.3 cards would be his and since we are only taking 3 cards that I had the best of it.

We ran it for forty hands straight at $5 a flop and I quit after losing $75. Afterwards he told me that mathmatically he was 53% to win. I've been stuggling with this and need some clarity as to the exact odds.

Re: Is this a good prop bet ?
 

P^3

Re: Is this a good prop bet ?
 

The bet was that if any jacks, sevens or dueces show up on the flop I lose.

Re: Is this a good prop bet ?
 

He loses if the flop contains no j,7, or 2. This will happen:

40/52 * 39/51 * 38/50= 44.7%

So he wins the other 55.3% of the time.

Re: Is this a good prop bet ?
 

[ QUOTE ]
He loses if the flop contains no j,7, or 2. This will happen:

40/52 * 39/51 * 38/50= 44.7%

So he wins the other 55.3% of the time.

[/ QUOTE ]

for bets like this you should also consider whether the cards that come and the fact that you're seeing a flop are independent.

for example, you could say that if a flop is seen it's less likely that an ace will flop because it's more likely that someone has an ace in their hand. conversely, it may be more likely that a deuce comes because people play less hands with deuces in them.

of course, in this lop-sided bet it's not enough to make the difference, but it could make a difference if the bet was very close to (or exactly) even... for example, if you're betting a prop where you win every time your pair flops, it's better to pick deuces than aces because given a flop is seen you're more likely to see two deuces than two aces.

food for thought...

Re: Is this a good prop bet ?
 

Damon Runyon quote

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“One of these days in your travels, a guy is going to come up to you and show you a nice brand-new deck of cards on which the seal is not yet broken, and this guy is going to offer to bet you that he can make the Jack of Spades jump out of the deck and squirt cider in your ear. But, son, do not bet this man, for as sure as you are standing there, you are going to end up with an earful of cider.”

[/ QUOTE ]

Re: Is this a good prop bet ?
 

jimmy are you serious, please show us the math that makes dueces more likely to flop than aces

Re: Is this a good prop bet ?
 

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jimmy are you serious, please show us the math that makes dueces more likely to flop than aces

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I think he just explained why, and also told it didn't have a big impact.

Re: Is this a good prop bet ?
 

dueces or aces have equal chances of flopping. the muck doesnt go back into the deck.

Re: Is this a good prop bet ?
 

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dueces or aces have equal chances of flopping. the muck doesnt go back into the deck.

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True.

But his point was that if a flop is actually seen, the chances are higher that someone actually has an Ace in their hand and is therefore less likely that one will come out on the flop than a card, such as a deuce, that people are less likely in general to have.
This is not based on probability, but based on knowing the tendancies of the majority of players. If no flop is seen, then it's likely that all four Aces are still in the deck and therefore more likely that one will be flopped.


But as was said, it makes a small impact and would only make a difference it the two outcomes were both closer to 50% likely. On the safe side it's better avoid cards that people are more likely to see flops with, but it won't make a difference in this case.

Re: Is this a good prop bet ?
 

i wholly disagree. well at least in no limit. if someone has an ace or two aces, they are going to raise it and you are less likely to see a flop because everyone else may fold. so the flop that is not happening because of the guy with aces raising, is the same flop that is more likely to have a deuce. so the deuces are being flopped less often because when the deuce has the advantage on the flop (because the guy has aces in the whole), that flop isnt being seen.

Re: Is this a good prop bet ?
 

No point in arguing this point. There must be many of you who have seen millions of flops stored in poker utilities. Just write a program to count the aces and deuces.

Re: Is this a good prop bet ?
 

bump jimmyfingers, good post

Re: Is this a good prop bet ?
 

[ QUOTE ]
bump jimmyfingers, good post

[/ QUOTE ]no it wasn't. the effect would be <0.1% if any at all. and there's reason for both sides. do you see flops more when aces are dealt because these hands enter pots or do you see less flops because these hands raise and end things preflop?

Re: Is this a good prop bet ?
 

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[ QUOTE ]
bump jimmyfingers, good post

[/ QUOTE ]no it wasn't. the effect would be <0.1% if any at all. and there's reason for both sides. do you see flops more when aces are dealt because these hands enter pots or do you see less flops because these hands raise and end things preflop?

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obviously it depends on the game. what i said was simply to keep it in mind because it makes a difference, in some games moreso than others.

for example, look at heads up limit hold 'em. if there is one ace dealt, we know at least that one player will want to see a flop. if two aces are out, there's a good chance both will want to (if the aces are split), or a decent chance if both aces are with one player (at least one player will want to). three or more aces and a flop is guaranteed.

on the other hand, look at deuces. if one deuce is out it's less likely that player will want to see a flop. if two deuces, one player will want to see the flop if he has both, but if they're split it's unlikely both players will want to see a flop. if three deuces are out, one guy has a pair and another guy will have 2x. most 2x's won't see a flop (23, 24, 25, 26...).

i think it's obvious in this case that the aces will be less likely to flop.

