Help me with my math here...am i missing anything on the analysis of whether to keep 4 to an opened ended straight vs a pair to go after 3ofk (around 6 minute mark) STRAIGHT: Eight cards in the deck (4 on each end) to hit your open-ended straight. 8 of 47, or roughly 1 in 5 (1 in 5.25) chance of getting the straight. Playing 10 hand, you are slightly longer than averaging 2 straights with this keep 3OAK: Two cards, the other two of your pair, exist to hit your 3 of a kind, but 3 cards are discarded and drawn, so you get 3 tries at a draw that has odds of 1 in 23.5, then 1 in 23, then 1 in 22.5 (as cards available go from 47 to 46 to 45). Going after 3OAK buys you three tickets to the 1 in 23 drawing, so 1 in 7.66 of winning? Ten hand should give you the 3oak just longer than 3 times in 20 hands (3 in 21.88 hands) STRAIGHT: A draw of a straight is the maxed out potential in that play. So 1 in 5.25 of a straight. Playing 10 hand, you are right around an expected (average...expectations are often skewed by non-mathematical bias) return of 2 straights. Your win amount is double the pay of 3oak, at 20 vs 10, on TDB. 3OAK: The 3 of a kind has longer odds, at 1 in 7.66 of getting the 3rd card or better. You do have some possibility of improvement by getting your third and another pair in the discard and redraw, or getting both for 4 of a kind. Your pay for 3oak is half that of a straight, and is a 32% less likely conversion. CONCLUSION: Hold 4 to the open-ended straight. Open-ended straight will hit more commonly than 3OAK, and is double the pay, with no loss to multiplier impact. The frequency of FH (1 in 86.88) or 4OAK (1 in 420) do not shift the favor enough to go pair over 4 to open ended straight. You should definitely go for an open-ended straight over 3OAK when the pair is not Jacks or better (a guaranteed winner), especially with high multipliers, if choosing between the two. A pair of A, 2, 3, or 4 may change that to being a considered gamble (not odds favorite) on DDB and TDB, but that wasn't the scenario here. EDITED TO ADD INFORMATION IN THE CONCLUSION: FH or 4OAK potential impacts the overall odds, but not enough to overcome the fact that a straight has equal multiplier impact for the next hand, is twice the pay, and a superior 1 in 5.25 chance vs the 1 in 7.66 odds of a 3OAK or better. This represents a 32% higher chance of conversion on an option that is double the pay table with no impact to multipliers to consider. The long shot of taking the pair to a full house is 1 in 86.88 (1.51%). Longer still is the chance of getting a 4OAK, at 1 in 420 (.236%). These two outcomes are included in the 1 in 7.66 odds of beating the pair...it's actually 1 in 9 to get a 3OAK, but the 1 in 86.88 chance of FH and 1 in 420 chance of 4OAK take the overall odds of improving a pair to 1 in 7.66.
There’s also the chances of getting two pair - which doesn’t increase the multipliers but pays back money. If you hold 4 to a straight you can only hit the straight.
@brianweinstein8272 yes, but the 1 in 7.66 odds includes all improvements (2 pair, 3OAK, FH, 4OAK), with 2 pair the most likely at 6 to 1, then 3OAK at 9 to 1, then FH at 87 to 1, then 4OAK at 420 to 1). You are correct that I didn't break out 2 pair, mostly because it doesn't pay more in DDB or TDB, but i should have mentioned it is already in the 1 in 7.66. As the straight gives you double the pay, and happens 1 in 5.25, or 32% more often, so competitive with a FH, and 4OAK, the only big ticket in all this, happens less than a quarter percent (1 in 420), the straight still comes out well ahead
Your catchphrase "Son you disappointed me again" t-shirts are sold out again in your merch store, and with Christmas just around the corner. Lol
You disappoint me son
What else is new?
Exactly!!!
Happy holidays!!!
How am I funny? Great quote.
Thanks for the videos, which are addictive! I wish I didn't know in advance whether or not you will win from the video title.
