{"id":754,"date":"2014-01-09T20:59:05","date_gmt":"2014-01-10T03:59:05","guid":{"rendered":"http:\/\/garagepoker.markclarkson.com\/?page_id=754"},"modified":"2018-08-19T20:31:40","modified_gmt":"2018-08-20T03:31:40","slug":"simple-odds-for-simple-donkeys","status":"publish","type":"page","link":"https:\/\/garagepoker.markclarkson.com\/?page_id=754","title":{"rendered":"Simple odds, for simple donkeys"},"content":{"rendered":"

Part I – What Are The Odds?<\/h2>\n

If you can count and multiply by two, you can compute the odds.<\/p>\n

Your odds of making your hand are approximately two times your number of outs times the number of cards left to come.<\/p>\n

For example, let\u2019s say that, after the turn, you need a seven to fill a straight.
\n\"needAsevenriver\"<\/a>
\nThere are four sevens un-accounted for. That is, you have four outs<\/b>. Multiply those outs by two. Four outs<\/b> times two<\/b> (4*2) is eight. You have roughly an 8% chance of filling your straight on the river. About one time in twelve, you\u2019ll hit a seven.<\/p>\n

After the flop, you have two cards to come, rather than just one. This doubles your chances of catching an out, if you stay in the hand all the way to the river<\/i>.<\/p>\n

Let\u2019s say you flop a gut-shot straight draw.
\n\"needAsevenTurn\"<\/a>
\nYou still need a seven to fill your straight, but now you have two chances of catching one: the turn and the river. Four outs<\/b> times two cards to come<\/b> times two<\/b> (4*2*2) is sixteen. You have approximately a 16% chance of catching your card by the river. You\u2019ll catch a seven by the river about one time in one time in six.<\/p>\n

Let\u2019s say you flop a four-card heart flush draw and push all in.
\n\"flopflushdraw\"<\/a>
\nYou have nine outs<\/b>; you need any one of the remaining nine hearts to complete your flush. Your odds of getting there are roughly nine outs<\/b> times two cards to come<\/b> times two<\/b> (9*2*2) or 36%. A little better that one time in three, you\u2019ll hit your flush.<\/p>\n

The odds for an up-and-down straight draw are approximately the same. You have eight outs<\/b>, instead of nine, giving you odds of roughly 8*2*2 or 32%. You\u2019ll fill your flopped straight draw about a third of the time.<\/p>\n

One last example. Let\u2019s say I turn two pair, but you turn a flush.
\n\"riverboat\"<\/a>
\nYou push all-in and I call you. You\u2019re ahead right now but I\u2019m not drawing dead. With one card left to come, I need to improve to a boat to beat your flush. That means one of my two pair needs to improve to trips. There are two of each card left in the deck, giving me four outs<\/b>. With one card left to come, my odds are about four outs<\/b> times two<\/b>, or 8%. 92% of the time, your flush will hold up to win.<\/p>\n

These odds are not precise \u2013 they slightly underestimate for low numbers of outs and overestimate for large numbers of outs \u2013 but they are close enough for rough at-the-table decisions. If I tell you that the odds of making my full house are actually 9.073%, rather than 8%, will that make any difference to the way you play the hand?<\/p>\n

Part II – Should I Call?<\/h2>\n

It\u2019s the turn. There\u2019s one card left to come. It\u2019s just you and me. Let\u2019s say there\u2019s $1,000 dollars in the pot. I bet $1,000. Should you call?<\/p>\n

Let\u2019s break it down. With my bet, there\u2019s now $2,000 in the pot. It will cost you $1,000 to play. The pot is offering you 2-to-1.<\/p>\n

Let\u2019s say you have an up-and-down straight draw. You have eight outs; any four or any nine will complete your draw. With one card to come, you have about a 16% chance of making your straight: eight outs<\/b> times two<\/b>. Roughly one time in six, you\u2019ll catch your card.<\/p>\n

The odds don\u2019t support a call. The pot is offering 2-to-1, but your odds are 5-to-1 against making your hand.<\/p>\n

One time in six, you\u2019ll win $2,000.
\nFive times in six, you\u2019ll lose $1,000.<\/p>\n\n\n\n\n\n\n\n\n\n\n
WINS<\/td>\nLOSSES<\/td>\n<\/tr>\n
$2,000<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n$1,000<\/td>\n<\/tr>\n
<\/td>\n$1,000<\/td>\n<\/tr>\n
<\/td>\n$1,000<\/td>\n<\/tr>\n
<\/td>\n$1,000<\/td>\n<\/tr>\n
<\/td>\n$1,000<\/td>\n<\/tr>\n
$2,000<\/b><\/td>\n$5,000<\/b><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Over time, for every dollar you win, you\u2019ll lose $2.50<\/i><\/b>.<\/p>\n

Let\u2019s re-visit that scenario. It\u2019s the turn. It\u2019s just you and me and your up-and-down straight draw. The pot is still $1,000. This time, however, I only bet $200.<\/p>\n

Now it costs you $200 to win $1200. The pot is paying 6-to-1. If you call:<\/p>\n

One time in six, you\u2019ll win $1,200.
\nFive times in six, you\u2019ll lose $200.<\/p>\n\n\n\n\n\n\n\n\n\n\n
WINS<\/td>\nLOSSES<\/td>\n<\/tr>\n
$1,200<\/td>\n<\/td>\n<\/tr>\n
<\/td>\n\n

$200<\/p>\n<\/td>\n<\/tr>\n

<\/td>\n\n

$200<\/p>\n<\/td>\n<\/tr>\n

<\/td>\n\n

$200<\/p>\n<\/td>\n<\/tr>\n

<\/td>\n\n

$200<\/p>\n<\/td>\n<\/tr>\n

<\/td>\n\n

$200<\/p>\n<\/td>\n<\/tr>\n

$1,200<\/b><\/td>\n\n

$1,000<\/b><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Now over time, for every dollar that you lose, you\u2019ll win $1.20.<\/i><\/b> Based on your odds, this is a good call.<\/p>\n

It\u2019s important to remember that, even though the odds make this a good call in the long run;<\/i>\u00a0in the short run you\u2019re still going to lose your money five out of six times.<\/p>\n","protected":false},"excerpt":{"rendered":"

Part I – What Are The Odds? If you can count and multiply by two, you can compute the odds. Your odds of making your hand are approximately two times your number of outs times the number of cards left … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-754","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/garagepoker.markclarkson.com\/index.php?rest_route=\/wp\/v2\/pages\/754","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/garagepoker.markclarkson.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/garagepoker.markclarkson.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/garagepoker.markclarkson.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/garagepoker.markclarkson.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=754"}],"version-history":[{"count":7,"href":"https:\/\/garagepoker.markclarkson.com\/index.php?rest_route=\/wp\/v2\/pages\/754\/revisions"}],"predecessor-version":[{"id":1491,"href":"https:\/\/garagepoker.markclarkson.com\/index.php?rest_route=\/wp\/v2\/pages\/754\/revisions\/1491"}],"wp:attachment":[{"href":"https:\/\/garagepoker.markclarkson.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=754"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}