Re: Is this a good prop bet ?
 

Isn't it impossible to lose $75 doing this 40 times. I'm assuming that it wasn't exactly 40.

I have a question. How do you determine the likelihood of winning 70% of the time out of 40 trials being a 55% favorite?

Re: Is this a good prop bet ?
 

Maybe this Aces vs. Deuces flop thing is best explained this way:

If, hypothetically, we dealt the flop EVERY HAND, even if the hand ended with the pre-flop betting, then yes, aces and deuces would flop equally often.

What everybody's saying is that when one or more aces are waiting atop the deck to be flopped, it makes it less likely that there will actually be a flop.

Re: Is this a good prop bet ?
 

[ QUOTE ]
Isn't it impossible to lose $75 doing this 40 times. I'm assuming that it wasn't exactly 40.

I have a question. How do you determine the likelihood of winning 70% of the time out of 40 trials being a 55% favorite?

[/ QUOTE ]

You'll win 28 or more trials (70%+) 3.86% of the time in the situation you described. You can get this using the binomial distribution. The math is messy, but Excel can do it for you.

Re: Is this a good prop bet ?
 

[ QUOTE ]
He loses if the flop contains no j,7, or 2. This will happen:

40/52 * 39/51 * 38/50= 44.7%

So he wins the other 55.3% of the time.

[/ QUOTE ]

You win 40^3/(52*51*50) = 48.3% of the time.

He wins 51.7% of the time.

That gives him about a 3.4% edge. For every $100 you bet you can expect to lose $3.40.

PairTheBoard

Re: Is this a good prop bet ?
 

[ QUOTE ]
[ QUOTE ]
He loses if the flop contains no j,7, or 2. This will happen:

40/52 * 39/51 * 38/50= 44.7%

So he wins the other 55.3% of the time.

[/ QUOTE ]

You win 40^3/(52*51*50) = 48.3% of the time.

He wins 51.7% of the time.

That gives him about a 3.4% edge. For every $100 you bet you can expect to lose $3.40.

PairTheBoard

[/ QUOTE ]

Why is it 40^3 instead of (40*39*38)?

We're trying to find out the chance that no J72 hits the flop, right? On the first card there are 40 such cards. One of them comes on the first card, so the next card has a 39/51 chance of not being a J72. And so on...

Right? Or where am I messing up?

Re: Is this a good prop bet ?
 

you lose if a J, 7, or 2 comes. not if a J, 7, and 2 comes.

Re: Is this a good prop bet ?
 

[ QUOTE ]
[ QUOTE ]
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He loses if the flop contains no j,7, or 2. This will happen:

40/52 * 39/51 * 38/50= 44.7%

So he wins the other 55.3% of the time.

[/ QUOTE ]

You win 40^3/(52*51*50) = 48.3% of the time.

He wins 51.7% of the time.

That gives him about a 3.4% edge. For every $100 you bet you can expect to lose $3.40.

PairTheBoard

[/ QUOTE ]

Why is it 40^3 instead of (40*39*38)?

We're trying to find out the chance that no J72 hits the flop, right? On the first card there are 40 such cards. One of them comes on the first card, so the next card has a 39/51 chance of not being a J72. And so on...

Right? Or where am I messing up?

[/ QUOTE ]

You're right, PTB is wrong.

Re: Is this a good prop bet ?
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
He loses if the flop contains no j,7, or 2. This will happen:

40/52 * 39/51 * 38/50= 44.7%

So he wins the other 55.3% of the time.

[/ QUOTE ]

You win 40^3/(52*51*50) = 48.3% of the time.

He wins 51.7% of the time.

That gives him about a 3.4% edge. For every $100 you bet you can expect to lose $3.40.

PairTheBoard

[/ QUOTE ]

Why is it 40^3 instead of (40*39*38)?

We're trying to find out the chance that no J72 hits the flop, right? On the first card there are 40 such cards. One of them comes on the first card, so the next card has a 39/51 chance of not being a J72. And so on...

Right? Or where am I messing up?

[/ QUOTE ]

You're right, PTB is wrong.

[/ QUOTE ]

[ QUOTE ]
Last night I was at my local casino and this guy says that he will bet even money all night that each flop will contain either a jack, seven or duece.


[/ QUOTE ]

You're right. My mistake. The 40 out of 52 cards are the Non J,7,2's. If a Non-J,7,2 comes on the first card there are 39 Non-J,7,2's left, etc. I've evidently been spending too much time with Sleeping Beauty on SMP.

That gives the OP about a 44.7% chance of winning, a 55.3% chance of losing, with about a 10.6% -EV. He loses about $10 for every $100 bet. Looks like a worse proposition than the guy in the bar claimed it was.

PairTheBoard