@@mmwilding we usually only spoil it in the title if we are on a losing streak and finally break it
You had a 12x and a 4x on the straight your Dad threw away.
These games have great potential but so rarely seem to hit.
Help me with my math here...am i missing anything on the analysis of whether to keep 4 to an opened ended straight vs a pair to go after 3ofk (around 6 minute mark)
STRAIGHT: Eight cards in the deck (4 on each end) to hit your open-ended straight. 8 of 47, or roughly 1 in 5 (1 in 5.25) chance of getting the straight. Playing 10 hand, you are slightly longer than averaging 2 straights with this keep
3OAK: Two cards, the other two of your pair, exist to hit your 3 of a kind, but 3 cards are discarded and drawn, so you get 3 tries at a draw that has odds of 1 in 23.5, then 1 in 23, then 1 in 22.5 (as cards available go from 47 to 46 to 45). Going after 3OAK buys you three tickets to the 1 in 23 drawing, so 1 in 7.66 of winning? Ten hand should give you the 3oak just longer than 3 times in 20 hands (3 in 21.88 hands)
STRAIGHT: A draw of a straight is the maxed out potential in that play. So 1 in 5.25 of a straight. Playing 10 hand, you are right around an expected (average...expectations are often skewed by non-mathematical bias) return of 2 straights. Your win amount is double the pay of 3oak, at 20 vs 10, on TDB.
3OAK: The 3 of a kind has longer odds, at 1 in 7.66 of getting the 3rd card or better. You do have some possibility of improvement by getting your third and another pair in the discard and redraw, or getting both for 4 of a kind. Your pay for 3oak is half that of a straight, and is a 32% less likely conversion.
CONCLUSION: Hold 4 to the open-ended straight. Open-ended straight will hit more commonly than 3OAK, and is double the pay, with no loss to multiplier impact. The frequency of FH (1 in 86.88) or 4OAK (1 in 420) do not shift the favor enough to go pair over 4 to open ended straight. You should definitely go for an open-ended straight over 3OAK when the pair is not Jacks or better (a guaranteed winner), especially with high multipliers, if choosing between the two.
A pair of A, 2, 3, or 4 may change that to being a considered gamble (not odds favorite) on DDB and TDB, but that wasn't the scenario here.
EDITED TO ADD INFORMATION IN THE CONCLUSION: FH or 4OAK potential impacts the overall odds, but not enough to overcome the fact that a straight has equal multiplier impact for the next hand, is twice the pay, and a superior 1 in 5.25 chance vs the 1 in 7.66 odds of a 3OAK or better. This represents a 32% higher chance of conversion on an option that is double the pay table with no impact to multipliers to consider. The long shot of taking the pair to a full house is 1 in 86.88 (1.51%). Longer still is the chance of getting a 4OAK, at 1 in 420 (.236%). These two outcomes are included in the 1 in 7.66 odds of beating the pair...it's actually 1 in 9 to get a 3OAK, but the 1 in 86.88 chance of FH and 1 in 420 chance of 4OAK take the overall odds of improving a pair to 1 in 7.66.
You need to collaborate with Mr. Brain on this to confirm your analysis. You may be right.
There’s also the chances of getting two pair - which doesn’t increase the multipliers but pays back money. If you hold 4 to a straight you can only hit the straight.
@brianweinstein8272 yes, but the 1 in 7.66 odds includes all improvements (2 pair, 3OAK, FH, 4OAK), with 2 pair the most likely at 6 to 1, then 3OAK at 9 to 1, then FH at 87 to 1, then 4OAK at 420 to 1). You are correct that I didn't break out 2 pair, mostly because it doesn't pay more in DDB or TDB, but i should have mentioned it is already in the 1 in 7.66. As the straight gives you double the pay, and happens 1 in 5.25, or 32% more often, so competitive with a FH, and 4OAK, the only big ticket in all this, happens less than a quarter percent (1 in 420), the straight still comes out well ahead